Solve p72 in python (85th solved!)

README.rst

@@ -107,7 +107,7 @@ Olivia's Project Euler Solutions
    |            |                            |        | |Lu-Cov| |br|     |
    |            |                            |        | |LuaCheck|        |
    +------------+----------------------------+--------+-------------------+
-   | Python     | CPython 3.6+ |br|          | 84     | |Python| |br|     |
+   | Python     | CPython 3.6+ |br|          | 85     | |Python| |br|     |
    |            | Pypy 3.6+ |br|             |        | |Py-Cov| |br|     |
    |            | GraalPy 23.1+ |br|         |        | |CodeQL| |br|     |
    |            | Browser [#]_               |        | |PythonLint|      |

_data/answers.tsv

@@ -64,6 +64,7 @@ ID	type	size	answer
 69	int	32	510510
 70	int	64	8319823
 71	int	32	428570
+72	int	64	303963552391
 73	int	32	7295372
 74	int	16	402
 76	int	32	190569291

docs/index.rst

@@ -208,6 +208,8 @@ Problems Solved
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+------------+
   |:prob:`071`|           |            |            |            |            |            |            |:py-d:`0071`|            |
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+------------+
+  |:prob:`072`|           |            |            |            |            |            |            |:py-d:`0072`|            |
+  +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+------------+
   |:prob:`073`|           |            |            |            |            |            |            |:py-d:`0073`|            |
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+------------+
   |:prob:`074`|           |            |            |            |            |            |            |:py-d:`0074`|            |

docs/src/python/lib/primes.rst

@@ -6,6 +6,8 @@ View source code :source:`python/src/lib/primes.py`
 Includes
 --------
 
+- :external:py:class:`fractions.Fraction`
+- :external:py:func:`functools.reduce`
 - :external:py:func:`itertools.count`
 - :external:py:func:`itertools.filterfalse`
 - :external:py:func:`itertools.takewhile`

docs/src/python/p0070.rst

@@ -6,6 +6,7 @@ View source code :source:`python/src/p0070.py`
 Includes
 --------
 
+- :py:func:`~python.src.lib.primes.fast_totient`
 - :external:py:func:`itertools.chain`
 - :external:py:func:`functools.reduce`
 

docs/src/python/p0072.rst

@@ -0,0 +1,24 @@
+Python Implementation of Problem 72
+===================================
+
+View source code :source:`python/src/p0072.py`
+
+Includes
+--------
+
+- :py:func:`~python.src.lib.primes.totient`
+- :external:py:func:`itertools.chain`
+- :external:py:func:`functools.reduce`
+
+Problem Solution
+----------------
+
+.. automodule:: python.src.p0072
+   :members:
+   :undoc-members:
+
+.. literalinclude:: ../../../python/src/p0072.py
+   :language: python
+   :linenos:
+
+.. tags:: fraction, gcd, stern-brocot-tree, coprime-numbers, totient-function

python/README.rst

@@ -191,6 +191,7 @@ Problems Solved
 -  ☒ `69 <./src/p0069.py>`__
 -  ☒ `70 <./src/p0070.py>`__
 -  ☒ `71 <./src/p0071.py>`__
+-  ☒ `72 <./src/p0072.py>`__
 -  ☒ `73 <./src/p0073.py>`__
 -  ☒ `74 <./src/p0074.py>`__
 -  ☒ `76 <./src/p0076.py>`__

python/src/lib/primes.py

@@ -1,3 +1,5 @@
+from fractions import Fraction
+from functools import reduce
 from itertools import count, filterfalse, takewhile
 from math import ceil, sqrt
 from pathlib import Path
@@ -138,3 +140,13 @@ def primes_and_negatives(*args: int) -> Iterator[int]:
     for p in primes(*args):
         yield p
         yield -p
+
+
+def fast_totient(n: int) -> int:
+    """A shortcut method to calculate Euler's totient function which assumes n has *distinct* prime factors."""
+    return reduce(lambda x, y: x * (y - 1), prime_factors(n), 1)
+
+
+def totient(n: int) -> int:
+    """Calculates Euler's totient function in the general case."""
+    return int(n * reduce(lambda x, y: x * (1 - Fraction(1, y)), set(prime_factors(n)), 1))

python/src/p0070.py

@@ -15,14 +15,9 @@
 Find the value of $n$, $1 \\lt n \\lt 10^7$, for which $\\phi(n)$ is a permutation of $n$ and the ratio $n/\\phi(n)$
 produces a minimum.
 """
-from functools import reduce
 from itertools import chain
 
-from .lib.primes import prime_factors
-
-
-def totient(n: int) -> int:
-    return reduce(lambda x, y: x * (y - 1), prime_factors(n), 1)
+from .lib.primes import fast_totient
 
 
 def main() -> int:
@@ -42,7 +37,7 @@ def main() -> int:
       range(6 + 17, stop, 30),  # 6k - 1, x ≡ 4 (mod 5)
       range(6 + 19, stop, 30)   # 6k + 1, x ≡ 4 (mod 5)
     )):
-        t = totient(x)
+        t = fast_totient(x)
         strx = str(x)
         strt = str(t)
         if not all(strx.count(d) == strt.count(d) for d in set(strx)):

python/src/p0072.py

@@ -0,0 +1,21 @@
+"""
+Project Euler Problem 72
+
+Problem:
+
+Consider the fraction, n / d, where n and d are positive integers. If n < d and HCF(n,d)=1, it is
+called a reduced proper fraction.
+
+If we list the set of reduced proper fractions for d <= 8 in ascending order of size, we get:
+
+(1 / 8), (1 / 7), (1 / 6), (1 / 5), (1 / 4), (2 / 7), (1 / 3), (3 / 8), (2 / 5), (3 / 7), (1 / 2),
+(4 / 7), (3 / 5), (5 / 8), (2 / 3), (5 / 7), (3 / 4), (4 / 5), (5 / 6), (6 / 7), (7 / 8)
+
+It can be seen that there are 21 elements in this set.
+How many elements would be contained in the set of reduced proper fractions for d <= 1000000?
+"""
+from .lib.primes import totient
+
+
+def main() -> int:
+    return sum(totient(n) for n in range(2, 1000001))

python/test_euler.py

@@ -23,8 +23,7 @@
         *range(55, 61),
         63,
         67,
-        *range(69, 72),
-        *range(73, 75),
+        *range(69, 75),
         *range(76, 78),
         79,
         81,