Created problem_34 in project_euler

project_euler/problem_34/__init__.py

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+#

project_euler/problem_34/sol1.py

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+"""
+145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
+Find the sum of all numbers which are equal to the sum of the factorial of their digits.
+Note: As 1! = 1 and 2! = 2 are not sums they are not included.
+"""
+
+
+def factorial(n: int) -> int:
+    """Return the factorial of n.
+    >>> factorial(5)
+    120
+    >>> factorial(1)
+    1
+    >>> factorial(0)
+    1
+    >>> factorial(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: n must be >= 0
+    >>> factorial(1.1)
+    Traceback (most recent call last):
+        ...
+    ValueError: n must be exact integer
+    """
+
+    if not n >= 0:
+        raise ValueError("n must be >= 0")
+    if int(n) != n:
+        raise ValueError("n must be exact integer")
+    if n + 1 == n:  # catch a value like 1e300
+        raise OverflowError("n too large")
+    result = 1
+    factor = 2
+    while factor <= n:
+        result *= factor
+        factor += 1
+    return result
+
+
+def sum_of_digit_factorial(n: int) -> int:
+    """
+    Returns the sum of the digits in n
+    >>> sum_of_digit_factorial(15)
+    121
+    >>> sum_of_digit_factorial(0)
+    1
+    """
+    return sum(factorial(int(digit)) for digit in str(n))
+
+
+def compute() -> int:
+    """
+    Returns the sum of all numbers whose
+    sum of the factorials of all digits
+    add up to the number itself.
+    >>> compute()
+    40730
+    """
+    return sum(
+        num
+        for num in range(3, 7 * factorial(9) + 1)
+        if sum_of_digit_factorial(num) == num
+    )
+
+
+if __name__ == "__main__":
+    print(compute())