Symbol(clack:cancel)

solutions/0000_0029/0028.NumDiagonals/euler_28.py

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+"""
+Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
+
+21 22 23 24 25
+20  7  8  9 10
+19  6  1  2 11
+18  5  4  3 12
+17 16 15 14 13
+
+It can be verified that the sum of the numbers on the diagonals is 101 .
+
+What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
+"""
+
+import time
+from functools import lru_cache
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start_time = time.time()
+        result = func(*args, **kwargs)
+        end_time = time.time()
+        print(f"{func.__name__} time: {end_time - start_time:.8f} seconds")
+        return result
+
+    return wrapper
+
+
+def sum_right(length: int) -> int:
+    sumo = 0
+    last = 1
+    for i in range(1, length + 1):
+        sumo += last + 2 * (i - 1)
+        last += 2 * (i - 1)
+    return sumo
+
+
+@lru_cache(maxsize=None)
+def sum_left(length: int) -> tuple[list[int], int]:
+    if length == 1:
+        return [1], 1
+    else:
+        two, sum_o = sum_left(length - 2)
+        i = length // 2
+        max_two = max(two)
+        new_two = [max_two + i * 4, max_two + i * 8]
+        return new_two, sum_o + sum(new_two)
+
+
+def sum_of_diagonals(length: int) -> int:
+    if length % 2 == 0:
+        raise ValueError("Input must be an odd number")
+    return sum_left(length)[1] + sum_right(length) - 1
+
+
+@timer
+def main_pro(length: int) -> None:
+    sum_o = sum_of_diagonals(length)
+    print(sum_o)
+
+
+@timer
+def main_math(length: int) -> None:
+    if length % 2 == 0:
+        raise ValueError("Input must be an odd number")
+    n = length // 2
+    sum_o = 1 + 10 * n**2 + (16 * n**3 + 26 * n) / 3
+    print(int(sum_o))
+
+
+@timer
+def main_math_pro(length: int) -> None:
+    if length % 2 == 0:
+        raise ValueError("Input must be an odd number")
+    n = length // 2
+    maxnum = int(length**2)
+    sumo = 1
+    for i in range(n, 0, -1):
+        delta = 2 * i
+        sumo += 4 * maxnum - 6 * delta
+        maxnum -= delta * 4
+    print(int(sumo))
+
+
+if __name__ == "__main__":
+    length = 1001
+    main_math(length)
+    main_pro(length)
+    main_math_pro(length)

solutions/0000_0029/0028.NumDiagonals/readme.md

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+https://oeis.org/A114254