Symbol(clack:cancel)

solutions/0000_0029/0006.SumSquareDifference/eular_6.py

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+"""
+The sum of the squares of the first ten natural numbers is 1^2 + 2^2 + ... + 10^2 = 385,
+The square of the sum of the first ten natural numbers is (1+2+...+10)^2 = 55^2 = 3025,
+Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.
+Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
+"""
+
+import time
+
+import numpy as np
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start = time.time()
+        result = func(*args, **kwargs)
+        end = time.time()
+        print(f"{func.__name__} took {end - start:.6f} seconds")
+        return result
+
+    return wrapper
+
+
+@timer
+def sum_square_difference(n: int) -> int:
+    res = 0
+    for i in range(1, n + 1):
+        res += sum(np.array(list(range(1, i))) * i)
+
+    return 2 * res
+
+
+@timer
+def better_sum_square(n: int) -> int:
+    """https://en.wikipedia.org/wiki/Faulhaber%27s_formula"""
+    su = ((1 + n) * n // 2) ** 2
+    sq = (2 * n + 1) * (n + 1) * n // 6
+    return su - sq
+
+
+if __name__ == "__main__":
+    print(sum_square_difference(100))
+    print(better_sum_square(100))