记录大学学习课程的一些课程笔记和思考。一些核心课程的课程笔记体系已经非常完善，所以不再继续造轮子，故只记录一些个人认为缺少精品或者不够完善的课程。
离散数学及其应用 - 命题的应用 - 数独游戏 +数据库系统 - 数据库系统导学
diff --git a/index.html b/index.html index 7709c59..46c82c5 100755 --- a/index.html +++ b/index.html @@ -1181,6 +1181,7 @@\u4e00\u99ac\u7576\u5148\uff0c\u842c\u99ac\u7121\u5149\u3002 Eclipse the first, the rest nowhere.
\u7b80\u5355\u7684\u7f51\u7ad9\uff0c\u653e\u4e00\u70b9\u5b66\u4e60\u7b14\u8bb0\uff0c\u653e\u4e00\u70b9\u751f\u6d3b\u5fc3\u5f97\u3002
A website recording study and life.
"},{"location":"#about-me","title":"About me","text":"ID: DDKing Major: Computer Science
Let's D\u2193ve into the ocean of knowledge!
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"},{"location":"Classnote/Database-System/termsintro/#2","title":"2. \u6570\u636e\u5b64\u5c9b","text":"\u2003\u2003\u8bbe\u60f3A\u75282004\u7248\u672c\u5236\u4f5c\u4e86\u4e00\u4efdppt\uff0c\u800cB\u75282024\u7248\u672c\u7684powerpoint\u6253\u5f00\uff0c\u56e0\u4e3a\u7248\u672c\u7684\u4e0d\u517c\u5bb9\uff0c\u4f1a\u5bfc\u81f4\u56fe\u50cf\u9519\u4f4d\uff0c\u5b57\u4f53\u4e22\u5931\u7b49\u7b49\u95ee\u9898\u3002\u8fd9\u662f\u56e0\u4e3a2004\u7248\u548c2024\u7248\u6570\u636e\u5b58\u50a8\u7684\u7ed3\u6784\u662f\u4e0d\u540c\u7684\u3002\u4f7f\u7528\u6570\u636e\u5e93\u7cfb\u7edf\u53ef\u4ee5\u8fbe\u5230\u6570\u636e\u5b58\u50a8\u7ed3\u6784\u7684\u7edf\u4e00\uff0c\u89c4\u907f\u6570\u636e\u5b64\u5c9b\u7684\u51fa\u73b0\u3002
"},{"location":"Classnote/Database-System/termsintro/#3","title":"3. \u6570\u636e\u8bbf\u95ee\u56f0\u96be","text":"\u2003\u2003\u5728\u8f6f\u4ef6\u7f16\u5199\u5c42\u9762\uff0c\u5982\u679c\u8981\u8bbf\u95ee\u67e5\u627e\u4e00\u9879\u6570\u636e\uff0c\u5982\u679c\u53ea\u7b80\u5355\u5730\u4f9d\u8d56\u4e8e\u6587\u4ef6\u7cfb\u7edf\u5219\u9700\u8981\u81ea\u884c\u7f16\u5199\u67e5\u8be2\u8bed\u53e5\uff08for\u5faa\u73af\u7b80\u6613\u4f46\u662f\u6548\u7387\u4f4e\uff0c\u6548\u7387\u9ad8\u7684b\u6811\u5b9e\u73b0\u7e41\u7410\uff09\uff0c\u8d39\u65f6\u8d39\u529b\u8d39\u7a7a\u95f4\u3002\u800c\u6570\u636e\u5e93\u7cfb\u7edf\u5219\u80fd\u63d0\u4f9b\u4e00\u79cd\u7edf\u4e00\u7684\u6570\u636e\u8bbf\u95ee\u63a5\u53e3\uff0c\u76f4\u63a5\u7528\u4e00\u6761\u8bed\u53e5\u5c31\u53ef\u4ee5\u5b8c\u6210\u6570\u636e\u7684\u8bbf\u95ee\u548c\u67e5\u627e\u3002
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\u2003\u2003\u5b9e\u73b0\u8fd9\u4e09\u4e2a\u5c42\u9762\u9700\u8981\u6d89\u53ca\u975e\u5e38\u591a\u7684\u5982\u5bc6\u7801\u5b66\u5404\u9886\u57df\u7684\u77e5\u8bc6\uff0c\u5982\u679c\u53ea\u4f7f\u7528\u7b80\u5355\u7684\u6587\u4ef6\u7ba1\u7406\u7cfb\u7edf\uff0c\u5b8c\u6574\u7684\u5b9e\u73b0\u4f9d\u7136\u662f\u8d39\u65f6\u8d39\u529b\u8d39\u7a7a\u95f4\u3002\u6570\u636e\u5e93\u7cfb\u7edf\u53ef\u4ee5\u63d0\u4f9b\u76f8\u5e94\u7684\u63a5\u53e3\uff0c\u5b9e\u73b0\u5bf9\u6570\u636e\u7684\u8bbf\u95ee\u63a7\u5236\uff0c\u8f7b\u677e\u89e3\u51b3\u5b89\u5168\u6027\u7684\u95ee\u9898\u3002
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\u2003\u2003\u5176\u4e2d 1. \u6765\u81ea\u6570\u636e\u5e93\u7cfb\u7edf\u7684\u5b9a\u4e49\uff0c2. 3. 4. 6. \u662f\u4e0a\u8ff0\u95ee\u9898\u7684\u89e3\u51b3\u65b9\u5f0f\uff0c5. \u662f\u5b9e\u73b0\u539f\u5b50\u6027\u7684\u4e00\u79cd\u5b9e\u9645\u64cd\u4f5c\u3002
"},{"location":"Classnote/Database-System/termsintro/#_8","title":"\u6570\u636e\u6a21\u578b","text":"\u2003\u2003\u65e2\u7136\u6211\u4eec\u9700\u8981\u6784\u5efa\u4e00\u4e2a\u9ad8\u6548\u7684\u6570\u636e\u5e93\u7cfb\u7edf\uff0c\u90a3\u4e48\u4e00\u4e2a\u6e05\u6670\u53ef\u89c2\u7684\u6570\u636e\u6a21\u578b\u662f\u5fc5\u4e0d\u53ef\u5c11\u7684\u3002\u5728\u6570\u636e\u5e93\u7684\u53d1\u5c55\u4e2d\uff0c\u8bde\u751f\u4e86\u975e\u5e38\u591a\u7c7b\u578b\u7684\u6570\u636e\u5e93\u3002
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CREATE TABLE instructor (\n ID char(5),\n name varchar(20),\n dept_name varchar(20),\n salary numeric(8,2),\n PRIMARY KEY (ID),\n FOREIGN KEY (dept_name) REFERENCES department(name)\n);\n\u2003\u2003\u7136\u800c\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u6570\u636e\u5b9a\u4e49\u8bed\u8a00\u7684\u7ed3\u6784\u548cC\u8bed\u8a00\u4e2d\u7684struct\u6709\u6240\u533a\u522b\uff0cC\u8bed\u8a00\u7684struct\u5728\u7ecf\u8fc7\u94fe\u63a5\u540e\u4f1a\u76f4\u63a5\u628a\u7b26\u53f7\u8868\u4e22\u5f03\uff0c\u7528\u6307\u9488\u6765\u4ee3\u66ff\uff0c\u4f46\u662f\u6570\u636e\u5e93\u7cfb\u7edf\u4e0d\u4f1a\u4e22\u5f03\u8fd9\u4e9b\u8868\u683c\u6a21\u677f\uff0c\u800c\u4f1a\u5b9e\u5b9e\u5728\u5728\u5730\u628a\u5b83\u4eec\u4f5c\u4e3a\u4e00\u79cd\u6570\u636e\u5b58\u50a8\u4e0b\u6765\uff0c\u8fd9\u79cd\u6570\u636e\u5c31\u53eb\u5143\u6570\u636e\u3002
\u6a21\u5f0f
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"},{"location":"Classnote/Database-System/termsintro/#_21","title":"\u6570\u636e\u64cd\u4f5c\u8bed\u8a00","text":"\u2003\u2003\u6570\u636e\u64cd\u4f5c\u8bed\u8a00\uff0c\u4e5f\u5c31\u662f\u67e5\u8be2\u8bed\u8a00\uff0c\u662f\u7528\u4e8e\u67e5\u627e\u548c\u64cd\u4f5c\u6570\u636e\u5e93\u4e2d\u7684\u6570\u636e\u7684\u8bed\u8a00\u3002\u5176\u4e2d\uff0c\u4f7f\u7528\u7684\u6700\u4e3a\u5e7f\u6cdb\u7684\u5c31\u662f\u7ed3\u6784\u5316\u67e5\u8be2\u8bed\u8a00\uff08SQL\uff09\u3002
SQL\u548c\u4f20\u7edf\u7f16\u7a0b\u8bed\u8a00\u7684\u533a\u522b
\u2003\u2003\u6211\u4eec\u4e4b\u524d\u5b66\u8fc7\u7684c\uff0cpython\uff0cjava\u7b49\u7f16\u7a0b\u8bed\u8a00\uff0c\u5b9e\u9645\u4e0a\u662f\u6309\u7167\u4e00\u4e2a\u6d41\u7a0b\u6765\u8fdb\u884c\u7f16\u7a0b\u7684\uff0c\u8fd9\u7c7b\u7f16\u7a0b\u8bed\u8a00\u88ab\u6210\u4e3a\u8fc7\u7a0b\u5f0f\u7684\u3002SQL\u4e0d\u540c\uff0c\u5b83\u7684\u8bed\u53e5\u6bd4\u8f83\u7b80\u5355\u7cbe\u70bc\uff0c\u5c31\u50cf\u8bf4\u4e00\u53e5\u8bdd\uff0c\u800c\u4e0d\u50cf\u5199\u4e00\u6bb5\u7a0b\u5e8f\u3002\u8fd9\u7c7b\u7f16\u7a0b\u8bed\u8a00\u88ab\u79f0\u4f5c\u9648\u8ff0\u5f0f\uff08\u975e\u8fc7\u7a0b\u5f0f\uff09\u8bed\u8a00\u3002
SQL\u7684\u4f8b\u5b50
select name\n from instructor\n where instructor.ID = '10129';\n select instructor.ID, department.building\n from instructor, department\n where instructor.dept_name = department.dept_name and department.dept_name = 'Physics';\n\u2003\u2003\u4f46\u662f\uff0c\u6211\u4eec\u53d1\u73b0\u8fd9\u79cd\u8bed\u53e5\u7684\u7528\u9014\u975e\u5e38\u6709\u9650\uff0c\u5b83\u4e0d\u80fd\u591f\u50cf\u6d41\u6c34\u7ebf\u4e00\u6837\u4e3a\u6211\u4eec\u5b9e\u73b0\u81ea\u52a8\u5316\uff0c\u5904\u7406\u8f93\u5165\u8f93\u51fa\u3002\u6240\u4ee5\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u4f1a\u628a\u6570\u636e\u64cd\u4f5c\u8bed\u8a00\u548c\u4f20\u7edf\u7684\u8fc7\u7a0b\u5f0f\u8bed\u8a00\u7ed3\u5408\u8d77\u6765\uff0c\u4f7f\u7528SQL\u6765\u4ece\u6570\u636e\u5e93\u4e2d\u8bfb\u53d6\u6570\u636e\uff0c\u7136\u540e\u4f7f\u7528C/C++,Python,Java\u6765\u5904\u7406\u6570\u636e\u3002\u540e\u8005\u88ab\u79f0\u4f5c\u5bbf\u4e3b\u8bed\u8a00\u3002
\u2003\u2003\u90a3\u4e48\u5982\u4f55\u5c06\u6570\u636e\u64cd\u4f5c\u8bed\u8a00\u5d4c\u5165\u5230\u5bbf\u4e3b\u8bed\u8a00\u5f53\u4e2d\u5462\uff1f\u5b9e\u9645\u4e0a\uff0c\u6570\u636e\u5e93\u63d0\u4f9b\u4e86\u4e00\u79cd\u63a5\u53e3\uff0c\u6bd4\u5982ODBC\uff0cJDBC\uff0cADO.NET\u7b49\uff0c\u8fd9\u4e9b\u63a5\u53e3\u53ef\u4ee5\u5141\u8bb8\u5916\u90e8\u7684\u6570\u636e\u64cd\u4f5c\u8bed\u8a00\u548c\u6570\u636e\u5e93\u4e4b\u95f4\u8fdb\u884c\u901a\u4fe1\u3002\u6b64\u5916\uff0c\u5bbf\u4e3b\u8bed\u8a00\u4f1a\u63d0\u4f9b\u5916\u90e8\u63d2\u4ef6\uff0c\u6765\u9002\u914d\u6570\u636e\u64cd\u4f5c\u8bed\u8a00\u5728\u5bbf\u4e3b\u8bed\u8a00\u4e2d\u7684\u4f7f\u7528\u3002
"},{"location":"Classnote/Database-System/termsintro/#_22","title":"\u6570\u636e\u5e93\u8bbe\u8ba1","text":"\u2003\u2003\u641e\u6e05\u695a\u4e86\u6574\u4e2a\u6570\u636e\u5e93\u7684\u7ed3\u6784\u548c\u64cd\u4f5c\u65b9\u5f0f\u4e4b\u540e\uff0c\u6211\u4eec\u4ece\u7528\u6237\u548c\u5f00\u53d1\u8005\u7684\u89c6\u89d2\u4e86\u89e3\u4e86\u6570\u636e\u5e93\uff0c\u7136\u800c\u8fd9\u662f\u4e0d\u591f\u7684\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u7ad9\u5728\u4e00\u4e2a\u8bbe\u8ba1\u8005\u7684\u89d2\u5ea6\u53bb\u5b66\u4e60\u6570\u636e\u5e93\u7684\u8bbe\u8ba1\u65b9\u5f0f\u3002
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\u2003\u2003\u5728\u8ba1\u7b97\u673a\u7684\u5b58\u50a8\u4e2d\uff0c\u6709\u5916\u90e8\u5b58\u50a8\u548c\u5185\u90e8\u5b58\u50a8\uff0c\u5916\u90e8\u5b58\u50a8\u7684\u8bfb\u53d6\u901f\u5ea6\u8fdc\u8fdc\u6162\u4e8e\u5185\u90e8\u5b58\u50a8\u3002\u4e3a\u4e86\u51cf\u5c11\u5185\u90e8\u5b58\u50a8\u7684\u6d6a\u8d39\uff0c\u6211\u4eec\u5c06\u90e8\u5206\u5916\u90e8\u5b58\u50a8\u8bfb\u5165\u7684\u6570\u636e\u6682\u65f6\u5730\u5b58\u5728\u5185\u5b58\u7684\u4e00\u4e2a\u4f4d\u7f6e\uff0c\u8fd9\u4e2a\u5c31\u662f\u7f13\u51b2\u533a\u3002\u5bf9\u7f13\u51b2\u533a\u7684\u8bbe\u8ba1\u3001\u7279\u522b\u662f\u5728\u7f13\u51b2\u533a\u5199\u6ee1\u540e\u7f13\u51b2\u533a\u7684\u8c03\u5ea6\u7b56\u7565\u8bbe\u8ba1\u5c31\u662f\u7f13\u5b58\u7ba1\u7406\u9700\u8981\u8003\u8651\u7684\u95ee\u9898\u3002
\u2003\u2003\u6570\u636e\u7684\u4f20\u8f93\u6709\u975e\u5e38\u591a\u6f5c\u5728\u7684\u98ce\u9669\uff0c\u6bd4\u5982\u5982\u679c\u4e00\u4e2a\u6570\u636e\u53ef\u4ee5\u968f\u610f\u8bbf\u95ee\uff0c\u90a3\u4e48\u5b83\u5f88\u5bb9\u6613\u88ab\u7a83\u53d6\uff1b\u53e6\u5916\uff0c\u5982\u679c\u78b0\u5230\u4f9b\u7535\u4e0d\u7a33\u5b9a\u7b49\u95ee\u9898\uff0c\u6570\u636e\u5f88\u6709\u53ef\u80fd\u4f1a\u88ab\u635f\u574f\uff0c\u8fd9\u65f6\u6388\u6743\u548c\u5b8c\u6574\u6027\u7ba1\u7406\u6a21\u5757\u5c31\u9700\u8981\u4ecb\u5165\uff0c\u5904\u7406\u8fd9\u4e9b\u95ee\u9898\uff0c\u786e\u4fdd\u6570\u636e\u7684\u5b89\u5168\u6027\u3002
\u2003\u2003\u4e8b\u52a1\u662f\u6570\u636e\u5e93\u9886\u57df\u4e2d\u6781\u5176\u91cd\u8981\u7684\u4e00\u4e2a\u6982\u5ff5\uff0c\u5b83\u6307\u6570\u636e\u5e93\u8fdb\u884c\u7684\u4e00\u6b21\u5b8c\u6574\u5408\u6cd5\u7684\u64cd\u4f5c\uff0c\u800c\u4e3a\u4e86\u4fdd\u8bc1\u5b83\u7684\u539f\u5b50\u6027\uff0c\u4ed6\u9700\u8981\u4e8b\u52a1\u7ba1\u7406\u7cfb\u7edf\u505a\u76f8\u5173\u7684\u5907\u4efd\u548c\u6062\u590d\u64cd\u4f5c\u3002\u540c\u65f6\uff0c\u8981\u5b9e\u73b0\u591a\u4e2a\u4e8b\u52a1\u7684\u5e76\u53d1\u6267\u884c\uff0c\u8fd8\u9700\u8981\u4e8b\u52a1\u7ba1\u7406\u7cfb\u7edf\u505a\u76f8\u5173\u7684\u8c03\u5ea6\u548c\u534f\u8c03\u3002
"},{"location":"Classnote/Database-System/termsintro/#_25","title":"\u8be2\u95ee\u5904\u7406\u6a21\u5757","text":"\u2003\u2003\u4f5c\u4e3a\u5904\u7406\u8be2\u95ee\u7684\u7f16\u7a0b\u6a21\u5757\uff0c\u8be2\u95ee\u5904\u7406\u6a21\u5757\u9700\u8981\u7f16\u8bd1\u7528\u6237\u63d0\u4f9b\u7684\u6570\u636e\u5e93\u8bed\u53e5\u3002\u56e0\u6b64\uff0c\u9488\u5bf9\u4e0d\u540c\u7c7b\u578b\u7684\u6570\u636e\u5e93\u8bed\u53e5\uff0c\u6bd4\u5982\u6570\u636e\u5b9a\u4e49\u8bed\u53e5\u548c\u6570\u636e\u5904\u7406\u8bed\u53e5\uff0c\u9700\u8981\u63d0\u4f9b\u4e0d\u540c\u7684\u7f16\u8bd1\u5668\u3002\u540c\u65f6\uff0c\u6709\u65f6\u7528\u6237\u63d0\u4f9b\u7684\u8bed\u53e5\u4f1a\u5e26\u6709\u5197\u4f59\uff0c\u53ef\u4ee5\u8fdb\u884c\u4e00\u5b9a\u7684\u4f18\u5316\uff0c\u6700\u540e\u6839\u636e\u4f18\u5316\u540e\u7684\u903b\u8f91\uff0c\u9009\u62e9\u6700\u4f73\u7684\u7b97\u6cd5\uff0c\u8c03\u7528\u5b58\u50a8\u6a21\u5757\u7684\u63a5\u53e3\u6765\u6267\u884c\u76f8\u5e94\u7684\u67e5\u8be2\u5904\u7406\u7b97\u6cd5\u3002
"},{"location":"Classnote/Database-System/termsintro/#_26","title":"\u4e8b\u52a1\u7ba1\u7406\u6a21\u5757","text":"\u2003\u2003\u6b64\u5904\u7684\u4e8b\u52a1\u7ba1\u7406\u4e0d\u540c\u4e8e\u5b58\u50a8\u7ba1\u7406\u6a21\u5757\u4e2d\u7684\u4e8b\u52a1\u7ba1\u7406\uff0c\u5b83\u5904\u7406\u7684\u4e0d\u662f\u786c\u4ef6\u4e4b\u95f4\u7684\u4e8b\u52a1\uff0c\u800c\u662f\u66f4\u9ad8\u4e00\u5c42\u8bed\u53e5\u5c42\u9762\u7684\u4e8b\u52a1\u3002\u529f\u80fd\u5219\u5927\u540c\u5c0f\u5f02\uff0c\u4e5f\u662f\u4e3a\u4e86\u4fdd\u969c\u539f\u5b50\u6027\u3001\u5b8c\u6574\u6027\u800c\u9700\u8981\u63d0\u4f9b\u56de\u590d\u6a21\u5757\u548c\u5e76\u53d1\u63a7\u5236\u6a21\u5757\u3002
"},{"location":"Classnote/Database-System/termsintro/#_27","title":"\u6570\u636e\u5e93\u4f7f\u7528\u8005","text":"\u2003\u2003\u6570\u636e\u5e93\u7684\u4f7f\u7528\u8005\u4e5f\u4f1a\u6839\u636e\u5e94\u7528\u573a\u666f\u5206\u6210\u4e0d\u540c\u7684\u89d2\u8272\u3002\u5728\u89c6\u56fe\u6a21\u5f0f\u5c42\u9762\uff0c\u6709\u7f16\u5199\u5e94\u7528\u7a0b\u5e8f\u7684\u7a0b\u5e8f\u5458\u548c\u76f4\u63a5\u4f7f\u7528\u7684\u7528\u6237\uff0c\u5728\u903b\u8f91\u6a21\u5f0f\u5c42\u9762\uff0c\u6570\u636e\u5206\u6790\u8005\u3001\u9ad8\u7ea7\u7528\u6237\u4f1a\u76f4\u63a5\u8c03\u7528\u6570\u636e\u5e93\u7684\u8bed\u53e5\u6765\u5bf9\u6570\u636e\u8fdb\u884c\u76f4\u63a5\u5904\u7406\u3002\u5728\u7269\u7406\u6a21\u5f0f\u5c42\u9762\uff0c\u6570\u636e\u5e93\u7ba1\u7406\u5458\u4f1a\u4fee\u6539\u6570\u636e\u5e93\u7684\u76f8\u5173\u53c2\u6570\uff0c\u5c3d\u91cf\u8ba9\u6570\u636e\u5e93\u8fbe\u5230\u6700\u597d\u7684\u6027\u80fd\u3002
"},{"location":"Classnote/Database-System/termsintro/#_28","title":"\u6570\u636e\u5e93\u9886\u57df\u7684\u5386\u53f2","text":""},{"location":"Classnote/Database-System/termsintro/#_29","title":"\u5173\u952e\u9886\u57df\u7684\u53d1\u5c55","text":"\u2003\u2003\u572820\u4e16\u7eaa50\u5e74\u4ee3\uff0c\u8ba1\u7b97\u673a\u9886\u57df\u7684\u6570\u636e\u5b58\u50a8\u4f7f\u7528\u7684\u662f\u7eb8\u5e26\uff0c\u7528\u6253\u5b54\u4e0e\u5426\u6765\u8868\u793a0\u548c1\u3002\u7136\u800c\u7269\u7406\u7684\u6253\u5b54\u5f88\u5bb9\u6613\u51fa\u9519\uff0c\u96be\u4fdd\u5b58\uff0c\u6570\u636e\u91cf\u5927\u7684\u65f6\u5019\u9700\u8981\u5f88\u5927\u7684\u6210\u672c\u3002
\u2003\u200320\u4e16\u7eaa60\u5e74\u4ee3\uff0c\u51fa\u73b0\u4e86\u78c1\u5e26\uff0c\u5b83\u53ef\u4ee5\u5c06\u6570\u636e\u957f\u671f\u5730\u5b58\u50a8\u5728\u78c1\u5e26\u4e0a\uff0c\u8f7b\u91cf\u4fbf\u6377\u3001\u5bb9\u6613\u4fdd\u5b58\u3002\u540c\u65f6\uff0c\u7f51\u7edc\u548c\u6570\u636e\u7ed3\u6784\u7684\u53d1\u5c55\u6b63\u5728\u5c06\u7406\u8bba\u4e0d\u65ad\u5730\u6ce8\u5165\u5e94\u7528\u5c42\u9762\u3002
\u2003\u20031961\u5e74\uff0c\u6570\u636e\u5e93\u4e4b\u7236\uff0cCharles W. Bachman\uff0c\u5728\u63d0\u51fa\u4e86\u96c6\u6210\u6570\u636e\u5e93\u7684\u6982\u5ff5\uff0c\u6570\u636e\u5e93\u521d\u5177\u96cf\u5f62\u3002\u4ed6\u56e0\u6b64\u83b7\u5f97\u4e861973\u5e74\u7684\u56fe\u7075\u5956\u3002
\u2003\u200370\u5e74\u4ee3\uff0c\u6570\u636e\u5e93\u5728\u8054\u673a\u4e8b\u52a1\u5904\u7406\u7684\u5546\u52a1\u5e94\u7528\u8d8a\u52a0\u5e7f\u6cdb\uff0c\u4e00\u79cd\u9ad8\u6548\u7684\u6570\u636e\u5b58\u50a8\u65b9\u5f0f\u4e5f\u5c31\u6210\u4e86\u521a\u9700\u3002\u57281970\u5e74\uff0cE.F. Codd\uff0c\u5728\u8bba\u6587\u300aA Relational Model of Data for Large Shared Data Banks\u300b\u4e2d\uff0c\u63d0\u51fa\u4e86\u5173\u7cfb\u6a21\u578b\u7684\u6982\u5ff5\uff0c\u5960\u5b9a\u4e86\u5173\u7cfb\u6570\u636e\u5e93\u7684\u57fa\u7840\uff0c\u4ed6\u4e5f\u56e0\u6b64\u83b7\u5f97\u4e861981\u5e74\u7684\u56fe\u7075\u5956\u3002
\u2003\u2003\u6709\u4e86\u575a\u5b9e\u7684\u7406\u8bba\u57fa\u7840\uff0c\u6570\u636e\u5e93\u5e94\u7528\u4e5f\u5f00\u59cb\u904d\u5730\u5f00\u82b1\u30021974\u5e74\uff0cIBM\u516c\u53f8\u7684Jim Gray\u5e26\u9886\u7814\u53d1\u4e86\u7b2c\u4e00\u4e2a\u5546\u7528\u5173\u7cfb\u6570\u636e\u5e93\uff0c\u540d\u4e3aSystem R\u3002\u540c\u5e74\uff0c\u7531UC Berkeley\u7684Michael Stonebraker\u7275\u5934\uff0c\u4e5f\u5b9e\u73b0\u4e86\u4e00\u4e2a\u5173\u7cfb\u6570\u636e\u5e93\uff0c\u540d\u4e3aIngres\u3002\u4ed6\u4eec\u4e5f\u56e0\u4e3a\u5bf9\u6570\u636e\u5e93\u9886\u57df\u7684\u5353\u8d8a\u6210\u5c31\u83b7\u5f97\u4e86\u56fe\u7075\u5956\uff081998\u5e74\uff0c2014\u5e74\uff09\u3002
"},{"location":"Classnote/Database-System/termsintro/#_30","title":"\u6280\u672f\u6808\u65f6\u95f4\u7ebf","text":"20\u4e16\u7eaa80\u5e74\u4ee3
20\u4e16\u7eaa90\u5e74\u4ee3
21\u4e16\u7eaa00\u5e74\u4ee3
\u4ec0\u4e48\u662fNoSQL
\u2003\u2003NoSQL\u4e0d\u662f\u4e00\u4e2a\u5177\u4f53\u7684SQL\u5e94\u7528\uff0c\u800c\u662f\u975e\u5173\u7cfb\u578b\u6570\u636e\u5e93\u7684\u603b\u79f0\u3002\u5b83\u6ca1\u6709\u4f7f\u7528\u4f20\u7edf\u7684\u5173\u7cfb\u578b\u6570\u636e\u6a21\u578b\uff0c\u800c\u662f\u4f7f\u7528\u66f4\u52a0\u81ea\u7531\u7684\u6a21\u578b\uff0c\u6765\u8fbe\u5230\u66f4\u9ad8\u7684\u6269\u5c55\u6027\u548c\u53ef\u7528\u6027\u3002 \u2003\u2003NoSQL\u6570\u636e\u5e93\u591a\u5e94\u7528\u5728\u4ee5\u5927\u6570\u636e\u4e3a\u5178\u578b\u7684\u5927\u91cf\u6570\u636e\u4e0a\uff0c\u56e0\u4e3a\u5b83\u4eec\u6ca1\u6709\u7279\u522b\u7684\u5173\u7cfb\u7ea6\u675f\uff0c\u4e0d\u9700\u8981\u4f7f\u7528\u5173\u7cfb\u578b\u7684\u6570\u636e\u6a21\u578b\u6765\u5b58\u50a8\u3002
\u6559\u5e08\uff1a\u7fc1\u5f66\u7433
\u2003\u2003\u79bb\u6563\u662f\u4e00\u95e8\u548c\u8ba1\u7b97\u673a\u606f\u606f\u76f8\u5173\u7684\u6570\u5b66\u8bfe\uff0c\u8fd9\u95e8\u8bfe\u987e\u540d\u601d\u4e49\uff0c\u9700\u8981\u89e3\u51b3\u4e00\u4e9b\u548c\u8ba1\u7b97\u673a\u76f8\u5173\u7684\u5e94\u7528\u5b9e\u9645\u95ee\u9898\uff0c\u56e0\u6b64\uff0c\u8bfe\u7a0b\u524d\u671f\u6d89\u53ca\u5927\u91cf\u7684\u903b\u8f91\u77e5\u8bc6\uff0c\u6bd4\u5982\u903b\u8f91\u4ee3\u6570\uff0c\u96c6\u5408\u5173\u7cfb\u8bba\uff0c\u8fd9\u4e9b\u5bf9\u5b66\u4e60\u6570\u5b57\u903b\u8f91\u7684\u8bbe\u8ba1\u9887\u6709\u5e2e\u52a9\uff0c\u800c\u5230\u540e\u9762\u4f1a\u6d89\u53ca\u548c\u8ba1\u7b97\u673a\u76f8\u5173\u7684\u7b97\u6cd5\u77e5\u8bc6\uff0c\u6bd4\u5982\u56fe\u8bba\u3001\u7ecf\u5178\u7b97\u6cd5\u548c\u6811\u7b49\uff0c\u901a\u8fc7\u8fd9\u4e00\u90e8\u5206\u7684\u5b66\u4e60\u53ef\u4ee5\u5e2e\u52a9\u7406\u89e3\u540e\u9762\u7684\u7b97\u6cd5\u8bfe\u7a0b\u3002
\u89c2\u524d\u63d0\u9192
\u2003\u2003\u56e0\u4e3a\u79bb\u6563\u6570\u5b66\u57fa\u7840\u77e5\u8bc6\u7684\u7b14\u8bb0\u5728GitHub,CC98\u4ee5\u53ca\u5176\u5b83\u4e2a\u4eba\u7b14\u8bb0\u7f51\u7ad9\u6709\u975e\u5e38\u5145\u5206\u8be6\u5c3d\u7684\u4f53\u7cfb\uff0c\u800c\u7531\u4e8e\u672c\u4eba\u65f6\u95f4\u7cbe\u529b\u6709\u9650\uff0c\u7b14\u8bb0\u53ea\u5173\u6ce8\u6211\u611f\u5174\u8da3\u3001\u6709\u601d\u8003\u7684\u90e8\u5206\uff0c\u4e0d\u5efa\u8bae\u62ff\u6211\u7684\u8fd9\u4efd\u7b14\u8bb0\u6765\u671f\u672b\u8003\u8bd5\u8865\u5929\u3002
\u8bfe\u7a0b\u8bc4\u5206\u4f53\u7cfb\uff1a
\u6210\u7ee9\u53ef\u4ee5\u76f4\u63a5\u7531\u671f\u672b\u8003\u8bd5\u8986\u76d6\u3002
\u4e0d\u8981\u6c42\u5230\u573a\u4e0a\u8bfe\uff0c\u4e0a\u8bfe\u79ef\u6781\u56de\u7b54\u95ee\u9898\u67091-2\u5206\u7684\u603b\u8bc4\u52a0\u5206\u3002
\u4f5c\u4e1a\u7ebf\u4e0b\u4ea4\uff0cDDL\u5728\u7b2c\u4e00\u8282\u4e0a\u8bfe\u524d\uff0c\u76f4\u63a5\u4ea4\u5230\u6559\u5ba4\u3002
"},{"location":"Classnote/Discrete-Mathematics/Casual/","title":"\u7410\u8bb0","text":"\u2003\u2003\u8bb0\u5f55\u4e00\u4e9b\u7410\u788e\u7684\u77e5\u8bc6\u70b9\uff0c\u4e3b\u8981\u662f\u4e0d\u719f\u6089\u7684\u77e5\u8bc6\u70b9\u548c\u6613\u9519\u70b9\u3002
\u5f85\u89e3\u51b3\u7684\u95ee\u9898
For any \u5728\u903b\u8f91\u7ffb\u8bd1\u4e2d\u6709\u6b67\u4e49\uff0c\u56e0\u4e3a\u82f1\u8bed\u4e2dany\u6709\u65f6\u662fsome\u7684\u610f\u601d\u3002
\u600e\u4e48\u628a\u65e0\u5173\u7684\u9879\u4eceQuantifier\u4e2d\u53bb\u9664\uff1a
\u8bb0\u5fc6\u65b9\u6cd5\uff1a\u76f4\u63a5\u62c6\u62ec\u53f7\uff0c\u5bf9\u4e8e\u6700\u540e\u4e24\u4e2a\u5f0f\u5b50\uff0c\u56e0\u4e3a\\(P(x)\\)\u5728\u524d\uff0c\u628a\u63a8\u5bfc\u7b26\u53f7\u8f6c\u6362\u6210\u6790\u53d6\u7684\u65f6\u5019\u8981\u53d6\u53cd\uff0c\u53d6\u53cd\u524d\u7f6e\u4f1a\u5bfc\u81f4\u8c13\u8bcd\u6539\u53d8\u3002
The necessary condition of \\(A\\) is \\(B\\) \u2014\u2014 \\(A \\rightarrow B\\)
\\(A\\) holds only if \\(B\\) holds \u2003\u2003\u2003\u2003\u2003\u2014\u2014 \\(A \\rightarrow B\\)
\u2003\u2003\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u63a8\u51fa\u7b26\u53f7\\(\\rightarrow \\leftarrow \\leftrightarrow\\)\u7684\u4f18\u5148\u7ea7\u8981\u5927\u4e8e\u5408\u53d6\u6790\u53d6\\(\\wedge \\vee\\)\uff0c\u6240\u4ee5\u5728\u8868\u793a\u9690\u542b\u5173\u7cfb\u65f6\uff0c\u5c3d\u91cf\u80fd\u5199\u62ec\u53f7\u5c31\u5199\u62ec\u53f7\u3002\u6bd4\u5982\\((p \\vee q) \\rightarrow r\\)
\u901a\u8fc7\u4e0a\u8ff0\u7684\u8c13\u8bcd\u516c\u5f0f\uff0c\u628a\\(\\forall\\)\u548c\\(\\exists\\)\u63d0\u5230\u6700\u524d\u9762\u3002\u6ce8\u610f\u8c13\u8bcd\u7684\u524d\u540e\u987a\u5e8f\uff0c\u5b9e\u9645\u4e0a\u5e26\u8c13\u8bcd\u7684\u53d8\u91cf\u672c\u8eab\u5c31\u7701\u7565\u4e86\u4e00\u5c42\u62ec\u53f7\u3002\u4f8b\u5982\\(\\exist xP(x) \\rightarrow \\forall yP(y) \\equiv \\forall y\\exist x(P(x) \\rightarrow P(y))\\)
\u8bc1\u4f2a\u53ef\u4ee5\u7528\u53cd\u4f8b\uff0c\u4e0d\u4e00\u5b9a\u786c\u4e0a\u516c\u5f0f\u8f6c\u5316\u3002
\u2003\u2003\u4f60\u8bf4\u5f97\u5bf9\uff0c\u4f46\u662f\u6570\u72ec\u6e38\u620f\u662f\u4e00\u6b3e\u7ecf\u5178\u7684\u6570\u5b57\u903b\u8f91\u6e38\u620f\u3002\u73a9\u5bb6\u9700\u8981\u6839\u636e9x9\u76d8\u9762\u4e0a\u7684\u5df2\u77e5\u6570\u5b57\uff0c\u63a8\u7b97\u51fa\u6240\u6709\u5269\u4f59\u7a7a\u683c\u7684\u6570\u5b57\uff0c\u5e76\u4e14\u6ee1\u8db3\u6bcf\u4e00\u884c\u3001\u6bcf\u4e00\u5217\u3001\u6bcf\u4e00\u4e2a\u7c97\u7ebf\u5bab\u5185\u7684\u6570\u5b57\u5747\u542b1-9\uff0c\u5e76\u4e14\u4e0d\u91cd\u590d\u3002
\u2003\u2003\u6570\u72ec\u6e38\u620f\u5bf9\u903b\u8f91\u7684\u6e05\u6670\u8981\u6c42\u548c\u7b80\u5355\u7684\u6e38\u620f\u89c4\u5b9a\uff0c\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u8054\u7cfb\u5230\u79bb\u6563\u6570\u5b66\u4e2d\u5b66\u4e60\u5230\u7684\u547d\u9898\uff0c\u628a\u903b\u8f91\u7528\u6570\u5b66\u7684\u65b9\u5f0f\u5199\u4e0b\u6765\u3002
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#_1","title":"\u6b65\u9aa4\u4e00 \u2014\u2014 \u5b9a\u4e49\u547d\u9898","text":"\u2003\u2003\u6211\u4eec\u89c4\u5b9a\uff0c\\(p(i,j,n)\\)\u4ee3\u8868\u628a\u6570\u5b57n\u653e\u5728i\u884cj\u5217\u7684\u65b9\u683c\u4e2d\u3002\u5bb9\u6613\u77e5\u9053\\(i\\)\uff0c\\(j\\)\uff0c\\(n\\)\u7684\u53d6\u503c\u603b\u5171\u53ef\u4ee5\u5bfc\u51fa\\(9 \\times 9 \\times 9 = 729\\)\u4e2a\u547d\u9898\u3002
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#_2","title":"\u6b65\u9aa4\u4e8c \u2014\u2014 \u7ffb\u8bd1\u83b7\u80dc\u903b\u8f91","text":"\u2003\u2003\u7531\u4e8e\u83b7\u80dc\u7684\u903b\u8f91\u9700\u8981\u7528\u5230\u547d\u9898\u7684\u6790\u53d6\u3001\u5408\u53d6\u7b49\u64cd\u4f5c\uff0c\u800c\u56e0\u4e3a\u547d\u9898\u8fc7\u591a\uff0c\u6211\u4eec\u9700\u8981\u4e00\u79cd\u7b80\u4fbf\u7684\u8868\u793a\u65b9\u6cd5\u3002
\u89c4\u5b9a\u4e00\uff1a\u591a\u9879\u5408\u53d6\u7b26\u53f7 $$ \\bigwedge_{i=x}^y p(i,j_0,n_0) = p(x,j_0,n_0) \\land p(x+1,j_0,n_0) \\land \\cdots \\land p(y,j_0,n_0) $$
\u89c4\u5b9a\u4e8c\uff1a\u591a\u9879\u6790\u53d6\u7b26\u53f7 $$ \\bigvee_{i=x}^y p(i,j_1,n_1) = p(x,j_1,n_1) \\lor p(x+1,j_1,n_1) \\lor \\cdots \\lor p(y,j_1,n_1) $$
\u2003\u2003\u6839\u636e\u89c4\u5b9a\u4e00\u548c\u89c4\u5b9a\u4e8c\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u51fa\u6570\u72ec\u6e38\u620f\u80dc\u5229\u7684\u903b\u8f91\uff1a
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#1-1-9","title":"1. \u6bcf\u4e00\u884c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002","text":"\u2003\u2003\u5148\u4f7f\u7528Quantifier\u53ef\u4ee5\u7b80\u5355\u5730\u628a\u201c\u6bcf\u4e00\u884c\u201d\u7ffb\u8bd1\u4e3a\\(\\forall i\\)\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u9700\u8981\u77e5\u9053\u600e\u4e48\u63cf\u8ff0\u201c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u201d\u3002
\u2003\u2003\u6211\u4eec\u4e0d\u59a8\u8003\u8651\u679a\u4e3e\u6bcf\u4e00\u4e2a\u6570\u5b57\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u628a\u6761\u4ef6\u8fdb\u4e00\u6b65\u5730\u62d3\u5c55\u6210\u4e3a\u201c\u5bf9\u4e8e1-9\u7684\u4efb\u610f\u4e00\u4e2a\u6570\u5b57\uff0c\u8fd9\u4e2a\u6570\u5b57\u90fd\u5728\u8fd9\u4e00\u884c\u201d\uff0c\u7528\u6570\u5b66\u8bed\u8a00\u63cf\u8ff0\u5373\\(\\forall nP(n)\\)\uff0c\\(P(n)\\)\u8868\u793a\u6570\u5b57\\(n\\)\u5728\u8fd9\u4e00\u884c\u3002
\u2003\u2003\u6700\u540e\uff0c\u6211\u4eec\u53ea\u9700\u8981\u63cf\u8ff0\u600e\u4e48\u8868\u793a\u6570\u5b57\u5728\u8fd9\u4e00\u884c\u3002\u6570\u5b57\u5728\u8fd9\u4e00\u884c\uff0c\u610f\u5473\u7740\u8fd9\u4e2a\u6570\u5b57\u5728\u8fd9\u4e00\u884c\u7684\u67d0\u4e00\u5217\u4e2d\u51fa\u73b0\u8fc7\u81f3\u5c11\u4e00\u6b21\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u628a\u6761\u4ef6\u62c6\u89e3\u4e3a\u201c\u8fd9\u4e2a\u6570\u5b57\u5728\u8fd9\u4e00\u884c\u7684\u67d0\u4e00\u5217\u5b58\u5728\u201d\uff0c\u5373\\(\\exist j \\space p(i_0,n_0,j)\\)\u3002
\u2003\u2003\u4e8e\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e00\u4e2a\u903b\u8f91\u7684\u5b8c\u6574\u7ffb\u8bd1\uff1a
\\[ \\forall i \\forall n \\exist j \\space p(i,j,n) \\\\ \\equiv \\bigwedge_{i=1}^9 \\bigwedge_{n=1}^9 \\bigvee_{j=1}^9 \\space p(i,j,n) \\]"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#2-1-9","title":"2. \u6bcf\u4e00\u5217\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002","text":"\u2003\u2003\u8fd9\u4e2a\u903b\u8f91\u7684\u7ffb\u8bd1\u4e0e\u4e0a\u9762\u7c7b\u4f3c\uff0c\u8fd9\u91cc\u5c31\u4e0d\u518d\u8d58\u8ff0\u4e86\u3002 $$ \\forall j \\forall n \\exist i \\space p(i,j,n) \\ \\equiv \\bigwedge_{j=1}^9 \\bigwedge_{n=1}^9 \\bigvee_{i=1}^9 \\space p(i,j,n) $$
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#3-1-9","title":"3. \u6bcf\u4e00\u5bab\u683c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002","text":"\u2003\u2003\u9996\u5148\uff0c\u5bab\u683c\u8fd9\u4e2a\u65b0\u6982\u5ff5\u610f\u5473\u7740\u6211\u4eec\u4e0d\u80fd\u5355\u7eaf\u5730\u50cf\u521a\u521a\u7684\u679a\u4e3e\u884c\u548c\u5217\u4e00\u6837\uff0c\u7528i\u548cj\u6765\u8868\u793a\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5f15\u5165\u4e00\u4e2a\u65b0\u7684\u53d8\u91cf\u3002
\u2003\u2003\u8bbe\u60f3\u6211\u4eec\u9700\u8981\u4e3a\u8fd9\u4e2a\u6570\u72ec\u5199\u4e00\u4e2a\u7a0b\u5e8f\uff0c\u90a3\u4e48\u4e00\u4e2a\u5f88\u5bb9\u6613\u60f3\u5230\u601d\u8def\u7684\u5c31\u662f\u5148\u679a\u4e3e\u6bcf\u4e00\u4e2a\u5bab\u683c\uff0c\u7136\u540e\u679a\u4e3e\u6bcf\u4e00\u4e2a\u6570\u5b57\uff0c\u6700\u540e\u5224\u65ad\u8fd9\u4e2a\u6570\u5b57\u5728\u8fd9\u4e2a\u5bab\u683c\u4e2d\u662f\u5426\u51fa\u73b0\u8fc7\u3002
\u2003\u2003\u5982\u4f55\u679a\u4e3e\u5bab\u683c\uff0c\u4e00\u4e2a\u7b80\u5355\u7684\u65b9\u6cd5\u5c31\u662f\u76f4\u63a5\u628a\u4e5d\u5bab\u683c\u770b\u4f5c\u4e00\u4e2a3x3\u7684\u77e9\u9635\uff0c\u7136\u540e\u901a\u8fc7\u884c\u548c\u5217\u7684\u679a\u4e3e\u5f97\u5230\u5bab\u683c\u3002\u6211\u4eec\u5047\u8bbe\\(x\\)\u662f\u4e5d\u5bab\u683c\u7684\u884c\uff0c\\(y\\)\u662f\u4e5d\u5bab\u683c\u7684\u5217\uff0c\u90a3\u4e48\u65e2\u7136\u5bf9\u4e8e\u67d0\u4e00\u4e2a\u4e5d\u5bab\u683c\u8fd9\u4e2a\u6761\u4ef6\u90fd\u6210\u7acb\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u628a\u6761\u4ef6\u5199\u4e3a\\(\\forall x \\forall y \\space P(x,y)\\)\uff0c\u5176\u4e2dP(x,y)\u8868\u793ax\u884cy\u5217\u7684\u5bab\u683c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002
\u2003\u2003\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u8003\u8651\u600e\u4e48\u8868\u793ax\u884cy\u5217\u7684\u5bab\u683c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002\u548c\u4e0a\u9762\u7684\u601d\u8def\u7c7b\u4f3c\uff0c\u6211\u4eec\u9996\u5148\u628a\u6761\u4ef6\u62c6\u5206\u6210\u201c\u5bf9\u4e8e1-9\u7684\u4efb\u610f\u4e00\u4e2a\u6570\u5b57\uff0c\u8fd9\u4e2a\u6570\u5b57\u90fd\u5728\u8fd9\u4e00\u5bab\u683c\u201d\uff0c\u5373\\(\\forall n \\space P(x,y,n)\\)\uff0c\\(P(x,y,n)\\)\u8868\u793ax\u884cy\u5217\u7684\u5bab\u683c\u4e2d\u6570\u5b57\\(n\\)\u51fa\u73b0\u8fc7\u3002
\u2003\u2003\u6700\u540e\uff0c\u6211\u4eec\u53ea\u9700\u8981\u63cf\u8ff0\u600e\u4e48\u8868\u793ax\u884cy\u5217\u7684\u5bab\u683c\u4e2d\u6570\u5b57\\(n\\)\u51fa\u73b0\u8fc7\u3002\u6570\u5b57\u5728x\u884cy\u5217\u7684\u5bab\u683c\u4e2d\u51fa\u73b0\u8fc7\uff0c\u610f\u5473\u7740\u8fd9\u4e2a\u6570\u5b57\u5728\u8fd9\u4e00\u5bab\u683c\u7684\u67d0\u4e00\u683c\u4e2d\u51fa\u73b0\u8fc7\u81f3\u5c11\u4e00\u6b21\uff0c\u901a\u8fc7\u518d\u6b21\u679a\u4e3e\u884c\u5217\u6765\u8ba1\u7b97\u5bab\u683c\u4e2d\u4e00\u683c\u7684\u4f4d\u7f6e\u3002\u7528\\(i\\)\u8868\u793a\u5bab\u683c\u7684\u7b2ci\u884c\uff0c\\(j\\)\u8868\u793a\u5bab\u683c\u7684\u7b2cj\u5217\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u77e5\u9053\u5bab\u683c\u4e2d\u4e00\u683c\u76f8\u5bf9\u4e8e\u5bab\u683c\u5de6\u4e0a\u89d2\u5750\u6807\u4e3a\\((i,j)\\)\uff0c\u603b\u5750\u6807\u5373\\((3(x-1)+i,3(y-1)+j)\\)\uff0cn\u5728\u8fd9\u4e9b\u5750\u6807\u4e2d\u5b58\u5728\uff0c\u5373\u53ef\u7ffb\u8bd1\u6210\\(\\exist i\\exist j \\space p(3(x-1)+i,3(y-1)+j,n)\\)\u3002
\u2003\u2003\u4e8e\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e2a\u903b\u8f91\u7684\u5b8c\u6574\u7ffb\u8bd1\uff1a
\\[ \\forall x \\forall y \\forall n\\exist i\\exist j \\space p(3(x-1)+i,3(y-1)+j,n) \\\\ \\equiv \\bigwedge_{x=1}^3 \\bigwedge_{y=1}^3 \\bigwedge_{n=1}^9 \\bigvee_{i=1}^3 \\bigvee_{j=1}^3 \\space p(3(x-1)+i,3(y-1)+j,n) \\]\u2003\u2003\u660e\u9762\u4e0a\u7684\u6570\u72ec\u89c4\u5219\u5c31\u662f\u8fd9\u4e48\u591a\uff0c\u4f46\u662f\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u56e0\u4e3a\u6211\u4eec\u8bbe\u8ba1\u7684\u7279\u6b8a\u6027\uff0c\u4f1a\u6709\u975e\u5e38\u591a\u9690\u542b\u7684\u6761\u4ef6\u9700\u8981\u6211\u4eec\u8003\u8651\uff0c\u5426\u5219\u5c31\u4f1a\u51fa\u5f88\u4e25\u91cd\u7684BUG\u3002\u5c31\u6bd4\u5982\u4e0b\u9762\u8fd9\u4e2a\u89c4\u5219\uff1a
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#4","title":"4. \u6bcf\u4e00\u683c\u53ea\u80fd\u586b\u4e00\u4e2a\u6570\u5b57\u3002","text":"\u2003\u2003\u56e0\u4e3a\u6211\u4eec\u4e4b\u524d\u7684\u601d\u8def\u662f\u679a\u4e3e\uff0c\u6240\u4ee5\u4e0d\u514d\u4f1a\u51fa\u73b0\u67d0\u4e2a\u683c\u5b50\u88ab\u91cd\u590d\u679a\u4e3e\u7684\u60c5\u51b5\uff0c\u6bd4\u5982\u5bf9\u4e8e\u4e00\u4e2a\u683c\u5b50\uff0c\u6211\u4eec\u586b\u5165\u4e86\u6570\u5b571\uff0c\u7136\u540e\u518d\u586b\u5165\u4e86\u6570\u5b572\uff0c\u90a3\u4e48\u6570\u5b572\u5c31\u4f1a\u88ab\u91cd\u590d\u679a\u4e3e\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u8fdb\u884c\u89c4\u5b9a\uff0c\u53bb\u9664\u8fd9\u79cd\u60c5\u51b5\u3002
\u2003\u2003\u201c\u6bcf\u4e00\u683c\u201d\u7684\u7ffb\u8bd1\u662f\u975e\u5e38\u7b80\u5355\u7684\uff0c\u5373\\(\\forall i \\forall j \\space P(i,j)\\)\uff0c\u5176\u4e2d\\(P(i,j)\\)\u8868\u793ai\u884cj\u5217\u7684\u683c\u5b50\u53ea\u6709\u4e00\u4e2a\u6570\u5b57\u3002
\u2003\u2003\u90a3\u4e48\u600e\u4e48\u63cf\u8ff0\u201c\u53ea\u6709\u4e00\u4e2a\u6570\u5b57\u201d\u5462\uff1f\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u901a\u5e38\u4f1a\u60f3\u5230\u7528\u903b\u8f91\u5206\u7c7b\u6765\u5224\u65ad\uff0c\u679a\u4e3e\u6240\u6709\u7684\u6570\u5b57\uff0c\u5982\u679c\u586b\u5165\u4e86\u6570\u5b57\uff0c\u90a3\u4e48\u5c31\u4e0d\u80fd\u518d\u586b\u5165\u5176\u4ed6\u7684\u6570\u5b57\uff0c\u53cd\u4e4b\u5219\u5408\u6cd5\u3002\u8fd9\u4e2a\u201c\u903b\u8f91\u5206\u7c7b\u201d\u7684\u601d\u60f3\u6070\u597d\u548c\u903b\u8f91\u63a8\u51fa\u7684\u8fd0\u7b97\u4e00\u62cd\u5373\u5408\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5b83\u6765\u5b8c\u6210\u7ffb\u8bd1\uff1a $$ \\forall i \\forall j (\\forall n (p(i,j,n) \\rightarrow \\neg \\exist n' \\space p(i,j,n'))) (n'>n) \\\\ \\begin{aligned} &\\equiv \\forall i \\forall j \\forall n (p(i,j,n) \\rightarrow \\forall n' \\neg p(i,j,n')) (n'>n) \\\\ &\\equiv \\forall i \\forall j \\forall n \\forall n' (p(i,j,n) \\rightarrow \\neg p(i,j,n')) (n'>n) \\\\ &\\equiv \\bigwedge_{i=1}^9 \\bigwedge_{j=1}^9 \\bigwedge_{n=1}^9 \\bigwedge_{n'=n+1}^9 (p(i,j,n) \\rightarrow \\neg p(i,j,n')) \\end{aligned} $$
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#_3","title":"\u6b65\u9aa4\u4e09 \u2014\u2014 \u5224\u65ad\u83b7\u80dc\u60c5\u51b5","text":"\u2003\u2003\u6211\u4eec\u65e2\u7136\u5df2\u7ecf\u77e5\u9053\u4e86\u83b7\u80dc\u6761\u4ef6\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4ece\u4efb\u610f\u4e00\u79cd\u7684\\(p(i,j,n)\\)\u6b63\u786e\u6027\u547d\u9898\u7684\u96c6\u5408\u5224\u65ad\u8fd9\u79cd\u72b6\u6001\u662f\u5426\u8fbe\u5230\u4e86\u80dc\u5229\u3002\u4ece\u4e0a\u9762\u83b7\u80dc\u6761\u4ef6\u7684\u5224\u65ad\u4e2d\uff0c\u6211\u4eec\u77e5\u9053\u5982\u679c\u6ee1\u8db3\u4e86\u4e00\u4e2a\u6761\u4ef6\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6761\u4ef6\u6700\u7ec8\u7684\u8ba1\u7b97\u5c31\u4f1a\u4e3a\u771f\uff0c\u5982\u679c\u56db\u4e2a\u6761\u4ef6\u90fd\u4e3a\u771f\uff0c\u90a3\u4e48\u8fd9\u4e2a\u72b6\u6001\u5c31\u8fbe\u5230\u4e86\u80dc\u5229\u3002\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u8981\u5224\u65ad\u8fd9\u56db\u4e2a\u6761\u4ef6\u662f\u5426\u90fd\u4e3a\u771f\u5373\u53ef\u3002
\u2003\u2003\u867d\u7136\u66b4\u529b\u679a\u4e3e\u83b7\u80dc\u60c5\u51b5\u9700\u8981\\(2^{729}\\)\u6b21\u5c1d\u8bd5\uff0c\u8fd9\u975e\u5e38\u7e41\u7410\uff0c\u4f46\u662f\u81f3\u5c11\u5728\u73b0\u5728\uff0c\u6211\u4eec\u53d1\u73b0\u4e86\u4e00\u4e2a\u89e3\u51b3\u6570\u72ec\u95ee\u9898\u7684\u65b9\u6cd5\uff0c\u4e5f\u4ece\u4e2d\u628a\u5b83\u548c\u79bb\u6563\u6570\u5b66\u7684\u5b66\u4e60\u8054\u7cfb\u5230\u4e86\u4e00\u8d77\u3002
"},{"location":"ScientificResearch/","title":"\u5bfc\u822a\u9875","text":"\u8bb0\u5f55\u79d1\u7814\u4e00\u4e9b\u57fa\u7840\u8bfe\u7684\u5b66\u4e60\u548c\u8bba\u6587\u7684\u9605\u8bfb\u3002
"},{"location":"ScientificResearch/#_2","title":"\u6700\u8fd1\u66f4\u65b0","text":"CS231N - \u56fe\u50cf\u5206\u7c7b\u5668
"},{"location":"ScientificResearch/CS231N/A1L1/","title":"\u5b9e\u9a8c\u4e00 \u2014\u2014 \u5b9e\u73b0\u524dK\u6700\u8fd1\u90bb\u5c45\u7b97\u6cd5","text":"\u2003\u2003\u5728\u56fe\u50cf\u5206\u7c7b\u5668\u7684\u6559\u5b66\u4e2d\uff0c\u6211\u4eec\u5b66\u4e60\u5230\u4e86\u8981\u5b9e\u73b0KNN\u7b97\u6cd5\u9700\u8981\u4e86\u89e3\u7684\u4e00\u4e9b\u77e5\u8bc6\uff0c\u63a5\u4e0b\u6765\u5c06\u901a\u8fc7\u5b9e\u9a8c\u6765\u8fdb\u4e00\u6b65\u5730\u9610\u91ca\u6574\u4e2a\u7b97\u6cd5\u7684\u5b9e\u73b0\u8fc7\u7a0b\u3002
"},{"location":"ScientificResearch/CS231N/A1L1/#_1","title":"\u6b65\u9aa4\u4e00\u3001\u521d\u59cb\u5316","text":"knn.ipynb# ipython notebook\u7684\u4e00\u4e9b\u521d\u59cb\u5316\u64cd\u4f5c\n\n# \u5bfc\u5165\u4e00\u4e9b\u524d\u7f6e\u5e93\uff0c\u5305\u62ecnumpy, random(\u62bd\u53d6\u6570\u636e\u7528)\nimport random\nimport numpy as np\nfrom cs231n.data_utils import load_CIFAR10\nimport matplotlib.pyplot as plt\n\n# matplot\u7684\u521d\u59cb\u5316\uff1a\u5185\u5d4c\u753b\u56fe\u3001\u7a97\u53e3\u8bbe\u7f6e\u3001\u63d2\u503c\u7c7b\u578b\u3001\u56fe\u7ebf\u989c\u8272\n%matplotlib inline\nplt.rcParams['figure.figsize'] = (10.0, 8.0) \nplt.rcParams['image.interpolation'] = 'nearest'\nplt.rcParams['image.cmap'] = 'gray'\n\n# Ipython\u4e2d\uff0c\u5bf9\u8c03\u7528\u7684\u6a21\u5757\u8fdb\u884c\u5b9e\u65f6\u7684\u66f4\u65b0\uff0c\u65e0\u9700\u624b\u52a8\u91cd\u8f7d\u3002\n# http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython\n%load_ext autoreload\n%autoreload 2\n\u2003\u2003\u5728\u8fd9\u6bb5\u4ee3\u7801\u4e2d\uff0c\u9664\u4e86\u7ecf\u5178\u7684numpy\u548c\u9700\u8981\u7684random\u6a21\u5757\u5916\u6211\u4eec\u8fd8\u53ef\u4ee5\u770b\u5230\u6574\u4e2a\u7a0b\u5e8f\u8c03\u7528\u4e86matplotlib\u7684pyplot\u6a21\u5757\uff0c\u8fd9\u662f\u7528\u4e8e\u4ea7\u751f\u6570\u636e\u56fe\u7684\u4e00\u4e2a\u6a21\u5757\uff0c\u5177\u4f53\u5982\u4f55\u4f7f\u7528\u53ef\u4ee5\u770b\u540e\u7eed\u4ee3\u7801\uff0c\u8fd9\u91cc\u8fdb\u884c\u4e86\u521d\u59cb\u5316\u8bbe\u7f6e\uff0c\u5148\u628a\u56fe\u50cf\u5185\u5d4c\u4ece\u800c\u4e0d\u5f39\u51fa\u65b0\u7684\u7a97\u53e3\uff0c\u7136\u540e\u8bbe\u7f6e\u7a97\u53e3\u5927\u5c0f\u3001\u63d2\u503c\u7c7b\u578b\u4ee5\u53ca\u56fe\u7ebf\u7684\u989c\u8272\u3002 \u2003\u2003\u6b64\u5916\u6211\u4eec\u8fd8\u53ef\u4ee5\u770b\u5230\u7a0b\u5e8f\u8c03\u7528\u4e86\u4e00\u4e2aload_CIFAR10\u7684\u51fd\u6570\u3002\u4e0b\u9762\u6211\u4eec\u6765\u89e3\u91ca\u5b83\u7684\u4f5c\u7528\u3002
\u2003\u2003CIFAR-10\u6570\u636e\u96c6\u662f\u975e\u5e38\u7ecf\u5178\uff0c\u4e5f\u662f\u975e\u5e38\u57fa\u7840\u7684\u4e00\u5957\u8bad\u7ec3\u96c6\uff0c\u5b83\u7531\u4e94\u4e07\u4e2a32px * 32px\u5927\u5c0f\u7684\u56fe\u50cf\u7ec4\u6210\uff0c\u6bcf\u4e2a\u50cf\u7d20\u5305\u542bRGB\u4e09\u4e2a\u989c\u8272\u901a\u9053\uff0c\u56e0\u4e3a\u50cf\u7d20\u5c11\uff0c\u6240\u4ee5\u6574\u4f53\u7684\u8bad\u7ec3\u96c6\u5927\u5c0f\u4e0d\u662f\u5f88\u5927\uff0c\u9002\u5408\u8f7b\u91cf\u7ea7\u7684\u6a21\u578b\u8bad\u7ec3\u3002\u5b83\u7684\u6587\u4ef6\u7ed3\u6784\u5982\u4e0b\uff1a
\u2003\u2003\u89c2\u5bdf\u76ee\u5f55\u7ed3\u6784\uff0c\u53ef\u4ee5\u53d1\u73b0\u5b83\u7531\u4e94\u4e2a\u8bad\u7ec3\u96c6\u6784\u6210\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\u5b83\u5e76\u4e0d\u662f\u4ee5\u56fe\u50cf\u7684\u5f62\u5f0f\u5b58\u50a8\uff0c\u800c\u662f\u76f4\u63a5\u4ee5\u4e8c\u8fdb\u5236\u683c\u5f0f\u5b58\u50a8\u3002\u5982\u679c\u4f7f\u7528\u4e8c\u8fdb\u5236\u6587\u672c\u67e5\u770b\u5668\u6765\u5206\u6790\uff0c\u53ef\u4ee5\u5927\u81f4\u770b\u51fa\u6574\u4f53\u7684\u6570\u636e\u96c6\u7684\u6587\u4ef6\u7ed3\u6784\uff0c\u9996\u5148\u662f\u6574\u4e2a\u6587\u4ef6\u7684\u6587\u4ef6\u5934\uff0c\u7136\u540e\u5b58\u50a8\u4e86\u56fe\u50cf\u7684\u7c7b\u578b\uff08\\(1 \\text{ Byte}\\)\u6570\u5b57\u8868\u793a\uff0c\\04B\u9694\u5f00\uff09\uff0c\u63a5\u4e0b\u6765\u662f\u56fe\u50cf\u5934\uff0c\u6700\u7ec8\u662f\u56fe\u50cf\u7684\u5185\u5bb9\uff0c\u5927\u81f4\u4e86\u89e3\u4e86\u5b83\u7684\u7ed3\u6784\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u597d\u7406\u89e3\u4e0b\u9762\u7a0b\u5e8f\u662f\u5982\u4f55\u5bfc\u5165\u6570\u636e\u7684\u3002
\u2003\u2003\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u770b\u770b\u51fd\u6570load_CIFAR10\u662f\u5982\u4f55\u8fd0\u4f5c\u7684\u3002
data_utils.py
from builtins import range\nfrom six.moves import cPickle as pickle\nimport os\nimport numpy as np\n\n# \u8bfb\u53d6\u6587\u4ef6\u4fe1\u606f\ndef load_pickle(f):\n version = platform.python_version_tuple()\n if version[0] == \"2\":\n return pickle.load(f)\n elif version[0] == \"3\":\n return pickle.load(f, encoding=\"latin1\")\n # CIFAR\u5bf9\u4e8epython\u6709\u6807\u51c6\u7684\u8fd4\u56de\u683c\u5f0f\u3002\n # \u8fd4\u56de\u4e00\u4e2a\u5b57\u5178\uff0c\u6bcf\u4e2a\u5b57\u5178\u4e2d\u662f\u8bbe\u7f6e\u597d\u7684\u540d\u5b57\u548c\u76f8\u5173\u6570\u636e\n raise ValueError(\"invalid python version: {}\".format(version))\n\n# \u8bfb\u53d6\u4e00\u4e2a\u6570\u636e\u5757\ndef load_CIFAR_batch(filename):\n with open(filename, \"rb\") as f:\n datadict = load_pickle(f)\n # \u8bfb\u53d6\u56fe\u50cf\u4fe1\u606f\u548c\u6807\u7b7e\u4fe1\u606f\n X = datadict[\"data\"]\n Y = datadict[\"labels\"]\n X = X.reshape(10000, 3, 32, 32).transpose(0, 2, 3, 1).astype(\"float\")\n # X\u7684RGB\u539f\u6765\u57281\u53f7\u7ef4\uff0c\u73b0\u5728\u628aXY\u4f4d\u7f6e\u7ef4\u5ea6\u524d\u79fb\uff0c\u65b9\u4fbf\u4e4b\u540e\u7684\u8ba1\u7b97\u3002\n Y = np.array(Y)\n # Y\u7684\u7c7b\u578b\u4eceList\u8f6c\u6210array\uff0c\u65b9\u4fbf\u540e\u7eed\u8ba1\u7b97\n return X, Y\n\n# \u8bfb\u53d6\u6240\u6709\u6570\u636e\ndef load_CIFAR10(ROOT):\n xs = []\n ys = []\n # \u4ece1\u52305\u8fdb\u884c\u904d\u5386\uff0c\u5bf9\u5e94data_batch_i(i = 1,2,3,4,5)\n for b in range(1, 6):\n f = os.path.join(ROOT, \"data_batch_%d\" % (b,))\n # \u8bfb\u53d6\u4e00\u4e2a\u6570\u636e\u5757\u7684\u56fe\u50cf\n X, Y = load_CIFAR_batch(f)\n # \u628a\u56fe\u50cf\u653e\u5230\u5217\u8868\u4e2d\n xs.append(X)\n ys.append(Y)\n # \u6574\u5408\u6570\u636e\u5757\n Xtr = np.concatenate(xs)\n Ytr = np.concatenate(ys)\n # \u91ca\u653e\u7a7a\u95f4\n del X, Y\n Xte, Yte = load_CIFAR_batch(os.path.join(ROOT, \"test_batch\"))\n return Xtr, Ytr, Xte, Yte\n\u952e\uff08Key\uff09 \u63cf\u8ff0 \u6837\u4f8b batch_label \u8fd9\u6279\u6570\u636e\u7684\u6807\u7b7e \u4e00\u4e2a\u5b57\u7b26\u4e32\u8868\u793a 'training batch 3 of 5', 'testing batch 1 of 1'... labels \u5404\u4e2a\u56fe\u50cf\u5c5e\u4e8e\u7684\u7c7b\u578b \u4e00\u4e2aList\u8868\u793a\uff0c\u6bcf\u627910000\u4e2a [0\uff0c1\uff0c2\uff0c3\uff0c4\uff0c5\uff0c6\uff0c7\uff0c8\uff0c9\uff0c0\uff0c1\uff0c..] data \u5404\u4e2a\u56fe\u50cf\u7684\u5177\u4f53\u5185\u5bb9 \u4e00\u4e2anumpy.darray\u8868\u793a10000\u5f20\u4e09\u4e2a\u901a\u9053\\(32\\times32\\)\u50cf\u7d20\u7684\u56fe\u7247 \u7ec4\u7ec7\u65b9\u5f0f\uff1a\u4e8c\u7ef4\u6570\u7ec4\uff1b \u56fe\u7247\u4e0b\u6807\uff0c(\u901a\u9053\u4e0b\u6807\uff0c\u884c\uff0c\u5217) \u7565 filenames \u56fe\u7247\u540d \u4e00\u4e2a\u5b57\u7b26\u4e32List\u8868\u793a\uff0c\u6bcf\u627910000\u4e2a ['auto_s_000241.png', \u2002 'bufo_viridis_s_001109.png', \u2002 'rana_catesbeiana_s_000111.png', .. ]
\u2003\u2003\u6211\u4eec\u53ea\u5173\u5fc3labels \u548c data\u4e2d\u7684\u6570\u636e\uff0c\u6240\u4ee5\u63d0\u53d6\u51fa\u6570\u636e\u540e\uff0c\u6211\u4eec\u505a\u4e86\u4e00\u6b65\u5bf9X\u7ef4\u5ea6\u7684\u91cd\u65b0\u8bbe\u8ba1\u2014\u2014\u9996\u5148\u628a\u4e8c\u7ef4\u62d3\u5c55\u6210\u56db\u7ef4\uff08\u56fe\u50cf\u4e0b\u6807\u3001\u901a\u9053\u4e0b\u6807\u3001\u884c\u3001\u5217\uff09\uff0c\u7136\u540e\u5c06\u56fe\u50cf\u8fdb\u884c\u4e86\u7ef4\u5ea6\u7684\u8f6c\u7f6e\uff0c\u628a\u901a\u9053\u4e0b\u6807\u653e\u5230\u6700\u540e\u4e00\u4e2a\u7ef4\u5ea6\uff0c\u65b9\u4fbf\u6211\u4eec\u8fdb\u884c\u5bf9\u5355\u4e2a\u50cf\u7d20\u7684\u4fee\u6539\u3002\u6700\u540e\u628a\u7c7b\u578b\u8f6c\u6362\u4e3afloat\u3002 \u2003\u2003\u6700\u7ec8\u6211\u4eec\u8c03\u7528load_CIFAR10\u51fd\u6570\uff0c\u5f97\u5230\u4e86\u539f\u59cb\u7684\u6570\u636e\u96c6\uff0c\u5176\u4e2d\u6709\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\uff0c\u6570\u636e\u5305\u542b\u7c7b\u578b\u4e3anumpy.darray\u7684\u5185\u5bb9\u56db\u7ef4\u6570\u7ec4\u548c\u7c7b\u578b\u4e3anumpy.darray\u7684\u4e00\u7ef4\u4e0b\u6807\u6570\u7ec4\u3002
cifar10_dir = 'cs231n/datasets/cifar-10-batches-py'\n\n# \u5982\u679c\u5df2\u7ecf\u6709\u5b58\u5728\u7684\u53d8\u91cf\uff0c\u8fdb\u884c\u91ca\u653e\u907f\u514d\u51fa\u73b0\u5185\u5b58\u51b2\u7a81\ntry:\n del X_train, y_train\n del X_test, y_test\n print('Clear previously loaded data.')\nexcept:\n pass\n\n# \u8bfb\u5165\u6570\u636e\nX_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)\n\n# \u89c2\u5bdf\u6570\u7ec4\u7684\u6784\u6210\uff0c\u6765\u68c0\u6d4b\u6211\u4eec\u662f\u5426\u5f97\u5230\u4e86\u6b63\u786e\u7684\u6570\u636e\u3002\u8fd9\u662f\u4e00\u4e2a\u7ecf\u5178\u7b80\u5355\u4e14\u6709\u6548\u7684\u68c0\u67e5\u65b9\u5f0f\u3002\nprint('Training data shape: ', X_train.shape)\nprint('Training labels shape: ', y_train.shape)\nprint('Test data shape: ', X_test.shape)\nprint('Test labels shape: ', y_test.shape)\n\u2003\u2003\u6211\u4eec\u89c2\u5bdf\u4e0a\u9762\u7684\u56db\u4e2aprint\uff0c\u5b83\u4eec\u662f\u4ece\u89c2\u5bdf\u6574\u4e2a\u6570\u7ec4\u6784\u6210\u6765\u770b\u56fe\u50cf\u8bfb\u5165\u662f\u5426\u6b63\u786e\uff0c\u6211\u4eec\u540c\u6837\u53ef\u4ee5\u7528\u66f4\u76f4\u89c2\u7684\u65b9\u5f0f\u6765\u5224\u65ad\u8bfb\u5165\u662f\u5426\u6b63\u786e\u3002
"},{"location":"ScientificResearch/CS231N/A1L1/#_2","title":"\u67e5\u770b\u8bfb\u5165\u7684\u56fe\u7247","text":"knn.ipynb# Visualize some examples from the dataset.\n# We show a few examples of training images from each class.\nclasses = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']\nnum_classes = len(classes)\nsamples_per_class = 7\nfor y, cls in enumerate(classes):\n idxs = np.flatnonzero(y_train == y)\n idxs = np.random.choice(idxs, samples_per_class, replace=False)\n for i, idx in enumerate(idxs):\n plt_idx = i * num_classes + y + 1\n plt.subplot(samples_per_class, num_classes, plt_idx)\n plt.imshow(X_train[idx].astype('uint8'))\n plt.axis('off')\n if i == 0:\n plt.title(cls)\nplt.show()\n\u8bad\u7ec3\u6a21\u578b \u2003\u2003\u56fe\u50cf\u7684\u8bc6\u522b\u4e0d\u662f\u51ed\u7a7a\u8fdb\u884c\u7684\uff0c\u5c31\u50cf\u8ba1\u7b97\u673a\u7684\u7b97\u6cd5\u6d41\u7a0b\u4e00\u6837\uff0c\u56fe\u50cf\u4f5c\u4e3a\u7b97\u6cd5\u7684\u8f93\u5165\uff0c\u7c7b\u522b\u4f5c\u4e3a\u7b97\u6cd5\u7684\u8f93\u51fa\uff0c\u6574\u4e2a\u7b97\u6cd5\u672c\u8eab\u8fd9\u4e2a\u9ed1\u7bb1\u5c31\u662f\u6211\u4eec\u9700\u8981\u8bad\u7ec3\u7684\u4e1c\u897f\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u4e00\u4e2a\u6a21\u578b\uff0c\u8ba9\u5b83\u7684\u8f93\u5165\u8f93\u51fa\u6620\u5c04\u5173\u7cfb\u548c\u56fe\u50cf\u8bc6\u522b\u8fc7\u7a0b\u76f8\u543b\u5408\u3002
\u9884\u6d4b\u56fe\u50cf \u2003\u2003\u6267\u884c\u9884\u6d4b\u56fe\u50cf\u7684\u8fc7\u7a0b\uff0c\u5c31\u662f\u4f7f\u7528\u6211\u4eec\u627e\u5230\u7684\u6a21\u578b\uff0c\u8fdb\u884c\u8f93\u5165\u3001\u5904\u7406\u548c\u8f93\u51fa\u7684\u8fc7\u7a0b\u3002\u5c31\u50cf\u54c8\u5e0c\u7b97\u6cd5\u628a\u539f\u6570\u636e\u5904\u7406\u6210\u54c8\u5e0c\u503c\u4e00\u6837\uff0c\u901a\u8fc7\u6a21\u578b\uff0c\u539f\u56fe\u50cf\u7684\u50cf\u7d20\u9635\u5217\u7ecf\u8fc7\u8ba1\u7b97\u53d8\u6210\u4e00\u4e9b\u5206\u6570\u503c\uff0c\u7136\u540e\u6211\u4eec\u901a\u8fc7\u6bd4\u8f83\u6bcf\u4e2a\u7c7b\u578b\u7684\u5f97\u5206\u6765\u8bc4\u4ef7\u8fd9\u4e2a\u56fe\u50cf\u5e94\u8be5\u5c5e\u4e8e\u54ea\u4e2a\u7c7b\u522b\u3002
\u4e00\u70b9\u8054\u60f3
\u2003\u2003\u8fd9\u5176\u5b9e\u5f88\u6709\u610f\u601d\uff0c\u5c31\u50cf\u5b66\u6821\u7ed9\u6211\u4eec\u5206\u53d1\u6d4b\u8bd5\u8bd5\u5377\u3001\u6539\u5377\u6253\u5206\u6765\u7ed9\u6211\u4eec\u8bc4\u4ef7\u5b66\u4e60\u6c34\u5e73\u4e00\u6837\uff0c\u6211\u4eec\u7efc\u5408\u673a\u5668\u6bcf\u4e00\u5757\u50cf\u7d20\uff0c\u7ed9\u5b83\u4eec\u6765\u6253\u5206\uff0c\u6700\u540e\u5f97\u51fa\u5b83\u5e94\u8be5\u5c5e\u4e8e\u54ea\u4e00\u4e2a\u7c7b\u522b\u3002\u5c31\u50cf\u4f60\u653f\u6cbb\u8003\u4e8690\u5206\uff0c\u800c\u7269\u7406\u53ea\u670960\u5206\uff0c\u4f60\u4f1a\u4e0b\u610f\u8bc6\u5224\u65ad\u4f60\u9002\u5408\u5b66\u6587\u79d1\u800c\u4e0d\u9002\u5408\u5b66\u7406\u79d1\u3002 \u2003\u2003\u4f46\u662f\uff0c\u6211\u4eec\u90fd\u77e5\u9053\u8fd9\u53ea\u662f\u4e00\u4e2a\u6982\u7387\u5224\u65ad\u3002\u5f71\u54cd\u8003\u8bd5\u5206\u6570\u7684\u56e0\u7d20\u592a\u591a\u4e86\uff0c\u6211\u4eec\u4e0d\u4f1a\u901a\u8fc7\u4ec5\u4ec5\u4e00\u6b21\u8003\u8bd5\u6765\u51b3\u5b9a\u4e00\u4e2a\u4eba\u662f\u5426\u9002\u5408\u5b66\u4e60\u6587\u79d1\u6216\u8005\u5b66\u4e60\u7406\u79d1\u3002\u5bf9\u56fe\u50cf\u4e5f\u4e00\u6837\uff0c\u5f53\u56fe\u50cf\u5bf9\u4e8e\u201c\u732b\u201d\u5f97\u5206\u6700\u9ad8\u7684\u65f6\u5019\uff0c\u5b83\u5927\u6982\u7387\u662f\u732b\uff0c\u4f46\u662f\u8fd9\u5fc5\u7136\u662f\u4e0d\u80fd\u767e\u5206\u767e\u5730\u786e\u5b9a\u7684\u3002 \u2003\u2003\u5c3d\u7ba1\u5982\u6b64\uff0c\u4f46\u5c31\u50cf\u7269\u7406\u6a21\u578b\u4e2d\u4f7f\u7528\u4e86\u975e\u5e38\u591a\u7684\u4e00\u9636\u8fd1\u4f3c\u4e5f\u80fd\u51c6\u786e\u9884\u6d4b\u81ea\u7136\u754c\u7684\u53d8\u5316\uff0c\u5bf9\u4e8e\u673a\u5668\uff0c\u4e5f\u53ef\u4ee5\u6709\u8fd9\u6837\u7684\u8bef\u5dee\u548c\u8fd1\u4f3c\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5f00\u53d1\u8bad\u7ec3\u543b\u5408\u7387\u66f4\u9ad8\u7684\u6a21\u578b\uff0c\u8fd9\u6837\u8ba9\u9519\u8bef\u964d\u5230\u53ef\u4ee5\u5bb9\u8bb8\u7684\u8303\u56f4\uff0c\u8ba9\u5b83\u505a\u51fa\u9ad8\u6982\u7387\u7684\u9884\u6d4b\uff0c\u8fd9\u6837\u8fd9\u4e2a\u6a21\u578b\u5c31\u6bd4\u8f83\u53ef\u4fe1\u4e86\u3002\u8bf4\u4e0d\u5b9a\u6709\u4e00\u5929\uff0c\u673a\u5668\u53ef\u4ee5\u505a\u5230\u6bd4\u4eba\u773c\u8bc6\u522b\u66f4\u7cbe\u51c6\u3002
"},{"location":"ScientificResearch/CS231N/L2/#l1","title":"L1\u8ddd\u79bb\uff08\u66fc\u54c8\u987f\u8ddd\u79bb\uff09","text":"\u2003\u2003\u6211\u4eec\u521a\u521a\u8bb2\u5230\uff0c\u5bf9\u56fe\u50cf\u8fdb\u884c\u5206\u7c7b\uff0c\u6700\u91cd\u8981\u7684\u662f\u5bf9\u56fe\u50cf\u786e\u5b9a\u4e00\u4e2a\u201c\u6253\u5206\u6807\u51c6\u201d\uff0c\u5f97\u5230\u8fd9\u4e2a\u56fe\u50cf\u5728\u6bcf\u4e00\u4e2a\u5206\u7c7b\u7684\u5206\u6570\uff0c\u65b9\u4fbf\u540e\u7eed\u7684\u9009\u62e9\u3002L1\u8ddd\u79bb\u5c31\u662f\u4e00\u4e2a\u7ecf\u5178\u7684\u6253\u5206\u6807\u51c6\u3002
L1\u8ddd\u79bb\u516c\u5f0f\uff1a $$ L_1 = \\sum_{p_{ij} \\in img}{|p_{ij}-q_{ij}|},q_{ij} = \\text{constant} $$
\u2003\u2003\u5728\u4e0a\u9762\u7684\u516c\u5f0f\u4e2d\uff0c\\(q\\)\u662f\u6211\u4eec\u9884\u5148\u8bbe\u7f6e\u597d\u7684\u5e38\u6570\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u5df2\u77e5\u7684\u56fe\u50cf\uff0c\u6211\u4eec\u77e5\u9053\u8fd9\u4e2a\u56fe\u50cf\u5bf9\u5e94\u7740\u4ec0\u4e48\uff0c\u800cL1\u8ddd\u79bb\u5c31\u662f\u628a\u73b0\u5728\u6d4b\u8bd5\u7684\u56fe\u50cf\u548c\u5df2\u77e5\u56fe\u50cf\u7684\u50cf\u7d20\u503c\u4e00\u4e00\u5bf9\u5e94\u76f8\u51cf\uff0c\u7136\u540e\u8fdb\u884c\u6c42\u548c\uff0c\u5c31\u50cf\u4e0b\u9762\u8fd9\u4e2a\u56fe\u663e\u793a\u7684\u4e00\u6837\u3002
\u2003\u2003\u6211\u4eec\u628a\u8fd9\u4e2a\u8ba1\u7b97\u51fa\u6765\u7684\u4e1c\u897f\u53eb\u505a\u201c\u8ddd\u79bb\u201d\uff0c\u662f\u56e0\u4e3a\u5b83\u4ece\u67d0\u79cd\u89d2\u5ea6\u4e0a\u786e\u5b9e\u53cd\u6620\u4e86\u6d4b\u8bd5\u56fe\u50cf\u548c\u5df2\u77e5\u56fe\u50cf\u7684\u5dee\u5f02\uff0c\u4ece\u62bd\u8c61\u7684\u89d2\u5ea6\u6765\u770b\u5c31\u662f\u4e00\u79cd\u8ddd\u79bb\uff0c\u800c\u4e14\u5b83\u7b26\u5408\u5dee\u5f02\u8d8a\u5927\uff0c\u8ddd\u79bb\u8d8a\u8fdc\u7684\u76f4\u89c2\u3002
"},{"location":"ScientificResearch/CS231N/L2/#_3","title":"\u6a21\u578b\u8bad\u7ec3\u2014\u2014\u8ddd\u79bb\u77e9\u9635","text":"\u2003\u2003\u56e0\u6b64\uff0c\u53ef\u4ee5\u8bbe\u60f3\uff0c\u5982\u679c\u6211\u4eec\u624b\u5934\u6709\\(N\\)\u4e2a\u5df2\u77e5\u7684\u5bf9\u8c61\uff0c\u540c\u65f6\u6709\\(M\\)\u4e2a\u9700\u8981\u9a8c\u8bc1\u7684\u56fe\u50cf\uff0c\u6211\u4eec\u4e00\u4e00\u8ba1\u7b97\u5b83\u4eec\u4e4b\u95f4\u8ddd\u79bb\uff0c\u4e8e\u662f\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a \\(M\\)\u884c\\(N\\)\u5217\u7684\u77e9\u9635\uff0c\u6211\u4eec\u5c06\u5b83\u79f0\u4f5c\u8ddd\u79bb\u77e9\u9635\uff08distance matrix\uff09\uff0c\u901a\u8fc7\u6bd4\u8f83\u6bcf\u4e00\u884c\u7684\u8ddd\u79bb\uff0c\u5c31\u53ef\u4ee5\u5f97\u51fa\u6bcf\u4e00\u4e2a\u9a8c\u8bc1\u56fe\u50cf\u7684\u9884\u6d4b\u7c7b\u578b\u3002
"},{"location":"ScientificResearch/CS231N/L2/#nn","title":"\u6700\u8fd1\u90bb\u5c45\u7b97\u6cd5(NN)","text":"\u2003\u2003\u6839\u636e\u76f4\u89c2\u611f\u53d7\uff0c\u6211\u4eec\u4e0d\u59a8\u505a\u51fa\u8fd9\u6837\u7684\u7ed3\u8bba\uff0c\u6211\u4eec\u8ba4\u4e3a\u5982\u679c\u4e24\u4e2a\u56fe\u50cf\u7684L1\u8ddd\u79bb\u8d8a\u5c0f\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u56fe\u50cf\u5c31\u8d8a\u76f8\u4f3c\u3002\u5bf9\u4e8e\u6d4b\u8bd5\u56fe\u50cf\uff0c\u6211\u4eec\u8ba1\u7b97\u5b83\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5df2\u77e5\u56fe\u50cf\u7684\u5df2\u6709\u8ddd\u79bb\uff0c\u770b\u770b\u5b83\u548c\u8c01\u8d70\u5f97\u66f4\u8fd1\uff0c\u5c31\u8ddf\u8c01\u5f52\u4e3a\u540c\u4e00\u7c7b\u2014\u2014\u8fd9\u5c31\u662f\u6700\u8fd1\u90bb\u5c45\uff08Nearest Neighbour\uff09\u7b97\u6cd5\u3002
NN.pyimport numpy as np\n\nclass NearestNeighbour:\n def __init__(self):\n pass\n\n def train(self,X,y):\n \"\"\" \u6ce8\u610f\uff0c\u6211\u4eec\u4e3a\u4e86\u5b58\u50a8\u7684\u65b9\u4fbf\uff0c\u628a\u56fe\u50cf\u7684\u6bcf\u4e00\u884c\u62fc\u63a5\u8d77\u6765\uff0c\u8fd9\u6837\u5c31\u628a\u4e8c\u7ef4\u7684\u56fe\u50cf\u6570\u636e\u8f6c\u5316\u6210\u4e86\u4e00\u7ef4\u6765\u5b58\u50a8\u3002 \"\"\"\n # X\u662f\u4e00\u4e2aM\u884cN\u5217\u7684\u4e8c\u7ef4\u6570\u7ec4\uff0cM\u4ee3\u8868\u5df2\u77e5\u56fe\u7684\u4e2a\u6570\uff0cN\u4ee3\u8868\u6bcf\u4e2a\u56fe\u7684\u5927\u5c0f \n # y\u662f\u4e00\u4e2a\u5927\u5c0f\u4e3aM\u7684\u4e00\u7ef4\u6570\u7ec4\uff0c\u5b58\u50a8\u7684\u662f\u6bcf\u4e00\u4e2a\u56fe\u50cf\u6240\u5bf9\u5e94\u7684\u7c7b\u522b\n self.Xtr = X\n self.ytr = y\n\n def predict(self,X):\n # \u6b64\u5904X\u662f\u4e00\u4e2aK\u884cN\u5217\u7684\u4e8c\u7ef4\u6570\u7ec4\uff0cK\u4ee3\u8868\u9700\u8981\u6d4b\u8bd5\u56fe\u50cf\u7684\u4e2a\u6570\uff0cN\u4ee3\u8868\u6bcf\u4e2a\u56fe\u7684\u5927\u5c0f\uff0c\u8fd9\u4e2aN\u5fc5\u987b\u548cXtr\u4e2d\u7684N\u5339\u914d\n num_test = X.shape[0]\n Ypred = np.zeros(num_test, dtype = self.ytr.dtype) # \u521d\u59cb\u5316\u7c7b\u578b\n\n for i in xrange(num_test):\n # \u8ba1\u7b97 L1\u8ddd\u79bb\u77e9\u9635\n distances = np.sum(np.abs(self.Xtr - X[i,:]), axis = 1)\n # \u5bfb\u627e\u8ddd\u79bb\u6700\u5c0f\u5bf9\u5e94\u56fe\u50cf\u7684\u4e0b\u6807\n min_index = np.argmin(distances)\n # \u4e0b\u6807\u6620\u5c04\u627e\u5230\u5bf9\u5e94\u5206\u7c7b\n Ypred[i] = self.ytr[min_index]\n\n return Yred\n \u4e00. \u7b2c16\u884c\u7684 X.shape[0] \u662f\u4ec0\u4e48\u610f\u601d\uff1f X.shape\u662f\u4e00\u4e2anumpy\u7684\u51fd\u6570\uff0c\u5176\u4e2dX.shape[N]\u4ee3\u8868\u7684\u662f\u8bfb\u53d6\u53d8\u91cfX\u7b2cN-1\u4e2a\u7ef4\u5ea6\u7684\u5927\u5c0f\uff0c\u8fd9\u91cc\u7684X.shape[0]\u5c31\u662f\u8bfb\u53d6\u884c\u6570\uff0c\u5982\u679c\u662fX.shape[1]\u8bfb\u53d6\u7684\u5c31\u662f\u5217\u6570\u3002 \u2003\u2003\u66f4\u8fdb\u4e00\u6b65\u5730\uff0c\u5982\u679c\u62d3\u5c55\u5230\u66f4\u9ad8\u7ef4\u5ea6\u7684\u60c5\u51b5\uff08\u6211\u4eec\u5f88\u591a\u65f6\u5019\u90fd\u4f1a\u4f7f\u7528\u591a\u7ef4\u6570\u7ec4\uff09\uff0c.shape[]\u51fd\u6570\u5c31\u4f1a\u975e\u5e38\u65b9\u4fbf\u3002\u6bd4\u5982\u5bf9\u4e8e\u4e00\u4e2anumpy\u7684array\u53d8\u91cf\uff0c\u5982\u679c\u5b83\u662f\u4e00\u4e2a\u7c7b\u4f3cX[A][B][C][D]\u56db\u7ef4\u6570\u7ec4\uff0c\u7531\u4e8epython\u5bf9\u89c4\u5b9a\u53d8\u91cf\u7684\u6a21\u7cca\u5316\uff0c\u6211\u4eec\u4e0d\u77e5\u9053ABCD\u7684\u5177\u4f53\u503c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u904d\u5386X.shape[0] ~ X.shape[3] \u6765\u5f97\u5230 A ~ D\u3002\u7279\u6b8a\u5730\uff0c\u5c31\u50cf-1\u5728\u6570\u7ec4\u4e2d\u7684\u4f7f\u7528\u4e00\u6837\uff0c\u5982\u679c\u6211\u4eec\u4f7f\u7528X.shape[-1]\uff0c\u5b83\u4f1a\u8fd4\u56de\u6700\u540e\u4e00\u4e2a\u7ef4\u5ea6\u7684\u5927\u5c0f\uff0c\u4e5f\u5c31\u662fX.shape[3]\u3002 \u4e8c\u3001\u7b2c17\u884c\u7684np.zeros()\u7528\u6765\u505a\u4ec0\u4e48\uff1f \u2003\u2003\u5c31\u50cf\u6211\u4eec\u5728C\u8bed\u8a00\u4e2d\u9700\u8981\u5b9a\u4e49\u53d8\u91cf\u5e76\u4e14\u8d4b\u521d\u503c\u4e00\u6837\uff0c\u5728python\u4e2d\u6211\u4eec\u540c\u65f6\u9700\u8981\u8fd9\u6837\u505a\uff0c\u4f46\u662fpython\u4f1a\u901a\u8fc7\u4f60\u8d4b\u7684\u503c\u6765\u81ea\u52a8\u4e3a\u53d8\u91cf\u5224\u65ad\u7c7b\u578b\uff0c\u6240\u4ee5\u7b80\u5316\u4e86\u53d8\u91cf\u7684\u5b9a\u4e49\u6b65\u9aa4\u3002array\u662fnumpy\u5e93\u4e2d\u7684\u4e00\u4e2a\u975e\u5e38\u7075\u6d3b\u7684\u53d8\u91cf\u683c\u5f0f\uff0c\u901a\u8fc7array\u4ee5\u53ca\u5b83\u9644\u5e26\u7684\u4e00\u4e9b\u51fd\u6570\uff0c\u53ef\u4ee5\u5224\u65ad\u6574\u4e2a\u6570\u7ec4\u7684\u7ef4\u5ea6\u3001\u5927\u5c0f\uff0c\u751a\u81f3\u53ef\u4ee5\u505a\u5c40\u90e8\u6c42\u548c\u3001\u8f6c\u7f6e\u3001\u77e9\u9635\u4e58\u6cd5\u7b49\u7b49\uff0c\u800c\u5bf9array\u8d4b\u521d\u503c\u5c31\u53ef\u4ee5\u4f7f\u7528np.zeros(tuple,type)\u5f97\u5230\u4e00\u4e2a\u786e\u5b9a\u5927\u5c0f\u7684\u3001\u6574\u4f53\u7684\u8d4b\u96f6\u6570\u7ec4\u3002tuple\u4ee3\u8868\u7684\u662f\u6574\u4e2aarray\u7684\u5f62\u72b6\uff0c\u6bd4\u5982(5,2,3)\u5f97\u51fa\u6765\u7684\u5c31\u662f\u6570\u7ec4a[5][2][3]\uff0ctype\u5c31\u662f\u6570\u7ec4\u7684\u6570\u636e\u7c7b\u578b\u3002 \u4e09\u3001\u7b2c21\u884c\u7684X[i, :]\u662f\u4ec0\u4e48\u610f\u601d\uff1f \u2003\u2003\u8fd9\u662fpython\u4e2d\u7684\u4e00\u79cd\u7701\u7565\u5f62\u5f0f\uff0c\u9996\u5148\uff0c\u5bf9\u4e8e\u7b26\u53f7:\u672c\u8eab\uff0c\u5b83\u672c\u8eab\u4ee3\u8868\u8303\u56f4\u7684\u9009\u53d6\uff0c\u6bd4\u5982[2:5]\u9009\u53d6\u7684\u5c31\u662f [2]\u3001[3]\u548c[4]\uff0c\u5373\\([2,5)\\)\u533a\u95f4\u7684\u6240\u6709\u6574\u6570\u53f7\u3002\u800c\u5982\u679c\u628a\u524d\u9762\u76842\u7701\u53bb\uff0c\u5219\u9ed8\u8ba4\u4ece\u4e0b\u68070\u5f00\u59cb\uff0c\u5982\u679c\u540e\u9762\u76845\u88ab\u7701\u53bb\uff0c\u5219\u9ed8\u8ba4\u5728\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u7ed3\u675f\u3002\u56e0\u6b64\uff0c\u5f53\u7b2c\u4e8c\u7ef4\u5ea6\u4ec5\u6709:\u65f6\uff0c\u524d\u540e\u6570\u5b57\u90fd\u88ab\u7701\u53bb\uff0c\u56e0\u6b64\u8fd9\u4e2a\u9009\u53d6\u662f\u4ece0\u5230\u6700\u540e\u4e00\u4e2a\u5143\u7d20\uff0c\u56e0\u6b64\u662f\u9009\u4e2d\u4e86\u4e00\u6574\u884c\u3002 \u4e09\u3001\u7b2c21\u884c\u7684axis = 1\u662f\u4ec0\u4e48\u610f\u601d\uff1f axis\u662fnp.sum()\u4e2d\u7684\u4e00\u4e2a\u53c2\u6570\uff0c\u800c\u51fd\u6570np.sum()\u662f\u628a\u6570\u7ec4\u7684\u67d0\u51e0\u4e2a\u7ef4\u5ea6\u7684\u6570\u5b57\u5168\u90e8\u52a0\u8d77\u6765\uff0c\u50cf\u662f\u505a\u4e00\u4e9b\u6295\u5f71\u64cd\u4f5c\uff0c\u628a\u6574\u4e2a\u6570\u7ec4\u964d\u4e86\u82e5\u5e72\u4e2a\u7ef4\u5ea6\u3002\u8fd9\u4e2aaxis\u5c31\u662f\u5bf9\u5e94\u7684\u7ef4\u5ea6\u3002\u6bd4\u5982\u6709\u4e09\u7ef4\u6570\u7ec4\uff0c\u6211\u4eec\u60f3\u8981\u628a\u5b83\u7684\u6700\u540e\u4e00\u4e2a\u4e2a\u7ef4\u5ea6\u5168\u90e8\u52a0\u8d77\u6765\uff0c\u5c31\u53ef\u4ee5\u8bbe\u7f6e\u53c2\u6570axis = -1\u3002\u5728\u8fd9\u4e2a\u4f8b\u7a0b\u4e2d\uff0c\u628aaxis\u8bbe\u7f6e\u4e3a1\uff0c\u8fd9\u610f\u5473\u7740\u6c42\u548c\u5c06\u5728\u5e8f\u53f71\u7684\u7ef4\u5ea6\u8fdb\u884c\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e2a\u4e8c\u7ef4\u6570\u7ec4\u7684\u6bcf\u4e00\u884c\u8fdb\u884c\u6c42\u548c\u3002
\u2003\u2003\u76f4\u63a5\u5730\u628a\u5404\u4e2a\u50cf\u7d20\u7684\u5dee\u8ddd\u76f8\u52a0\u4f3c\u4e4e\u8fdd\u80cc\u6211\u4eec\u5bf9\u8ddd\u79bb\u7684\u8ba4\u8bc6\uff0c\u5c31\u50cf\u6211\u5411\u4e1c\u8d70\u4e86100\u7c73\uff0c\u5411\u5317\u8d70\u4e86100\u7c73\uff0c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u6211\u4eec\u8d70\u5230\u4e86\u8ddd\u79bb\u539f\u70b9200\u7c73\u7684\u5730\u65b9\u3002\u56e0\u6b64\uff0cL2\u8ddd\u79bb\u8fd0\u7528\u4e86\u6b27\u6c0f\u7a7a\u95f4\u7684\u523b\u753b\uff0c\u5c06\u6bcf\u4e00\u4e2a\u50cf\u7d20\u770b\u4f5c\u4e00\u4e2a\u7ef4\u5ea6\uff0c\u7136\u540e\u8ba1\u7b97\u591a\u7ef4\u7a7a\u95f4\u4e2d\u7684\u8ddd\u79bb\u3002
L2\u8ddd\u79bb\u516c\u5f0f\uff1a
\\[ L_2 = \\sqrt{\\sum_{p_{ij} \\in img}(p_{ij} - q_{ij})^2}, q_{ij} = \\text{constant} \\]L2\u8ddd\u79bb\u548c\u8fd0\u884c\u4f18\u5316
\u56e0\u4e3aL2\u8ddd\u79bb\u7684\u516c\u5f0f\u7279\u6027\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u901a\u8fc7\u4e00\u5b9a\u7684\u62c6\u5206\uff0c\u53ef\u4ee5\u5927\u5927\u4f18\u5316\u7a0b\u5e8f\u7684\u8fd0\u884c\u901f\u5ea6\u3002\u67e5\u770b\u5177\u4f53\u4f18\u5316
"},{"location":"ScientificResearch/CS231N/L2/#kknn","title":"\u524dK\u6700\u8fd1\u90bb\u5c45\u7b97\u6cd5\uff08KNN\uff09","text":"\u2003\u2003\u5728\u5148\u524d\u7684\u6700\u8fd1\u90bb\u5c45\u7b97\u6cd5\u4e2d\uff0c\u6211\u4eec\u76f4\u63a5\u91c7\u7528\u6700\u8fd1\u7684\u90bb\u5c45\u4f5c\u4e3a\u6211\u4eec\u56fe\u50cf\u7684\u5206\u7c7b\u4f9d\u636e\u3002\u8fd9\u5f88\u65b9\u4fbf\uff0c\u4f46\u662f\u5b83\u5bf9\u4e8e\u4e00\u4e9b\u8fb9\u754c\u60c5\u51b5\u7684\u5224\u65ad\u662f\u975e\u5e38\u7cdf\u7cd5\u7684\u3002\u6bd4\u5982\uff0c\u5982\u679c\u6211\u4eec\u7528\u4e8c\u7ef4\u5e73\u9762\u7684\u683c\u70b9\u6765\u8868\u793a\u5df2\u77e5\u7684\u70b9\uff0c\u5e76\u7528\u989c\u8272\u6765\u8868\u793a\u5b83\u4eec\u7684\u7c7b\u578b\uff0c\u800c\u8ba9\u70b9\u4e0e\u70b9\u95f4\u7684\u8ddd\u79bb\u6765\u8868\u793a\u56fe\u50cf\u95f4\u7684\u8ddd\u79bb\uff08\u8fd9\u6837\u7684\u8868\u793a\u5e76\u4e0d\u5b8c\u5168\u5408\u9002\uff0c\u4f46\u662f\u81f3\u5c11\u53ef\u4ee5\u8bf4\u660e\u95ee\u9898\uff09\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u5982\u4e0b\u7684\u56fe\uff1a
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\u6570\u636e\u5b9a\u4e49\u8bed\u8a00\u7684\u4f8b\u5b50
CREATE TABLE instructor (\n ID char(5),\n name varchar(20),\n dept_name varchar(20),\n salary numeric(8,2),\n PRIMARY KEY (ID),\n FOREIGN KEY (dept_name) REFERENCES department(name)\n);\n\u2003\u2003\u7136\u800c\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u6570\u636e\u5b9a\u4e49\u8bed\u8a00\u7684\u7ed3\u6784\u548cC\u8bed\u8a00\u4e2d\u7684struct\u6709\u6240\u533a\u522b\uff0cC\u8bed\u8a00\u7684struct\u5728\u7ecf\u8fc7\u94fe\u63a5\u540e\u4f1a\u76f4\u63a5\u628a\u7b26\u53f7\u8868\u4e22\u5f03\uff0c\u7528\u6307\u9488\u6765\u4ee3\u66ff\uff0c\u4f46\u662f\u6570\u636e\u5e93\u7cfb\u7edf\u4e0d\u4f1a\u4e22\u5f03\u8fd9\u4e9b\u8868\u683c\u6a21\u677f\uff0c\u800c\u4f1a\u5b9e\u5b9e\u5728\u5728\u5730\u628a\u5b83\u4eec\u4f5c\u4e3a\u4e00\u79cd\u6570\u636e\u5b58\u50a8\u4e0b\u6765\uff0c\u8fd9\u79cd\u6570\u636e\u5c31\u53eb\u5143\u6570\u636e\u3002
\u6a21\u5f0f
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"},{"location":"Classnote/Database-System/termsintro/#_21","title":"\u6570\u636e\u64cd\u4f5c\u8bed\u8a00","text":"\u2003\u2003\u6570\u636e\u64cd\u4f5c\u8bed\u8a00\uff0c\u4e5f\u5c31\u662f\u67e5\u8be2\u8bed\u8a00\uff0c\u662f\u7528\u4e8e\u67e5\u627e\u548c\u64cd\u4f5c\u6570\u636e\u5e93\u4e2d\u7684\u6570\u636e\u7684\u8bed\u8a00\u3002\u5176\u4e2d\uff0c\u4f7f\u7528\u7684\u6700\u4e3a\u5e7f\u6cdb\u7684\u5c31\u662f\u7ed3\u6784\u5316\u67e5\u8be2\u8bed\u8a00\uff08SQL\uff09\u3002
SQL\u548c\u4f20\u7edf\u7f16\u7a0b\u8bed\u8a00\u7684\u533a\u522b
\u2003\u2003\u6211\u4eec\u4e4b\u524d\u5b66\u8fc7\u7684c\uff0cpython\uff0cjava\u7b49\u7f16\u7a0b\u8bed\u8a00\uff0c\u5b9e\u9645\u4e0a\u662f\u6309\u7167\u4e00\u4e2a\u6d41\u7a0b\u6765\u8fdb\u884c\u7f16\u7a0b\u7684\uff0c\u8fd9\u7c7b\u7f16\u7a0b\u8bed\u8a00\u88ab\u6210\u4e3a\u8fc7\u7a0b\u5f0f\u7684\u3002SQL\u4e0d\u540c\uff0c\u5b83\u7684\u8bed\u53e5\u6bd4\u8f83\u7b80\u5355\u7cbe\u70bc\uff0c\u5c31\u50cf\u8bf4\u4e00\u53e5\u8bdd\uff0c\u800c\u4e0d\u50cf\u5199\u4e00\u6bb5\u7a0b\u5e8f\u3002\u8fd9\u7c7b\u7f16\u7a0b\u8bed\u8a00\u88ab\u79f0\u4f5c\u9648\u8ff0\u5f0f\uff08\u975e\u8fc7\u7a0b\u5f0f\uff09\u8bed\u8a00\u3002
SQL\u7684\u4f8b\u5b50
select name\n from instructor\n where instructor.ID = '10129';\n select instructor.ID, department.building\n from instructor, department\n where instructor.dept_name = department.dept_name and department.dept_name = 'Physics';\n\u2003\u2003\u4f46\u662f\uff0c\u6211\u4eec\u53d1\u73b0\u8fd9\u79cd\u8bed\u53e5\u7684\u7528\u9014\u975e\u5e38\u6709\u9650\uff0c\u5b83\u4e0d\u80fd\u591f\u50cf\u6d41\u6c34\u7ebf\u4e00\u6837\u4e3a\u6211\u4eec\u5b9e\u73b0\u81ea\u52a8\u5316\uff0c\u5904\u7406\u8f93\u5165\u8f93\u51fa\u3002\u6240\u4ee5\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u4f1a\u628a\u6570\u636e\u64cd\u4f5c\u8bed\u8a00\u548c\u4f20\u7edf\u7684\u8fc7\u7a0b\u5f0f\u8bed\u8a00\u7ed3\u5408\u8d77\u6765\uff0c\u4f7f\u7528SQL\u6765\u4ece\u6570\u636e\u5e93\u4e2d\u8bfb\u53d6\u6570\u636e\uff0c\u7136\u540e\u4f7f\u7528C/C++,Python,Java\u6765\u5904\u7406\u6570\u636e\u3002\u540e\u8005\u88ab\u79f0\u4f5c\u5bbf\u4e3b\u8bed\u8a00\u3002
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"},{"location":"Classnote/Database-System/termsintro/#_22","title":"\u6570\u636e\u5e93\u8bbe\u8ba1","text":"\u2003\u2003\u641e\u6e05\u695a\u4e86\u6574\u4e2a\u6570\u636e\u5e93\u7684\u7ed3\u6784\u548c\u64cd\u4f5c\u65b9\u5f0f\u4e4b\u540e\uff0c\u6211\u4eec\u4ece\u7528\u6237\u548c\u5f00\u53d1\u8005\u7684\u89c6\u89d2\u4e86\u89e3\u4e86\u6570\u636e\u5e93\uff0c\u7136\u800c\u8fd9\u662f\u4e0d\u591f\u7684\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u7ad9\u5728\u4e00\u4e2a\u8bbe\u8ba1\u8005\u7684\u89d2\u5ea6\u53bb\u5b66\u4e60\u6570\u636e\u5e93\u7684\u8bbe\u8ba1\u65b9\u5f0f\u3002
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\u2003\u20031961\u5e74\uff0c\u6570\u636e\u5e93\u4e4b\u7236\uff0cCharles W. Bachman\uff0c\u5728\u63d0\u51fa\u4e86\u96c6\u6210\u6570\u636e\u5e93\u7684\u6982\u5ff5\uff0c\u6570\u636e\u5e93\u521d\u5177\u96cf\u5f62\u3002\u4ed6\u56e0\u6b64\u83b7\u5f97\u4e861973\u5e74\u7684\u56fe\u7075\u5956\u3002
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20\u4e16\u7eaa90\u5e74\u4ee3
21\u4e16\u7eaa00\u5e74\u4ee3
\u4ec0\u4e48\u662fNoSQL
\u2003\u2003NoSQL\u4e0d\u662f\u4e00\u4e2a\u5177\u4f53\u7684SQL\u5e94\u7528\uff0c\u800c\u662f\u975e\u5173\u7cfb\u578b\u6570\u636e\u5e93\u7684\u603b\u79f0\u3002\u5b83\u6ca1\u6709\u4f7f\u7528\u4f20\u7edf\u7684\u5173\u7cfb\u578b\u6570\u636e\u6a21\u578b\uff0c\u800c\u662f\u4f7f\u7528\u66f4\u52a0\u81ea\u7531\u7684\u6a21\u578b\uff0c\u6765\u8fbe\u5230\u66f4\u9ad8\u7684\u6269\u5c55\u6027\u548c\u53ef\u7528\u6027\u3002 \u2003\u2003NoSQL\u6570\u636e\u5e93\u591a\u5e94\u7528\u5728\u4ee5\u5927\u6570\u636e\u4e3a\u5178\u578b\u7684\u5927\u91cf\u6570\u636e\u4e0a\uff0c\u56e0\u4e3a\u5b83\u4eec\u6ca1\u6709\u7279\u522b\u7684\u5173\u7cfb\u7ea6\u675f\uff0c\u4e0d\u9700\u8981\u4f7f\u7528\u5173\u7cfb\u578b\u7684\u6570\u636e\u6a21\u578b\u6765\u5b58\u50a8\u3002
\u6559\u5e08\uff1a\u7fc1\u5f66\u7433
\u2003\u2003\u79bb\u6563\u662f\u4e00\u95e8\u548c\u8ba1\u7b97\u673a\u606f\u606f\u76f8\u5173\u7684\u6570\u5b66\u8bfe\uff0c\u8fd9\u95e8\u8bfe\u987e\u540d\u601d\u4e49\uff0c\u9700\u8981\u89e3\u51b3\u4e00\u4e9b\u548c\u8ba1\u7b97\u673a\u76f8\u5173\u7684\u5e94\u7528\u5b9e\u9645\u95ee\u9898\uff0c\u56e0\u6b64\uff0c\u8bfe\u7a0b\u524d\u671f\u6d89\u53ca\u5927\u91cf\u7684\u903b\u8f91\u77e5\u8bc6\uff0c\u6bd4\u5982\u903b\u8f91\u4ee3\u6570\uff0c\u96c6\u5408\u5173\u7cfb\u8bba\uff0c\u8fd9\u4e9b\u5bf9\u5b66\u4e60\u6570\u5b57\u903b\u8f91\u7684\u8bbe\u8ba1\u9887\u6709\u5e2e\u52a9\uff0c\u800c\u5230\u540e\u9762\u4f1a\u6d89\u53ca\u548c\u8ba1\u7b97\u673a\u76f8\u5173\u7684\u7b97\u6cd5\u77e5\u8bc6\uff0c\u6bd4\u5982\u56fe\u8bba\u3001\u7ecf\u5178\u7b97\u6cd5\u548c\u6811\u7b49\uff0c\u901a\u8fc7\u8fd9\u4e00\u90e8\u5206\u7684\u5b66\u4e60\u53ef\u4ee5\u5e2e\u52a9\u7406\u89e3\u540e\u9762\u7684\u7b97\u6cd5\u8bfe\u7a0b\u3002
\u89c2\u524d\u63d0\u9192
\u2003\u2003\u56e0\u4e3a\u79bb\u6563\u6570\u5b66\u57fa\u7840\u77e5\u8bc6\u7684\u7b14\u8bb0\u5728GitHub,CC98\u4ee5\u53ca\u5176\u5b83\u4e2a\u4eba\u7b14\u8bb0\u7f51\u7ad9\u6709\u975e\u5e38\u5145\u5206\u8be6\u5c3d\u7684\u4f53\u7cfb\uff0c\u800c\u7531\u4e8e\u672c\u4eba\u65f6\u95f4\u7cbe\u529b\u6709\u9650\uff0c\u7b14\u8bb0\u53ea\u5173\u6ce8\u6211\u611f\u5174\u8da3\u3001\u6709\u601d\u8003\u7684\u90e8\u5206\uff0c\u4e0d\u5efa\u8bae\u62ff\u6211\u7684\u8fd9\u4efd\u7b14\u8bb0\u6765\u671f\u672b\u8003\u8bd5\u8865\u5929\u3002
\u8bfe\u7a0b\u8bc4\u5206\u4f53\u7cfb\uff1a
\u6210\u7ee9\u53ef\u4ee5\u76f4\u63a5\u7531\u671f\u672b\u8003\u8bd5\u8986\u76d6\u3002
\u4e0d\u8981\u6c42\u5230\u573a\u4e0a\u8bfe\uff0c\u4e0a\u8bfe\u79ef\u6781\u56de\u7b54\u95ee\u9898\u67091-2\u5206\u7684\u603b\u8bc4\u52a0\u5206\u3002
\u4f5c\u4e1a\u7ebf\u4e0b\u4ea4\uff0cDDL\u5728\u7b2c\u4e00\u8282\u4e0a\u8bfe\u524d\uff0c\u76f4\u63a5\u4ea4\u5230\u6559\u5ba4\u3002
"},{"location":"Classnote/Discrete-Mathematics/Casual/","title":"\u7410\u8bb0","text":"\u2003\u2003\u8bb0\u5f55\u4e00\u4e9b\u7410\u788e\u7684\u77e5\u8bc6\u70b9\uff0c\u4e3b\u8981\u662f\u4e0d\u719f\u6089\u7684\u77e5\u8bc6\u70b9\u548c\u6613\u9519\u70b9\u3002
\u5f85\u89e3\u51b3\u7684\u95ee\u9898
For any \u5728\u903b\u8f91\u7ffb\u8bd1\u4e2d\u6709\u6b67\u4e49\uff0c\u56e0\u4e3a\u82f1\u8bed\u4e2dany\u6709\u65f6\u662fsome\u7684\u610f\u601d\u3002
\u600e\u4e48\u628a\u65e0\u5173\u7684\u9879\u4eceQuantifier\u4e2d\u53bb\u9664\uff1a
\u8bb0\u5fc6\u65b9\u6cd5\uff1a\u76f4\u63a5\u62c6\u62ec\u53f7\uff0c\u5bf9\u4e8e\u6700\u540e\u4e24\u4e2a\u5f0f\u5b50\uff0c\u56e0\u4e3a\\(P(x)\\)\u5728\u524d\uff0c\u628a\u63a8\u5bfc\u7b26\u53f7\u8f6c\u6362\u6210\u6790\u53d6\u7684\u65f6\u5019\u8981\u53d6\u53cd\uff0c\u53d6\u53cd\u524d\u7f6e\u4f1a\u5bfc\u81f4\u8c13\u8bcd\u6539\u53d8\u3002
The necessary condition of \\(A\\) is \\(B\\) \u2014\u2014 \\(A \\rightarrow B\\)
\\(A\\) holds only if \\(B\\) holds \u2003\u2003\u2003\u2003\u2003\u2014\u2014 \\(A \\rightarrow B\\)
\u2003\u2003\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u63a8\u51fa\u7b26\u53f7\\(\\rightarrow \\leftarrow \\leftrightarrow\\)\u7684\u4f18\u5148\u7ea7\u8981\u5927\u4e8e\u5408\u53d6\u6790\u53d6\\(\\wedge \\vee\\)\uff0c\u6240\u4ee5\u5728\u8868\u793a\u9690\u542b\u5173\u7cfb\u65f6\uff0c\u5c3d\u91cf\u80fd\u5199\u62ec\u53f7\u5c31\u5199\u62ec\u53f7\u3002\u6bd4\u5982\\((p \\vee q) \\rightarrow r\\)
\u901a\u8fc7\u4e0a\u8ff0\u7684\u8c13\u8bcd\u516c\u5f0f\uff0c\u628a\\(\\forall\\)\u548c\\(\\exists\\)\u63d0\u5230\u6700\u524d\u9762\u3002\u6ce8\u610f\u8c13\u8bcd\u7684\u524d\u540e\u987a\u5e8f\uff0c\u5b9e\u9645\u4e0a\u5e26\u8c13\u8bcd\u7684\u53d8\u91cf\u672c\u8eab\u5c31\u7701\u7565\u4e86\u4e00\u5c42\u62ec\u53f7\u3002\u4f8b\u5982\\(\\exist xP(x) \\rightarrow \\forall yP(y) \\equiv \\forall y\\exist x(P(x) \\rightarrow P(y))\\)
\u8bc1\u4f2a\u53ef\u4ee5\u7528\u53cd\u4f8b\uff0c\u4e0d\u4e00\u5b9a\u786c\u4e0a\u516c\u5f0f\u8f6c\u5316\u3002
\u2003\u2003\u4f60\u8bf4\u5f97\u5bf9\uff0c\u4f46\u662f\u6570\u72ec\u6e38\u620f\u662f\u4e00\u6b3e\u7ecf\u5178\u7684\u6570\u5b57\u903b\u8f91\u6e38\u620f\u3002\u73a9\u5bb6\u9700\u8981\u6839\u636e9x9\u76d8\u9762\u4e0a\u7684\u5df2\u77e5\u6570\u5b57\uff0c\u63a8\u7b97\u51fa\u6240\u6709\u5269\u4f59\u7a7a\u683c\u7684\u6570\u5b57\uff0c\u5e76\u4e14\u6ee1\u8db3\u6bcf\u4e00\u884c\u3001\u6bcf\u4e00\u5217\u3001\u6bcf\u4e00\u4e2a\u7c97\u7ebf\u5bab\u5185\u7684\u6570\u5b57\u5747\u542b1-9\uff0c\u5e76\u4e14\u4e0d\u91cd\u590d\u3002
\u2003\u2003\u6570\u72ec\u6e38\u620f\u5bf9\u903b\u8f91\u7684\u6e05\u6670\u8981\u6c42\u548c\u7b80\u5355\u7684\u6e38\u620f\u89c4\u5b9a\uff0c\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u8054\u7cfb\u5230\u79bb\u6563\u6570\u5b66\u4e2d\u5b66\u4e60\u5230\u7684\u547d\u9898\uff0c\u628a\u903b\u8f91\u7528\u6570\u5b66\u7684\u65b9\u5f0f\u5199\u4e0b\u6765\u3002
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#_1","title":"\u6b65\u9aa4\u4e00 \u2014\u2014 \u5b9a\u4e49\u547d\u9898","text":"\u2003\u2003\u6211\u4eec\u89c4\u5b9a\uff0c\\(p(i,j,n)\\)\u4ee3\u8868\u628a\u6570\u5b57n\u653e\u5728i\u884cj\u5217\u7684\u65b9\u683c\u4e2d\u3002\u5bb9\u6613\u77e5\u9053\\(i\\)\uff0c\\(j\\)\uff0c\\(n\\)\u7684\u53d6\u503c\u603b\u5171\u53ef\u4ee5\u5bfc\u51fa\\(9 \\times 9 \\times 9 = 729\\)\u4e2a\u547d\u9898\u3002
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#_2","title":"\u6b65\u9aa4\u4e8c \u2014\u2014 \u7ffb\u8bd1\u83b7\u80dc\u903b\u8f91","text":"\u2003\u2003\u7531\u4e8e\u83b7\u80dc\u7684\u903b\u8f91\u9700\u8981\u7528\u5230\u547d\u9898\u7684\u6790\u53d6\u3001\u5408\u53d6\u7b49\u64cd\u4f5c\uff0c\u800c\u56e0\u4e3a\u547d\u9898\u8fc7\u591a\uff0c\u6211\u4eec\u9700\u8981\u4e00\u79cd\u7b80\u4fbf\u7684\u8868\u793a\u65b9\u6cd5\u3002
\u89c4\u5b9a\u4e00\uff1a\u591a\u9879\u5408\u53d6\u7b26\u53f7 $$ \\bigwedge_{i=x}^y p(i,j_0,n_0) = p(x,j_0,n_0) \\land p(x+1,j_0,n_0) \\land \\cdots \\land p(y,j_0,n_0) $$
\u89c4\u5b9a\u4e8c\uff1a\u591a\u9879\u6790\u53d6\u7b26\u53f7 $$ \\bigvee_{i=x}^y p(i,j_1,n_1) = p(x,j_1,n_1) \\lor p(x+1,j_1,n_1) \\lor \\cdots \\lor p(y,j_1,n_1) $$
\u2003\u2003\u6839\u636e\u89c4\u5b9a\u4e00\u548c\u89c4\u5b9a\u4e8c\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u51fa\u6570\u72ec\u6e38\u620f\u80dc\u5229\u7684\u903b\u8f91\uff1a
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#1-1-9","title":"1. \u6bcf\u4e00\u884c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002","text":"\u2003\u2003\u5148\u4f7f\u7528Quantifier\u53ef\u4ee5\u7b80\u5355\u5730\u628a\u201c\u6bcf\u4e00\u884c\u201d\u7ffb\u8bd1\u4e3a\\(\\forall i\\)\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u9700\u8981\u77e5\u9053\u600e\u4e48\u63cf\u8ff0\u201c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u201d\u3002
\u2003\u2003\u6211\u4eec\u4e0d\u59a8\u8003\u8651\u679a\u4e3e\u6bcf\u4e00\u4e2a\u6570\u5b57\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u628a\u6761\u4ef6\u8fdb\u4e00\u6b65\u5730\u62d3\u5c55\u6210\u4e3a\u201c\u5bf9\u4e8e1-9\u7684\u4efb\u610f\u4e00\u4e2a\u6570\u5b57\uff0c\u8fd9\u4e2a\u6570\u5b57\u90fd\u5728\u8fd9\u4e00\u884c\u201d\uff0c\u7528\u6570\u5b66\u8bed\u8a00\u63cf\u8ff0\u5373\\(\\forall nP(n)\\)\uff0c\\(P(n)\\)\u8868\u793a\u6570\u5b57\\(n\\)\u5728\u8fd9\u4e00\u884c\u3002
\u2003\u2003\u6700\u540e\uff0c\u6211\u4eec\u53ea\u9700\u8981\u63cf\u8ff0\u600e\u4e48\u8868\u793a\u6570\u5b57\u5728\u8fd9\u4e00\u884c\u3002\u6570\u5b57\u5728\u8fd9\u4e00\u884c\uff0c\u610f\u5473\u7740\u8fd9\u4e2a\u6570\u5b57\u5728\u8fd9\u4e00\u884c\u7684\u67d0\u4e00\u5217\u4e2d\u51fa\u73b0\u8fc7\u81f3\u5c11\u4e00\u6b21\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u628a\u6761\u4ef6\u62c6\u89e3\u4e3a\u201c\u8fd9\u4e2a\u6570\u5b57\u5728\u8fd9\u4e00\u884c\u7684\u67d0\u4e00\u5217\u5b58\u5728\u201d\uff0c\u5373\\(\\exist j \\space p(i_0,n_0,j)\\)\u3002
\u2003\u2003\u4e8e\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e00\u4e2a\u903b\u8f91\u7684\u5b8c\u6574\u7ffb\u8bd1\uff1a
\\[ \\forall i \\forall n \\exist j \\space p(i,j,n) \\\\ \\equiv \\bigwedge_{i=1}^9 \\bigwedge_{n=1}^9 \\bigvee_{j=1}^9 \\space p(i,j,n) \\]"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#2-1-9","title":"2. \u6bcf\u4e00\u5217\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002","text":"\u2003\u2003\u8fd9\u4e2a\u903b\u8f91\u7684\u7ffb\u8bd1\u4e0e\u4e0a\u9762\u7c7b\u4f3c\uff0c\u8fd9\u91cc\u5c31\u4e0d\u518d\u8d58\u8ff0\u4e86\u3002 $$ \\forall j \\forall n \\exist i \\space p(i,j,n) \\ \\equiv \\bigwedge_{j=1}^9 \\bigwedge_{n=1}^9 \\bigvee_{i=1}^9 \\space p(i,j,n) $$
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#3-1-9","title":"3. \u6bcf\u4e00\u5bab\u683c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002","text":"\u2003\u2003\u9996\u5148\uff0c\u5bab\u683c\u8fd9\u4e2a\u65b0\u6982\u5ff5\u610f\u5473\u7740\u6211\u4eec\u4e0d\u80fd\u5355\u7eaf\u5730\u50cf\u521a\u521a\u7684\u679a\u4e3e\u884c\u548c\u5217\u4e00\u6837\uff0c\u7528i\u548cj\u6765\u8868\u793a\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5f15\u5165\u4e00\u4e2a\u65b0\u7684\u53d8\u91cf\u3002
\u2003\u2003\u8bbe\u60f3\u6211\u4eec\u9700\u8981\u4e3a\u8fd9\u4e2a\u6570\u72ec\u5199\u4e00\u4e2a\u7a0b\u5e8f\uff0c\u90a3\u4e48\u4e00\u4e2a\u5f88\u5bb9\u6613\u60f3\u5230\u601d\u8def\u7684\u5c31\u662f\u5148\u679a\u4e3e\u6bcf\u4e00\u4e2a\u5bab\u683c\uff0c\u7136\u540e\u679a\u4e3e\u6bcf\u4e00\u4e2a\u6570\u5b57\uff0c\u6700\u540e\u5224\u65ad\u8fd9\u4e2a\u6570\u5b57\u5728\u8fd9\u4e2a\u5bab\u683c\u4e2d\u662f\u5426\u51fa\u73b0\u8fc7\u3002
\u2003\u2003\u5982\u4f55\u679a\u4e3e\u5bab\u683c\uff0c\u4e00\u4e2a\u7b80\u5355\u7684\u65b9\u6cd5\u5c31\u662f\u76f4\u63a5\u628a\u4e5d\u5bab\u683c\u770b\u4f5c\u4e00\u4e2a3x3\u7684\u77e9\u9635\uff0c\u7136\u540e\u901a\u8fc7\u884c\u548c\u5217\u7684\u679a\u4e3e\u5f97\u5230\u5bab\u683c\u3002\u6211\u4eec\u5047\u8bbe\\(x\\)\u662f\u4e5d\u5bab\u683c\u7684\u884c\uff0c\\(y\\)\u662f\u4e5d\u5bab\u683c\u7684\u5217\uff0c\u90a3\u4e48\u65e2\u7136\u5bf9\u4e8e\u67d0\u4e00\u4e2a\u4e5d\u5bab\u683c\u8fd9\u4e2a\u6761\u4ef6\u90fd\u6210\u7acb\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u628a\u6761\u4ef6\u5199\u4e3a\\(\\forall x \\forall y \\space P(x,y)\\)\uff0c\u5176\u4e2dP(x,y)\u8868\u793ax\u884cy\u5217\u7684\u5bab\u683c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002
\u2003\u2003\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u8003\u8651\u600e\u4e48\u8868\u793ax\u884cy\u5217\u7684\u5bab\u683c\u90fd\u67091-9\u7684\u6240\u6709\u6570\u5b57\u3002\u548c\u4e0a\u9762\u7684\u601d\u8def\u7c7b\u4f3c\uff0c\u6211\u4eec\u9996\u5148\u628a\u6761\u4ef6\u62c6\u5206\u6210\u201c\u5bf9\u4e8e1-9\u7684\u4efb\u610f\u4e00\u4e2a\u6570\u5b57\uff0c\u8fd9\u4e2a\u6570\u5b57\u90fd\u5728\u8fd9\u4e00\u5bab\u683c\u201d\uff0c\u5373\\(\\forall n \\space P(x,y,n)\\)\uff0c\\(P(x,y,n)\\)\u8868\u793ax\u884cy\u5217\u7684\u5bab\u683c\u4e2d\u6570\u5b57\\(n\\)\u51fa\u73b0\u8fc7\u3002
\u2003\u2003\u6700\u540e\uff0c\u6211\u4eec\u53ea\u9700\u8981\u63cf\u8ff0\u600e\u4e48\u8868\u793ax\u884cy\u5217\u7684\u5bab\u683c\u4e2d\u6570\u5b57\\(n\\)\u51fa\u73b0\u8fc7\u3002\u6570\u5b57\u5728x\u884cy\u5217\u7684\u5bab\u683c\u4e2d\u51fa\u73b0\u8fc7\uff0c\u610f\u5473\u7740\u8fd9\u4e2a\u6570\u5b57\u5728\u8fd9\u4e00\u5bab\u683c\u7684\u67d0\u4e00\u683c\u4e2d\u51fa\u73b0\u8fc7\u81f3\u5c11\u4e00\u6b21\uff0c\u901a\u8fc7\u518d\u6b21\u679a\u4e3e\u884c\u5217\u6765\u8ba1\u7b97\u5bab\u683c\u4e2d\u4e00\u683c\u7684\u4f4d\u7f6e\u3002\u7528\\(i\\)\u8868\u793a\u5bab\u683c\u7684\u7b2ci\u884c\uff0c\\(j\\)\u8868\u793a\u5bab\u683c\u7684\u7b2cj\u5217\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u77e5\u9053\u5bab\u683c\u4e2d\u4e00\u683c\u76f8\u5bf9\u4e8e\u5bab\u683c\u5de6\u4e0a\u89d2\u5750\u6807\u4e3a\\((i,j)\\)\uff0c\u603b\u5750\u6807\u5373\\((3(x-1)+i,3(y-1)+j)\\)\uff0cn\u5728\u8fd9\u4e9b\u5750\u6807\u4e2d\u5b58\u5728\uff0c\u5373\u53ef\u7ffb\u8bd1\u6210\\(\\exist i\\exist j \\space p(3(x-1)+i,3(y-1)+j,n)\\)\u3002
\u2003\u2003\u4e8e\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e2a\u903b\u8f91\u7684\u5b8c\u6574\u7ffb\u8bd1\uff1a
\\[ \\forall x \\forall y \\forall n\\exist i\\exist j \\space p(3(x-1)+i,3(y-1)+j,n) \\\\ \\equiv \\bigwedge_{x=1}^3 \\bigwedge_{y=1}^3 \\bigwedge_{n=1}^9 \\bigvee_{i=1}^3 \\bigvee_{j=1}^3 \\space p(3(x-1)+i,3(y-1)+j,n) \\]\u2003\u2003\u660e\u9762\u4e0a\u7684\u6570\u72ec\u89c4\u5219\u5c31\u662f\u8fd9\u4e48\u591a\uff0c\u4f46\u662f\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u56e0\u4e3a\u6211\u4eec\u8bbe\u8ba1\u7684\u7279\u6b8a\u6027\uff0c\u4f1a\u6709\u975e\u5e38\u591a\u9690\u542b\u7684\u6761\u4ef6\u9700\u8981\u6211\u4eec\u8003\u8651\uff0c\u5426\u5219\u5c31\u4f1a\u51fa\u5f88\u4e25\u91cd\u7684BUG\u3002\u5c31\u6bd4\u5982\u4e0b\u9762\u8fd9\u4e2a\u89c4\u5219\uff1a
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#4","title":"4. \u6bcf\u4e00\u683c\u53ea\u80fd\u586b\u4e00\u4e2a\u6570\u5b57\u3002","text":"\u2003\u2003\u56e0\u4e3a\u6211\u4eec\u4e4b\u524d\u7684\u601d\u8def\u662f\u679a\u4e3e\uff0c\u6240\u4ee5\u4e0d\u514d\u4f1a\u51fa\u73b0\u67d0\u4e2a\u683c\u5b50\u88ab\u91cd\u590d\u679a\u4e3e\u7684\u60c5\u51b5\uff0c\u6bd4\u5982\u5bf9\u4e8e\u4e00\u4e2a\u683c\u5b50\uff0c\u6211\u4eec\u586b\u5165\u4e86\u6570\u5b571\uff0c\u7136\u540e\u518d\u586b\u5165\u4e86\u6570\u5b572\uff0c\u90a3\u4e48\u6570\u5b572\u5c31\u4f1a\u88ab\u91cd\u590d\u679a\u4e3e\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u8fdb\u884c\u89c4\u5b9a\uff0c\u53bb\u9664\u8fd9\u79cd\u60c5\u51b5\u3002
\u2003\u2003\u201c\u6bcf\u4e00\u683c\u201d\u7684\u7ffb\u8bd1\u662f\u975e\u5e38\u7b80\u5355\u7684\uff0c\u5373\\(\\forall i \\forall j \\space P(i,j)\\)\uff0c\u5176\u4e2d\\(P(i,j)\\)\u8868\u793ai\u884cj\u5217\u7684\u683c\u5b50\u53ea\u6709\u4e00\u4e2a\u6570\u5b57\u3002
\u2003\u2003\u90a3\u4e48\u600e\u4e48\u63cf\u8ff0\u201c\u53ea\u6709\u4e00\u4e2a\u6570\u5b57\u201d\u5462\uff1f\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u901a\u5e38\u4f1a\u60f3\u5230\u7528\u903b\u8f91\u5206\u7c7b\u6765\u5224\u65ad\uff0c\u679a\u4e3e\u6240\u6709\u7684\u6570\u5b57\uff0c\u5982\u679c\u586b\u5165\u4e86\u6570\u5b57\uff0c\u90a3\u4e48\u5c31\u4e0d\u80fd\u518d\u586b\u5165\u5176\u4ed6\u7684\u6570\u5b57\uff0c\u53cd\u4e4b\u5219\u5408\u6cd5\u3002\u8fd9\u4e2a\u201c\u903b\u8f91\u5206\u7c7b\u201d\u7684\u601d\u60f3\u6070\u597d\u548c\u903b\u8f91\u63a8\u51fa\u7684\u8fd0\u7b97\u4e00\u62cd\u5373\u5408\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5b83\u6765\u5b8c\u6210\u7ffb\u8bd1\uff1a $$ \\forall i \\forall j (\\forall n (p(i,j,n) \\rightarrow \\neg \\exist n' \\space p(i,j,n'))) (n'>n) \\\\ \\begin{aligned} &\\equiv \\forall i \\forall j \\forall n (p(i,j,n) \\rightarrow \\forall n' \\neg p(i,j,n')) (n'>n) \\\\ &\\equiv \\forall i \\forall j \\forall n \\forall n' (p(i,j,n) \\rightarrow \\neg p(i,j,n')) (n'>n) \\\\ &\\equiv \\bigwedge_{i=1}^9 \\bigwedge_{j=1}^9 \\bigwedge_{n=1}^9 \\bigwedge_{n'=n+1}^9 (p(i,j,n) \\rightarrow \\neg p(i,j,n')) \\end{aligned} $$
"},{"location":"Classnote/Discrete-Mathematics/Sudoku/#_3","title":"\u6b65\u9aa4\u4e09 \u2014\u2014 \u5224\u65ad\u83b7\u80dc\u60c5\u51b5","text":"\u2003\u2003\u6211\u4eec\u65e2\u7136\u5df2\u7ecf\u77e5\u9053\u4e86\u83b7\u80dc\u6761\u4ef6\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4ece\u4efb\u610f\u4e00\u79cd\u7684\\(p(i,j,n)\\)\u6b63\u786e\u6027\u547d\u9898\u7684\u96c6\u5408\u5224\u65ad\u8fd9\u79cd\u72b6\u6001\u662f\u5426\u8fbe\u5230\u4e86\u80dc\u5229\u3002\u4ece\u4e0a\u9762\u83b7\u80dc\u6761\u4ef6\u7684\u5224\u65ad\u4e2d\uff0c\u6211\u4eec\u77e5\u9053\u5982\u679c\u6ee1\u8db3\u4e86\u4e00\u4e2a\u6761\u4ef6\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6761\u4ef6\u6700\u7ec8\u7684\u8ba1\u7b97\u5c31\u4f1a\u4e3a\u771f\uff0c\u5982\u679c\u56db\u4e2a\u6761\u4ef6\u90fd\u4e3a\u771f\uff0c\u90a3\u4e48\u8fd9\u4e2a\u72b6\u6001\u5c31\u8fbe\u5230\u4e86\u80dc\u5229\u3002\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u8981\u5224\u65ad\u8fd9\u56db\u4e2a\u6761\u4ef6\u662f\u5426\u90fd\u4e3a\u771f\u5373\u53ef\u3002
\u2003\u2003\u867d\u7136\u66b4\u529b\u679a\u4e3e\u83b7\u80dc\u60c5\u51b5\u9700\u8981\\(2^{729}\\)\u6b21\u5c1d\u8bd5\uff0c\u8fd9\u975e\u5e38\u7e41\u7410\uff0c\u4f46\u662f\u81f3\u5c11\u5728\u73b0\u5728\uff0c\u6211\u4eec\u53d1\u73b0\u4e86\u4e00\u4e2a\u89e3\u51b3\u6570\u72ec\u95ee\u9898\u7684\u65b9\u6cd5\uff0c\u4e5f\u4ece\u4e2d\u628a\u5b83\u548c\u79bb\u6563\u6570\u5b66\u7684\u5b66\u4e60\u8054\u7cfb\u5230\u4e86\u4e00\u8d77\u3002
"},{"location":"ScientificResearch/","title":"\u5bfc\u822a\u9875","text":"\u8bb0\u5f55\u79d1\u7814\u4e00\u4e9b\u57fa\u7840\u8bfe\u7684\u5b66\u4e60\u548c\u8bba\u6587\u7684\u9605\u8bfb\u3002
"},{"location":"ScientificResearch/#_2","title":"\u6700\u8fd1\u66f4\u65b0","text":"CS231N - \u56fe\u50cf\u5206\u7c7b\u5668
"},{"location":"ScientificResearch/CS231N/A1L1/","title":"\u5b9e\u9a8c\u4e00 \u2014\u2014 \u5b9e\u73b0\u524dK\u6700\u8fd1\u90bb\u5c45\u7b97\u6cd5","text":"\u2003\u2003\u5728\u56fe\u50cf\u5206\u7c7b\u5668\u7684\u6559\u5b66\u4e2d\uff0c\u6211\u4eec\u5b66\u4e60\u5230\u4e86\u8981\u5b9e\u73b0KNN\u7b97\u6cd5\u9700\u8981\u4e86\u89e3\u7684\u4e00\u4e9b\u77e5\u8bc6\uff0c\u63a5\u4e0b\u6765\u5c06\u901a\u8fc7\u5b9e\u9a8c\u6765\u8fdb\u4e00\u6b65\u5730\u9610\u91ca\u6574\u4e2a\u7b97\u6cd5\u7684\u5b9e\u73b0\u8fc7\u7a0b\u3002
"},{"location":"ScientificResearch/CS231N/A1L1/#_1","title":"\u6b65\u9aa4\u4e00\u3001\u521d\u59cb\u5316","text":"knn.ipynb# ipython notebook\u7684\u4e00\u4e9b\u521d\u59cb\u5316\u64cd\u4f5c\n\n# \u5bfc\u5165\u4e00\u4e9b\u524d\u7f6e\u5e93\uff0c\u5305\u62ecnumpy, random(\u62bd\u53d6\u6570\u636e\u7528)\nimport random\nimport numpy as np\nfrom cs231n.data_utils import load_CIFAR10\nimport matplotlib.pyplot as plt\n\n# matplot\u7684\u521d\u59cb\u5316\uff1a\u5185\u5d4c\u753b\u56fe\u3001\u7a97\u53e3\u8bbe\u7f6e\u3001\u63d2\u503c\u7c7b\u578b\u3001\u56fe\u7ebf\u989c\u8272\n%matplotlib inline\nplt.rcParams['figure.figsize'] = (10.0, 8.0) \nplt.rcParams['image.interpolation'] = 'nearest'\nplt.rcParams['image.cmap'] = 'gray'\n\n# Ipython\u4e2d\uff0c\u5bf9\u8c03\u7528\u7684\u6a21\u5757\u8fdb\u884c\u5b9e\u65f6\u7684\u66f4\u65b0\uff0c\u65e0\u9700\u624b\u52a8\u91cd\u8f7d\u3002\n# http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython\n%load_ext autoreload\n%autoreload 2\n\u2003\u2003\u5728\u8fd9\u6bb5\u4ee3\u7801\u4e2d\uff0c\u9664\u4e86\u7ecf\u5178\u7684numpy\u548c\u9700\u8981\u7684random\u6a21\u5757\u5916\u6211\u4eec\u8fd8\u53ef\u4ee5\u770b\u5230\u6574\u4e2a\u7a0b\u5e8f\u8c03\u7528\u4e86matplotlib\u7684pyplot\u6a21\u5757\uff0c\u8fd9\u662f\u7528\u4e8e\u4ea7\u751f\u6570\u636e\u56fe\u7684\u4e00\u4e2a\u6a21\u5757\uff0c\u5177\u4f53\u5982\u4f55\u4f7f\u7528\u53ef\u4ee5\u770b\u540e\u7eed\u4ee3\u7801\uff0c\u8fd9\u91cc\u8fdb\u884c\u4e86\u521d\u59cb\u5316\u8bbe\u7f6e\uff0c\u5148\u628a\u56fe\u50cf\u5185\u5d4c\u4ece\u800c\u4e0d\u5f39\u51fa\u65b0\u7684\u7a97\u53e3\uff0c\u7136\u540e\u8bbe\u7f6e\u7a97\u53e3\u5927\u5c0f\u3001\u63d2\u503c\u7c7b\u578b\u4ee5\u53ca\u56fe\u7ebf\u7684\u989c\u8272\u3002 \u2003\u2003\u6b64\u5916\u6211\u4eec\u8fd8\u53ef\u4ee5\u770b\u5230\u7a0b\u5e8f\u8c03\u7528\u4e86\u4e00\u4e2aload_CIFAR10\u7684\u51fd\u6570\u3002\u4e0b\u9762\u6211\u4eec\u6765\u89e3\u91ca\u5b83\u7684\u4f5c\u7528\u3002
\u2003\u2003CIFAR-10\u6570\u636e\u96c6\u662f\u975e\u5e38\u7ecf\u5178\uff0c\u4e5f\u662f\u975e\u5e38\u57fa\u7840\u7684\u4e00\u5957\u8bad\u7ec3\u96c6\uff0c\u5b83\u7531\u4e94\u4e07\u4e2a32px * 32px\u5927\u5c0f\u7684\u56fe\u50cf\u7ec4\u6210\uff0c\u6bcf\u4e2a\u50cf\u7d20\u5305\u542bRGB\u4e09\u4e2a\u989c\u8272\u901a\u9053\uff0c\u56e0\u4e3a\u50cf\u7d20\u5c11\uff0c\u6240\u4ee5\u6574\u4f53\u7684\u8bad\u7ec3\u96c6\u5927\u5c0f\u4e0d\u662f\u5f88\u5927\uff0c\u9002\u5408\u8f7b\u91cf\u7ea7\u7684\u6a21\u578b\u8bad\u7ec3\u3002\u5b83\u7684\u6587\u4ef6\u7ed3\u6784\u5982\u4e0b\uff1a
\u2003\u2003\u89c2\u5bdf\u76ee\u5f55\u7ed3\u6784\uff0c\u53ef\u4ee5\u53d1\u73b0\u5b83\u7531\u4e94\u4e2a\u8bad\u7ec3\u96c6\u6784\u6210\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\u5b83\u5e76\u4e0d\u662f\u4ee5\u56fe\u50cf\u7684\u5f62\u5f0f\u5b58\u50a8\uff0c\u800c\u662f\u76f4\u63a5\u4ee5\u4e8c\u8fdb\u5236\u683c\u5f0f\u5b58\u50a8\u3002\u5982\u679c\u4f7f\u7528\u4e8c\u8fdb\u5236\u6587\u672c\u67e5\u770b\u5668\u6765\u5206\u6790\uff0c\u53ef\u4ee5\u5927\u81f4\u770b\u51fa\u6574\u4f53\u7684\u6570\u636e\u96c6\u7684\u6587\u4ef6\u7ed3\u6784\uff0c\u9996\u5148\u662f\u6574\u4e2a\u6587\u4ef6\u7684\u6587\u4ef6\u5934\uff0c\u7136\u540e\u5b58\u50a8\u4e86\u56fe\u50cf\u7684\u7c7b\u578b\uff08\\(1 \\text{ Byte}\\)\u6570\u5b57\u8868\u793a\uff0c\\04B\u9694\u5f00\uff09\uff0c\u63a5\u4e0b\u6765\u662f\u56fe\u50cf\u5934\uff0c\u6700\u7ec8\u662f\u56fe\u50cf\u7684\u5185\u5bb9\uff0c\u5927\u81f4\u4e86\u89e3\u4e86\u5b83\u7684\u7ed3\u6784\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u597d\u7406\u89e3\u4e0b\u9762\u7a0b\u5e8f\u662f\u5982\u4f55\u5bfc\u5165\u6570\u636e\u7684\u3002
\u2003\u2003\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u770b\u770b\u51fd\u6570load_CIFAR10\u662f\u5982\u4f55\u8fd0\u4f5c\u7684\u3002
data_utils.py
from builtins import range\nfrom six.moves import cPickle as pickle\nimport os\nimport numpy as np\n\n# \u8bfb\u53d6\u6587\u4ef6\u4fe1\u606f\ndef load_pickle(f):\n version = platform.python_version_tuple()\n if version[0] == \"2\":\n return pickle.load(f)\n elif version[0] == \"3\":\n return pickle.load(f, encoding=\"latin1\")\n # CIFAR\u5bf9\u4e8epython\u6709\u6807\u51c6\u7684\u8fd4\u56de\u683c\u5f0f\u3002\n # \u8fd4\u56de\u4e00\u4e2a\u5b57\u5178\uff0c\u6bcf\u4e2a\u5b57\u5178\u4e2d\u662f\u8bbe\u7f6e\u597d\u7684\u540d\u5b57\u548c\u76f8\u5173\u6570\u636e\n raise ValueError(\"invalid python version: {}\".format(version))\n\n# \u8bfb\u53d6\u4e00\u4e2a\u6570\u636e\u5757\ndef load_CIFAR_batch(filename):\n with open(filename, \"rb\") as f:\n datadict = load_pickle(f)\n # \u8bfb\u53d6\u56fe\u50cf\u4fe1\u606f\u548c\u6807\u7b7e\u4fe1\u606f\n X = datadict[\"data\"]\n Y = datadict[\"labels\"]\n X = X.reshape(10000, 3, 32, 32).transpose(0, 2, 3, 1).astype(\"float\")\n # X\u7684RGB\u539f\u6765\u57281\u53f7\u7ef4\uff0c\u73b0\u5728\u628aXY\u4f4d\u7f6e\u7ef4\u5ea6\u524d\u79fb\uff0c\u65b9\u4fbf\u4e4b\u540e\u7684\u8ba1\u7b97\u3002\n Y = np.array(Y)\n # Y\u7684\u7c7b\u578b\u4eceList\u8f6c\u6210array\uff0c\u65b9\u4fbf\u540e\u7eed\u8ba1\u7b97\n return X, Y\n\n# \u8bfb\u53d6\u6240\u6709\u6570\u636e\ndef load_CIFAR10(ROOT):\n xs = []\n ys = []\n # \u4ece1\u52305\u8fdb\u884c\u904d\u5386\uff0c\u5bf9\u5e94data_batch_i(i = 1,2,3,4,5)\n for b in range(1, 6):\n f = os.path.join(ROOT, \"data_batch_%d\" % (b,))\n # \u8bfb\u53d6\u4e00\u4e2a\u6570\u636e\u5757\u7684\u56fe\u50cf\n X, Y = load_CIFAR_batch(f)\n # \u628a\u56fe\u50cf\u653e\u5230\u5217\u8868\u4e2d\n xs.append(X)\n ys.append(Y)\n # \u6574\u5408\u6570\u636e\u5757\n Xtr = np.concatenate(xs)\n Ytr = np.concatenate(ys)\n # \u91ca\u653e\u7a7a\u95f4\n del X, Y\n Xte, Yte = load_CIFAR_batch(os.path.join(ROOT, \"test_batch\"))\n return Xtr, Ytr, Xte, Yte\n\u952e\uff08Key\uff09 \u63cf\u8ff0 \u6837\u4f8b batch_label \u8fd9\u6279\u6570\u636e\u7684\u6807\u7b7e \u4e00\u4e2a\u5b57\u7b26\u4e32\u8868\u793a 'training batch 3 of 5', 'testing batch 1 of 1'... labels \u5404\u4e2a\u56fe\u50cf\u5c5e\u4e8e\u7684\u7c7b\u578b \u4e00\u4e2aList\u8868\u793a\uff0c\u6bcf\u627910000\u4e2a [0\uff0c1\uff0c2\uff0c3\uff0c4\uff0c5\uff0c6\uff0c7\uff0c8\uff0c9\uff0c0\uff0c1\uff0c..] data \u5404\u4e2a\u56fe\u50cf\u7684\u5177\u4f53\u5185\u5bb9 \u4e00\u4e2anumpy.darray\u8868\u793a10000\u5f20\u4e09\u4e2a\u901a\u9053\\(32\\times32\\)\u50cf\u7d20\u7684\u56fe\u7247 \u7ec4\u7ec7\u65b9\u5f0f\uff1a\u4e8c\u7ef4\u6570\u7ec4\uff1b \u56fe\u7247\u4e0b\u6807\uff0c(\u901a\u9053\u4e0b\u6807\uff0c\u884c\uff0c\u5217) \u7565 filenames \u56fe\u7247\u540d \u4e00\u4e2a\u5b57\u7b26\u4e32List\u8868\u793a\uff0c\u6bcf\u627910000\u4e2a ['auto_s_000241.png', \u2002 'bufo_viridis_s_001109.png', \u2002 'rana_catesbeiana_s_000111.png', .. ]
\u2003\u2003\u6211\u4eec\u53ea\u5173\u5fc3labels \u548c data\u4e2d\u7684\u6570\u636e\uff0c\u6240\u4ee5\u63d0\u53d6\u51fa\u6570\u636e\u540e\uff0c\u6211\u4eec\u505a\u4e86\u4e00\u6b65\u5bf9X\u7ef4\u5ea6\u7684\u91cd\u65b0\u8bbe\u8ba1\u2014\u2014\u9996\u5148\u628a\u4e8c\u7ef4\u62d3\u5c55\u6210\u56db\u7ef4\uff08\u56fe\u50cf\u4e0b\u6807\u3001\u901a\u9053\u4e0b\u6807\u3001\u884c\u3001\u5217\uff09\uff0c\u7136\u540e\u5c06\u56fe\u50cf\u8fdb\u884c\u4e86\u7ef4\u5ea6\u7684\u8f6c\u7f6e\uff0c\u628a\u901a\u9053\u4e0b\u6807\u653e\u5230\u6700\u540e\u4e00\u4e2a\u7ef4\u5ea6\uff0c\u65b9\u4fbf\u6211\u4eec\u8fdb\u884c\u5bf9\u5355\u4e2a\u50cf\u7d20\u7684\u4fee\u6539\u3002\u6700\u540e\u628a\u7c7b\u578b\u8f6c\u6362\u4e3afloat\u3002 \u2003\u2003\u6700\u7ec8\u6211\u4eec\u8c03\u7528load_CIFAR10\u51fd\u6570\uff0c\u5f97\u5230\u4e86\u539f\u59cb\u7684\u6570\u636e\u96c6\uff0c\u5176\u4e2d\u6709\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\uff0c\u6570\u636e\u5305\u542b\u7c7b\u578b\u4e3anumpy.darray\u7684\u5185\u5bb9\u56db\u7ef4\u6570\u7ec4\u548c\u7c7b\u578b\u4e3anumpy.darray\u7684\u4e00\u7ef4\u4e0b\u6807\u6570\u7ec4\u3002
cifar10_dir = 'cs231n/datasets/cifar-10-batches-py'\n\n# \u5982\u679c\u5df2\u7ecf\u6709\u5b58\u5728\u7684\u53d8\u91cf\uff0c\u8fdb\u884c\u91ca\u653e\u907f\u514d\u51fa\u73b0\u5185\u5b58\u51b2\u7a81\ntry:\n del X_train, y_train\n del X_test, y_test\n print('Clear previously loaded data.')\nexcept:\n pass\n\n# \u8bfb\u5165\u6570\u636e\nX_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)\n\n# \u89c2\u5bdf\u6570\u7ec4\u7684\u6784\u6210\uff0c\u6765\u68c0\u6d4b\u6211\u4eec\u662f\u5426\u5f97\u5230\u4e86\u6b63\u786e\u7684\u6570\u636e\u3002\u8fd9\u662f\u4e00\u4e2a\u7ecf\u5178\u7b80\u5355\u4e14\u6709\u6548\u7684\u68c0\u67e5\u65b9\u5f0f\u3002\nprint('Training data shape: ', X_train.shape)\nprint('Training labels shape: ', y_train.shape)\nprint('Test data shape: ', X_test.shape)\nprint('Test labels shape: ', y_test.shape)\n\u2003\u2003\u6211\u4eec\u89c2\u5bdf\u4e0a\u9762\u7684\u56db\u4e2aprint\uff0c\u5b83\u4eec\u662f\u4ece\u89c2\u5bdf\u6574\u4e2a\u6570\u7ec4\u6784\u6210\u6765\u770b\u56fe\u50cf\u8bfb\u5165\u662f\u5426\u6b63\u786e\uff0c\u6211\u4eec\u540c\u6837\u53ef\u4ee5\u7528\u66f4\u76f4\u89c2\u7684\u65b9\u5f0f\u6765\u5224\u65ad\u8bfb\u5165\u662f\u5426\u6b63\u786e\u3002
"},{"location":"ScientificResearch/CS231N/A1L1/#_2","title":"\u67e5\u770b\u8bfb\u5165\u7684\u56fe\u7247","text":"knn.ipynb# Visualize some examples from the dataset.\n# We show a few examples of training images from each class.\nclasses = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']\nnum_classes = len(classes)\nsamples_per_class = 7\nfor y, cls in enumerate(classes):\n idxs = np.flatnonzero(y_train == y)\n idxs = np.random.choice(idxs, samples_per_class, replace=False)\n for i, idx in enumerate(idxs):\n plt_idx = i * num_classes + y + 1\n plt.subplot(samples_per_class, num_classes, plt_idx)\n plt.imshow(X_train[idx].astype('uint8'))\n plt.axis('off')\n if i == 0:\n plt.title(cls)\nplt.show()\n\u8bad\u7ec3\u6a21\u578b \u2003\u2003\u56fe\u50cf\u7684\u8bc6\u522b\u4e0d\u662f\u51ed\u7a7a\u8fdb\u884c\u7684\uff0c\u5c31\u50cf\u8ba1\u7b97\u673a\u7684\u7b97\u6cd5\u6d41\u7a0b\u4e00\u6837\uff0c\u56fe\u50cf\u4f5c\u4e3a\u7b97\u6cd5\u7684\u8f93\u5165\uff0c\u7c7b\u522b\u4f5c\u4e3a\u7b97\u6cd5\u7684\u8f93\u51fa\uff0c\u6574\u4e2a\u7b97\u6cd5\u672c\u8eab\u8fd9\u4e2a\u9ed1\u7bb1\u5c31\u662f\u6211\u4eec\u9700\u8981\u8bad\u7ec3\u7684\u4e1c\u897f\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u4e00\u4e2a\u6a21\u578b\uff0c\u8ba9\u5b83\u7684\u8f93\u5165\u8f93\u51fa\u6620\u5c04\u5173\u7cfb\u548c\u56fe\u50cf\u8bc6\u522b\u8fc7\u7a0b\u76f8\u543b\u5408\u3002
\u9884\u6d4b\u56fe\u50cf \u2003\u2003\u6267\u884c\u9884\u6d4b\u56fe\u50cf\u7684\u8fc7\u7a0b\uff0c\u5c31\u662f\u4f7f\u7528\u6211\u4eec\u627e\u5230\u7684\u6a21\u578b\uff0c\u8fdb\u884c\u8f93\u5165\u3001\u5904\u7406\u548c\u8f93\u51fa\u7684\u8fc7\u7a0b\u3002\u5c31\u50cf\u54c8\u5e0c\u7b97\u6cd5\u628a\u539f\u6570\u636e\u5904\u7406\u6210\u54c8\u5e0c\u503c\u4e00\u6837\uff0c\u901a\u8fc7\u6a21\u578b\uff0c\u539f\u56fe\u50cf\u7684\u50cf\u7d20\u9635\u5217\u7ecf\u8fc7\u8ba1\u7b97\u53d8\u6210\u4e00\u4e9b\u5206\u6570\u503c\uff0c\u7136\u540e\u6211\u4eec\u901a\u8fc7\u6bd4\u8f83\u6bcf\u4e2a\u7c7b\u578b\u7684\u5f97\u5206\u6765\u8bc4\u4ef7\u8fd9\u4e2a\u56fe\u50cf\u5e94\u8be5\u5c5e\u4e8e\u54ea\u4e2a\u7c7b\u522b\u3002
\u4e00\u70b9\u8054\u60f3
\u2003\u2003\u8fd9\u5176\u5b9e\u5f88\u6709\u610f\u601d\uff0c\u5c31\u50cf\u5b66\u6821\u7ed9\u6211\u4eec\u5206\u53d1\u6d4b\u8bd5\u8bd5\u5377\u3001\u6539\u5377\u6253\u5206\u6765\u7ed9\u6211\u4eec\u8bc4\u4ef7\u5b66\u4e60\u6c34\u5e73\u4e00\u6837\uff0c\u6211\u4eec\u7efc\u5408\u673a\u5668\u6bcf\u4e00\u5757\u50cf\u7d20\uff0c\u7ed9\u5b83\u4eec\u6765\u6253\u5206\uff0c\u6700\u540e\u5f97\u51fa\u5b83\u5e94\u8be5\u5c5e\u4e8e\u54ea\u4e00\u4e2a\u7c7b\u522b\u3002\u5c31\u50cf\u4f60\u653f\u6cbb\u8003\u4e8690\u5206\uff0c\u800c\u7269\u7406\u53ea\u670960\u5206\uff0c\u4f60\u4f1a\u4e0b\u610f\u8bc6\u5224\u65ad\u4f60\u9002\u5408\u5b66\u6587\u79d1\u800c\u4e0d\u9002\u5408\u5b66\u7406\u79d1\u3002 \u2003\u2003\u4f46\u662f\uff0c\u6211\u4eec\u90fd\u77e5\u9053\u8fd9\u53ea\u662f\u4e00\u4e2a\u6982\u7387\u5224\u65ad\u3002\u5f71\u54cd\u8003\u8bd5\u5206\u6570\u7684\u56e0\u7d20\u592a\u591a\u4e86\uff0c\u6211\u4eec\u4e0d\u4f1a\u901a\u8fc7\u4ec5\u4ec5\u4e00\u6b21\u8003\u8bd5\u6765\u51b3\u5b9a\u4e00\u4e2a\u4eba\u662f\u5426\u9002\u5408\u5b66\u4e60\u6587\u79d1\u6216\u8005\u5b66\u4e60\u7406\u79d1\u3002\u5bf9\u56fe\u50cf\u4e5f\u4e00\u6837\uff0c\u5f53\u56fe\u50cf\u5bf9\u4e8e\u201c\u732b\u201d\u5f97\u5206\u6700\u9ad8\u7684\u65f6\u5019\uff0c\u5b83\u5927\u6982\u7387\u662f\u732b\uff0c\u4f46\u662f\u8fd9\u5fc5\u7136\u662f\u4e0d\u80fd\u767e\u5206\u767e\u5730\u786e\u5b9a\u7684\u3002 \u2003\u2003\u5c3d\u7ba1\u5982\u6b64\uff0c\u4f46\u5c31\u50cf\u7269\u7406\u6a21\u578b\u4e2d\u4f7f\u7528\u4e86\u975e\u5e38\u591a\u7684\u4e00\u9636\u8fd1\u4f3c\u4e5f\u80fd\u51c6\u786e\u9884\u6d4b\u81ea\u7136\u754c\u7684\u53d8\u5316\uff0c\u5bf9\u4e8e\u673a\u5668\uff0c\u4e5f\u53ef\u4ee5\u6709\u8fd9\u6837\u7684\u8bef\u5dee\u548c\u8fd1\u4f3c\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5f00\u53d1\u8bad\u7ec3\u543b\u5408\u7387\u66f4\u9ad8\u7684\u6a21\u578b\uff0c\u8fd9\u6837\u8ba9\u9519\u8bef\u964d\u5230\u53ef\u4ee5\u5bb9\u8bb8\u7684\u8303\u56f4\uff0c\u8ba9\u5b83\u505a\u51fa\u9ad8\u6982\u7387\u7684\u9884\u6d4b\uff0c\u8fd9\u6837\u8fd9\u4e2a\u6a21\u578b\u5c31\u6bd4\u8f83\u53ef\u4fe1\u4e86\u3002\u8bf4\u4e0d\u5b9a\u6709\u4e00\u5929\uff0c\u673a\u5668\u53ef\u4ee5\u505a\u5230\u6bd4\u4eba\u773c\u8bc6\u522b\u66f4\u7cbe\u51c6\u3002
"},{"location":"ScientificResearch/CS231N/L2/#l1","title":"L1\u8ddd\u79bb\uff08\u66fc\u54c8\u987f\u8ddd\u79bb\uff09","text":"\u2003\u2003\u6211\u4eec\u521a\u521a\u8bb2\u5230\uff0c\u5bf9\u56fe\u50cf\u8fdb\u884c\u5206\u7c7b\uff0c\u6700\u91cd\u8981\u7684\u662f\u5bf9\u56fe\u50cf\u786e\u5b9a\u4e00\u4e2a\u201c\u6253\u5206\u6807\u51c6\u201d\uff0c\u5f97\u5230\u8fd9\u4e2a\u56fe\u50cf\u5728\u6bcf\u4e00\u4e2a\u5206\u7c7b\u7684\u5206\u6570\uff0c\u65b9\u4fbf\u540e\u7eed\u7684\u9009\u62e9\u3002L1\u8ddd\u79bb\u5c31\u662f\u4e00\u4e2a\u7ecf\u5178\u7684\u6253\u5206\u6807\u51c6\u3002
L1\u8ddd\u79bb\u516c\u5f0f\uff1a $$ L_1 = \\sum_{p_{ij} \\in img}{|p_{ij}-q_{ij}|},q_{ij} = \\text{constant} $$
\u2003\u2003\u5728\u4e0a\u9762\u7684\u516c\u5f0f\u4e2d\uff0c\\(q\\)\u662f\u6211\u4eec\u9884\u5148\u8bbe\u7f6e\u597d\u7684\u5e38\u6570\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u5df2\u77e5\u7684\u56fe\u50cf\uff0c\u6211\u4eec\u77e5\u9053\u8fd9\u4e2a\u56fe\u50cf\u5bf9\u5e94\u7740\u4ec0\u4e48\uff0c\u800cL1\u8ddd\u79bb\u5c31\u662f\u628a\u73b0\u5728\u6d4b\u8bd5\u7684\u56fe\u50cf\u548c\u5df2\u77e5\u56fe\u50cf\u7684\u50cf\u7d20\u503c\u4e00\u4e00\u5bf9\u5e94\u76f8\u51cf\uff0c\u7136\u540e\u8fdb\u884c\u6c42\u548c\uff0c\u5c31\u50cf\u4e0b\u9762\u8fd9\u4e2a\u56fe\u663e\u793a\u7684\u4e00\u6837\u3002
\u2003\u2003\u6211\u4eec\u628a\u8fd9\u4e2a\u8ba1\u7b97\u51fa\u6765\u7684\u4e1c\u897f\u53eb\u505a\u201c\u8ddd\u79bb\u201d\uff0c\u662f\u56e0\u4e3a\u5b83\u4ece\u67d0\u79cd\u89d2\u5ea6\u4e0a\u786e\u5b9e\u53cd\u6620\u4e86\u6d4b\u8bd5\u56fe\u50cf\u548c\u5df2\u77e5\u56fe\u50cf\u7684\u5dee\u5f02\uff0c\u4ece\u62bd\u8c61\u7684\u89d2\u5ea6\u6765\u770b\u5c31\u662f\u4e00\u79cd\u8ddd\u79bb\uff0c\u800c\u4e14\u5b83\u7b26\u5408\u5dee\u5f02\u8d8a\u5927\uff0c\u8ddd\u79bb\u8d8a\u8fdc\u7684\u76f4\u89c2\u3002
"},{"location":"ScientificResearch/CS231N/L2/#_3","title":"\u6a21\u578b\u8bad\u7ec3\u2014\u2014\u8ddd\u79bb\u77e9\u9635","text":"\u2003\u2003\u56e0\u6b64\uff0c\u53ef\u4ee5\u8bbe\u60f3\uff0c\u5982\u679c\u6211\u4eec\u624b\u5934\u6709\\(N\\)\u4e2a\u5df2\u77e5\u7684\u5bf9\u8c61\uff0c\u540c\u65f6\u6709\\(M\\)\u4e2a\u9700\u8981\u9a8c\u8bc1\u7684\u56fe\u50cf\uff0c\u6211\u4eec\u4e00\u4e00\u8ba1\u7b97\u5b83\u4eec\u4e4b\u95f4\u8ddd\u79bb\uff0c\u4e8e\u662f\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a \\(M\\)\u884c\\(N\\)\u5217\u7684\u77e9\u9635\uff0c\u6211\u4eec\u5c06\u5b83\u79f0\u4f5c\u8ddd\u79bb\u77e9\u9635\uff08distance matrix\uff09\uff0c\u901a\u8fc7\u6bd4\u8f83\u6bcf\u4e00\u884c\u7684\u8ddd\u79bb\uff0c\u5c31\u53ef\u4ee5\u5f97\u51fa\u6bcf\u4e00\u4e2a\u9a8c\u8bc1\u56fe\u50cf\u7684\u9884\u6d4b\u7c7b\u578b\u3002
"},{"location":"ScientificResearch/CS231N/L2/#nn","title":"\u6700\u8fd1\u90bb\u5c45\u7b97\u6cd5(NN)","text":"\u2003\u2003\u6839\u636e\u76f4\u89c2\u611f\u53d7\uff0c\u6211\u4eec\u4e0d\u59a8\u505a\u51fa\u8fd9\u6837\u7684\u7ed3\u8bba\uff0c\u6211\u4eec\u8ba4\u4e3a\u5982\u679c\u4e24\u4e2a\u56fe\u50cf\u7684L1\u8ddd\u79bb\u8d8a\u5c0f\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u56fe\u50cf\u5c31\u8d8a\u76f8\u4f3c\u3002\u5bf9\u4e8e\u6d4b\u8bd5\u56fe\u50cf\uff0c\u6211\u4eec\u8ba1\u7b97\u5b83\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5df2\u77e5\u56fe\u50cf\u7684\u5df2\u6709\u8ddd\u79bb\uff0c\u770b\u770b\u5b83\u548c\u8c01\u8d70\u5f97\u66f4\u8fd1\uff0c\u5c31\u8ddf\u8c01\u5f52\u4e3a\u540c\u4e00\u7c7b\u2014\u2014\u8fd9\u5c31\u662f\u6700\u8fd1\u90bb\u5c45\uff08Nearest Neighbour\uff09\u7b97\u6cd5\u3002
NN.pyimport numpy as np\n\nclass NearestNeighbour:\n def __init__(self):\n pass\n\n def train(self,X,y):\n \"\"\" \u6ce8\u610f\uff0c\u6211\u4eec\u4e3a\u4e86\u5b58\u50a8\u7684\u65b9\u4fbf\uff0c\u628a\u56fe\u50cf\u7684\u6bcf\u4e00\u884c\u62fc\u63a5\u8d77\u6765\uff0c\u8fd9\u6837\u5c31\u628a\u4e8c\u7ef4\u7684\u56fe\u50cf\u6570\u636e\u8f6c\u5316\u6210\u4e86\u4e00\u7ef4\u6765\u5b58\u50a8\u3002 \"\"\"\n # X\u662f\u4e00\u4e2aM\u884cN\u5217\u7684\u4e8c\u7ef4\u6570\u7ec4\uff0cM\u4ee3\u8868\u5df2\u77e5\u56fe\u7684\u4e2a\u6570\uff0cN\u4ee3\u8868\u6bcf\u4e2a\u56fe\u7684\u5927\u5c0f \n # y\u662f\u4e00\u4e2a\u5927\u5c0f\u4e3aM\u7684\u4e00\u7ef4\u6570\u7ec4\uff0c\u5b58\u50a8\u7684\u662f\u6bcf\u4e00\u4e2a\u56fe\u50cf\u6240\u5bf9\u5e94\u7684\u7c7b\u522b\n self.Xtr = X\n self.ytr = y\n\n def predict(self,X):\n # \u6b64\u5904X\u662f\u4e00\u4e2aK\u884cN\u5217\u7684\u4e8c\u7ef4\u6570\u7ec4\uff0cK\u4ee3\u8868\u9700\u8981\u6d4b\u8bd5\u56fe\u50cf\u7684\u4e2a\u6570\uff0cN\u4ee3\u8868\u6bcf\u4e2a\u56fe\u7684\u5927\u5c0f\uff0c\u8fd9\u4e2aN\u5fc5\u987b\u548cXtr\u4e2d\u7684N\u5339\u914d\n num_test = X.shape[0]\n Ypred = np.zeros(num_test, dtype = self.ytr.dtype) # \u521d\u59cb\u5316\u7c7b\u578b\n\n for i in xrange(num_test):\n # \u8ba1\u7b97 L1\u8ddd\u79bb\u77e9\u9635\n distances = np.sum(np.abs(self.Xtr - X[i,:]), axis = 1)\n # \u5bfb\u627e\u8ddd\u79bb\u6700\u5c0f\u5bf9\u5e94\u56fe\u50cf\u7684\u4e0b\u6807\n min_index = np.argmin(distances)\n # \u4e0b\u6807\u6620\u5c04\u627e\u5230\u5bf9\u5e94\u5206\u7c7b\n Ypred[i] = self.ytr[min_index]\n\n return Yred\n \u4e00. \u7b2c16\u884c\u7684 X.shape[0] \u662f\u4ec0\u4e48\u610f\u601d\uff1f X.shape\u662f\u4e00\u4e2anumpy\u7684\u51fd\u6570\uff0c\u5176\u4e2dX.shape[N]\u4ee3\u8868\u7684\u662f\u8bfb\u53d6\u53d8\u91cfX\u7b2cN-1\u4e2a\u7ef4\u5ea6\u7684\u5927\u5c0f\uff0c\u8fd9\u91cc\u7684X.shape[0]\u5c31\u662f\u8bfb\u53d6\u884c\u6570\uff0c\u5982\u679c\u662fX.shape[1]\u8bfb\u53d6\u7684\u5c31\u662f\u5217\u6570\u3002 \u2003\u2003\u66f4\u8fdb\u4e00\u6b65\u5730\uff0c\u5982\u679c\u62d3\u5c55\u5230\u66f4\u9ad8\u7ef4\u5ea6\u7684\u60c5\u51b5\uff08\u6211\u4eec\u5f88\u591a\u65f6\u5019\u90fd\u4f1a\u4f7f\u7528\u591a\u7ef4\u6570\u7ec4\uff09\uff0c.shape[]\u51fd\u6570\u5c31\u4f1a\u975e\u5e38\u65b9\u4fbf\u3002\u6bd4\u5982\u5bf9\u4e8e\u4e00\u4e2anumpy\u7684array\u53d8\u91cf\uff0c\u5982\u679c\u5b83\u662f\u4e00\u4e2a\u7c7b\u4f3cX[A][B][C][D]\u56db\u7ef4\u6570\u7ec4\uff0c\u7531\u4e8epython\u5bf9\u89c4\u5b9a\u53d8\u91cf\u7684\u6a21\u7cca\u5316\uff0c\u6211\u4eec\u4e0d\u77e5\u9053ABCD\u7684\u5177\u4f53\u503c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u904d\u5386X.shape[0] ~ X.shape[3] \u6765\u5f97\u5230 A ~ D\u3002\u7279\u6b8a\u5730\uff0c\u5c31\u50cf-1\u5728\u6570\u7ec4\u4e2d\u7684\u4f7f\u7528\u4e00\u6837\uff0c\u5982\u679c\u6211\u4eec\u4f7f\u7528X.shape[-1]\uff0c\u5b83\u4f1a\u8fd4\u56de\u6700\u540e\u4e00\u4e2a\u7ef4\u5ea6\u7684\u5927\u5c0f\uff0c\u4e5f\u5c31\u662fX.shape[3]\u3002 \u4e8c\u3001\u7b2c17\u884c\u7684np.zeros()\u7528\u6765\u505a\u4ec0\u4e48\uff1f \u2003\u2003\u5c31\u50cf\u6211\u4eec\u5728C\u8bed\u8a00\u4e2d\u9700\u8981\u5b9a\u4e49\u53d8\u91cf\u5e76\u4e14\u8d4b\u521d\u503c\u4e00\u6837\uff0c\u5728python\u4e2d\u6211\u4eec\u540c\u65f6\u9700\u8981\u8fd9\u6837\u505a\uff0c\u4f46\u662fpython\u4f1a\u901a\u8fc7\u4f60\u8d4b\u7684\u503c\u6765\u81ea\u52a8\u4e3a\u53d8\u91cf\u5224\u65ad\u7c7b\u578b\uff0c\u6240\u4ee5\u7b80\u5316\u4e86\u53d8\u91cf\u7684\u5b9a\u4e49\u6b65\u9aa4\u3002array\u662fnumpy\u5e93\u4e2d\u7684\u4e00\u4e2a\u975e\u5e38\u7075\u6d3b\u7684\u53d8\u91cf\u683c\u5f0f\uff0c\u901a\u8fc7array\u4ee5\u53ca\u5b83\u9644\u5e26\u7684\u4e00\u4e9b\u51fd\u6570\uff0c\u53ef\u4ee5\u5224\u65ad\u6574\u4e2a\u6570\u7ec4\u7684\u7ef4\u5ea6\u3001\u5927\u5c0f\uff0c\u751a\u81f3\u53ef\u4ee5\u505a\u5c40\u90e8\u6c42\u548c\u3001\u8f6c\u7f6e\u3001\u77e9\u9635\u4e58\u6cd5\u7b49\u7b49\uff0c\u800c\u5bf9array\u8d4b\u521d\u503c\u5c31\u53ef\u4ee5\u4f7f\u7528np.zeros(tuple,type)\u5f97\u5230\u4e00\u4e2a\u786e\u5b9a\u5927\u5c0f\u7684\u3001\u6574\u4f53\u7684\u8d4b\u96f6\u6570\u7ec4\u3002tuple\u4ee3\u8868\u7684\u662f\u6574\u4e2aarray\u7684\u5f62\u72b6\uff0c\u6bd4\u5982(5,2,3)\u5f97\u51fa\u6765\u7684\u5c31\u662f\u6570\u7ec4a[5][2][3]\uff0ctype\u5c31\u662f\u6570\u7ec4\u7684\u6570\u636e\u7c7b\u578b\u3002 \u4e09\u3001\u7b2c21\u884c\u7684X[i, :]\u662f\u4ec0\u4e48\u610f\u601d\uff1f \u2003\u2003\u8fd9\u662fpython\u4e2d\u7684\u4e00\u79cd\u7701\u7565\u5f62\u5f0f\uff0c\u9996\u5148\uff0c\u5bf9\u4e8e\u7b26\u53f7:\u672c\u8eab\uff0c\u5b83\u672c\u8eab\u4ee3\u8868\u8303\u56f4\u7684\u9009\u53d6\uff0c\u6bd4\u5982[2:5]\u9009\u53d6\u7684\u5c31\u662f [2]\u3001[3]\u548c[4]\uff0c\u5373\\([2,5)\\)\u533a\u95f4\u7684\u6240\u6709\u6574\u6570\u53f7\u3002\u800c\u5982\u679c\u628a\u524d\u9762\u76842\u7701\u53bb\uff0c\u5219\u9ed8\u8ba4\u4ece\u4e0b\u68070\u5f00\u59cb\uff0c\u5982\u679c\u540e\u9762\u76845\u88ab\u7701\u53bb\uff0c\u5219\u9ed8\u8ba4\u5728\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u7ed3\u675f\u3002\u56e0\u6b64\uff0c\u5f53\u7b2c\u4e8c\u7ef4\u5ea6\u4ec5\u6709:\u65f6\uff0c\u524d\u540e\u6570\u5b57\u90fd\u88ab\u7701\u53bb\uff0c\u56e0\u6b64\u8fd9\u4e2a\u9009\u53d6\u662f\u4ece0\u5230\u6700\u540e\u4e00\u4e2a\u5143\u7d20\uff0c\u56e0\u6b64\u662f\u9009\u4e2d\u4e86\u4e00\u6574\u884c\u3002 \u4e09\u3001\u7b2c21\u884c\u7684axis = 1\u662f\u4ec0\u4e48\u610f\u601d\uff1f axis\u662fnp.sum()\u4e2d\u7684\u4e00\u4e2a\u53c2\u6570\uff0c\u800c\u51fd\u6570np.sum()\u662f\u628a\u6570\u7ec4\u7684\u67d0\u51e0\u4e2a\u7ef4\u5ea6\u7684\u6570\u5b57\u5168\u90e8\u52a0\u8d77\u6765\uff0c\u50cf\u662f\u505a\u4e00\u4e9b\u6295\u5f71\u64cd\u4f5c\uff0c\u628a\u6574\u4e2a\u6570\u7ec4\u964d\u4e86\u82e5\u5e72\u4e2a\u7ef4\u5ea6\u3002\u8fd9\u4e2aaxis\u5c31\u662f\u5bf9\u5e94\u7684\u7ef4\u5ea6\u3002\u6bd4\u5982\u6709\u4e09\u7ef4\u6570\u7ec4\uff0c\u6211\u4eec\u60f3\u8981\u628a\u5b83\u7684\u6700\u540e\u4e00\u4e2a\u4e2a\u7ef4\u5ea6\u5168\u90e8\u52a0\u8d77\u6765\uff0c\u5c31\u53ef\u4ee5\u8bbe\u7f6e\u53c2\u6570axis = -1\u3002\u5728\u8fd9\u4e2a\u4f8b\u7a0b\u4e2d\uff0c\u628aaxis\u8bbe\u7f6e\u4e3a1\uff0c\u8fd9\u610f\u5473\u7740\u6c42\u548c\u5c06\u5728\u5e8f\u53f71\u7684\u7ef4\u5ea6\u8fdb\u884c\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e2a\u4e8c\u7ef4\u6570\u7ec4\u7684\u6bcf\u4e00\u884c\u8fdb\u884c\u6c42\u548c\u3002
\u2003\u2003\u76f4\u63a5\u5730\u628a\u5404\u4e2a\u50cf\u7d20\u7684\u5dee\u8ddd\u76f8\u52a0\u4f3c\u4e4e\u8fdd\u80cc\u6211\u4eec\u5bf9\u8ddd\u79bb\u7684\u8ba4\u8bc6\uff0c\u5c31\u50cf\u6211\u5411\u4e1c\u8d70\u4e86100\u7c73\uff0c\u5411\u5317\u8d70\u4e86100\u7c73\uff0c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u6211\u4eec\u8d70\u5230\u4e86\u8ddd\u79bb\u539f\u70b9200\u7c73\u7684\u5730\u65b9\u3002\u56e0\u6b64\uff0cL2\u8ddd\u79bb\u8fd0\u7528\u4e86\u6b27\u6c0f\u7a7a\u95f4\u7684\u523b\u753b\uff0c\u5c06\u6bcf\u4e00\u4e2a\u50cf\u7d20\u770b\u4f5c\u4e00\u4e2a\u7ef4\u5ea6\uff0c\u7136\u540e\u8ba1\u7b97\u591a\u7ef4\u7a7a\u95f4\u4e2d\u7684\u8ddd\u79bb\u3002
L2\u8ddd\u79bb\u516c\u5f0f\uff1a
\\[ L_2 = \\sqrt{\\sum_{p_{ij} \\in img}(p_{ij} - q_{ij})^2}, q_{ij} = \\text{constant} \\]L2\u8ddd\u79bb\u548c\u8fd0\u884c\u4f18\u5316
\u56e0\u4e3aL2\u8ddd\u79bb\u7684\u516c\u5f0f\u7279\u6027\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u901a\u8fc7\u4e00\u5b9a\u7684\u62c6\u5206\uff0c\u53ef\u4ee5\u5927\u5927\u4f18\u5316\u7a0b\u5e8f\u7684\u8fd0\u884c\u901f\u5ea6\u3002\u67e5\u770b\u5177\u4f53\u4f18\u5316
"},{"location":"ScientificResearch/CS231N/L2/#kknn","title":"\u524dK\u6700\u8fd1\u90bb\u5c45\u7b97\u6cd5\uff08KNN\uff09","text":"\u2003\u2003\u5728\u5148\u524d\u7684\u6700\u8fd1\u90bb\u5c45\u7b97\u6cd5\u4e2d\uff0c\u6211\u4eec\u76f4\u63a5\u91c7\u7528\u6700\u8fd1\u7684\u90bb\u5c45\u4f5c\u4e3a\u6211\u4eec\u56fe\u50cf\u7684\u5206\u7c7b\u4f9d\u636e\u3002\u8fd9\u5f88\u65b9\u4fbf\uff0c\u4f46\u662f\u5b83\u5bf9\u4e8e\u4e00\u4e9b\u8fb9\u754c\u60c5\u51b5\u7684\u5224\u65ad\u662f\u975e\u5e38\u7cdf\u7cd5\u7684\u3002\u6bd4\u5982\uff0c\u5982\u679c\u6211\u4eec\u7528\u4e8c\u7ef4\u5e73\u9762\u7684\u683c\u70b9\u6765\u8868\u793a\u5df2\u77e5\u7684\u70b9\uff0c\u5e76\u7528\u989c\u8272\u6765\u8868\u793a\u5b83\u4eec\u7684\u7c7b\u578b\uff0c\u800c\u8ba9\u70b9\u4e0e\u70b9\u95f4\u7684\u8ddd\u79bb\u6765\u8868\u793a\u56fe\u50cf\u95f4\u7684\u8ddd\u79bb\uff08\u8fd9\u6837\u7684\u8868\u793a\u5e76\u4e0d\u5b8c\u5168\u5408\u9002\uff0c\u4f46\u662f\u81f3\u5c11\u53ef\u4ee5\u8bf4\u660e\u95ee\u9898\uff09\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u5982\u4e0b\u7684\u56fe\uff1a
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