Add third solution for the Euler project problem 16.

Author: mindaugl

project_euler/problem_016/sol3.py

@@ -0,0 +1,44 @@
+"""
+Problem 16: https://projecteuler.net/problem=16
+
+2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
+
+What is the sum of the digits of the number 2^1000?
+"""
+
+from numpy import log10, zeros
+
+
+def solution(power: int = 1000) -> int:
+    """
+    Calculates the sum of digits by explicit construction of digits array
+    without the help of Python's large integer property.
+
+    >>> solution(50)
+    76
+    >>> solution(20)
+    31
+    >>> solution(15)
+    26
+    >>> solution(3)
+    8
+    """
+
+    digits = zeros(int(power * log10(2)) + 1)
+    digits[0] = 1
+    dig_count = 1
+    for _ in range(power):
+        carry = 0
+        for d in range(dig_count):
+            digits[d] = digits[d] * 2 + carry
+            carry = digits[d] // 10
+            digits[d] %= 10
+        if carry > 0:
+            digits[dig_count] = carry
+            dig_count += 1
+
+    return int(sum(digits))
+
+
+if __name__ == "__main__":
+    print(solution())