subarray_sums_divisble_by_k.ipynb

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    "## 974. Subarray Sums Divisible by K\n",
    "**Medium**\n",
    "\n",
    "Given an integer array nums and an integer k, return the number of non-empty subarrays that have a sum divisible by k.\n",
    "\n",
    "A subarray is a contiguous part of an array.\n",
    "\n",
    "Example 1:\\\n",
    "**Input**: nums = `[4,5,0,-2,-3,1]`, `k = 5`\\\n",
    "**Output**: `7`\n",
    "\n",
    "Explanation: There are 7 subarrays with a sum divisible by `k = 5`:\\\n",
    "`[4, 5, 0, -2, -3, 1], [5], [5, 0], [5, 0, -2, -3], [0], [0, -2, -3], [-2, -3]`\\\n",
    "Example 2:\n",
    "Input: nums = [5], k = 9\n",
    "Output: 0"
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    "class Solution:\n",
    "    def subarraysDivByK(self, nums: list[int], k: int) -> int:\n",
    "        prefix_sum = 0s\n",
    "        count = 0\n",
    "        mod_count = {0: 1}  # Initialize with 0:1 to handle the case where the prefix sum itself is divisible by k\n",
    "        \n",
    "        for num in nums:\n",
    "            prefix_sum += num\n",
    "            mod = prefix_sum % k\n",
    "            \n",
    "            # If mod is negative, convert it to a positive equivalent\n",
    "            if mod < 0:\n",
    "                mod += k\n",
    "            \n",
    "            # If mod is in the hashmap, it means we have seen this mod value before\n",
    "            if mod in mod_count:\n",
    "                count += mod_count[mod]\n",
    "            \n",
    "            # Update the count of this mod value in the hashmap\n",
    "            if mod in mod_count:\n",
    "                mod_count[mod] += 1\n",
    "            else:\n",
    "                mod_count[mod] = 1\n",
    "        \n",
    "        return count"
   ]
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    "solution = Solution()\n",
    "nums = [4,5,0,-2,-3,1]\n",
    "k = 2\n",
    "\n",
    "solution.subarraysDivByK(nums, k)"
   ]
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