Project Euler 62 Solution (TheAlgorithms#3029)

* Add solution for Project Euler 62

* Add doctests and annotate function params and return values for get_digits()

* Add extra newline between functions to fix flake8 errors

* Add extra newlines between function names

* Add missing return type for solution()

* Remove parenthesis from if statement

* Remove parentheses from while loop

* Add to explanation and fix second Travis build

* Compress get_digits(), add tests for solution(), add fstring and positional arg for solution()

* Remove input param when calling solution()

* Remove test case for the answer

Author: peteryao7

Diff for: DIRECTORY.md

@@ -666,6 +666,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_551/sol1.py)
   * Problem 56
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_56/sol1.py)
+  * Problem 62
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_62/sol1.py)
   * Problem 63
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_63/sol1.py)
   * Problem 67

Diff for: project_euler/problem_62/__init__.py

@@ -0,0 +1,62 @@
+"""
+Project Euler 62
+https://projecteuler.net/problem=62
+
+The cube, 41063625 (345^3), can be permuted to produce two other cubes:
+56623104 (384^3) and 66430125 (405^3). In fact, 41063625 is the smallest cube
+which has exactly three permutations of its digits which are also cube.
+
+Find the smallest cube for which exactly five permutations of its digits are
+cube.
+"""
+
+from collections import defaultdict
+
+
+def solution(max_base: int = 5) -> int:
+    """
+    Iterate through every possible cube and sort the cube's digits in
+    ascending order. Sorting maintains an ordering of the digits that allows
+    you to compare permutations. Store each sorted sequence of digits in a
+    dictionary, whose key is the sequence of digits and value is a list of
+    numbers that are the base of the cube.
+
+    Once you find 5 numbers that produce the same sequence of digits, return
+    the smallest one, which is at index 0 since we insert each base number in
+    ascending order.
+
+    >>> solution(2)
+    125
+    >>> solution(3)
+    41063625
+    """
+    freqs = defaultdict(list)
+    num = 0
+
+    while True:
+        digits = get_digits(num)
+        freqs[digits].append(num)
+
+        if len(freqs[digits]) == max_base:
+            base = freqs[digits][0] ** 3
+            return base
+
+        num += 1
+
+
+def get_digits(num: int) -> str:
+    """
+    Computes the sorted sequence of digits of the cube of num.
+
+    >>> get_digits(3)
+    '27'
+    >>> get_digits(99)
+    '027999'
+    >>> get_digits(123)
+    '0166788'
+    """
+    return "".join(sorted(list(str(num ** 3))))
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")