結果

問題 No.1143 面積Nの三角形
ユーザー lam6er
提出日時 2025-03-31 17:35:04
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 72 ms / 800 ms
コード長 2,063 bytes
コンパイル時間 216 ms
コンパイル使用メモリ 82,256 KB
実行使用メモリ 76,652 KB
最終ジャッジ日時 2025-03-31 17:36:12
合計ジャッジ時間 2,073 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
sample AC * 2
other AC * 18
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

import math
def factorize(n):
    factors = {}
    while n % 2 == 0:
        factors[2] = factors.get(2, 0) + 1
        n //= 2
    i = 3
    while i * i <= n:
        while n % i == 0:
            factors[i] = factors.get(i, 0) + 1
            n //= i
        i += 2
    if n > 1:
        factors[n] = 1
    return factors
def generate_divisors(factors):
    divisors = [1]
    for p in factors:
        exp = factors[p]
        new_divisors = []
        current_power = 1
        for _ in range(exp + 1):
            for d in divisors:
                new_divisors.append(d * current_power)
            current_power *= p
        divisors = list(set(new_divisors))  # Remove duplicates
    divisors.sort()
    return divisors
def main():
    N = int(input().strip())
    if N == 0:
        print(0)
        return
    K = N * N
    factors_n = factorize(N)
    # Prepare factors for N^2 (each exponent doubled)
    factors_k = {}
    for p in factors_n:
        factors_k[p] = factors_n[p] * 2
    divisors = generate_divisors(factors_k)
    count = 0
    for z in divisors:
        if z == 0:
            continue
        if K % z != 0:
            continue  # Ensure divisibility, though should always be true
        Kz = K // z
        if Kz == 0:
            continue
        max_y = int(Kz ** (1/3)) + 2  # Estimate the cube root and add buffer
        max_y = min(max_y, Kz)  # Ensure y doesn't exceed Kz
        y_start = z
        y_end = max_y
        for y in range(y_start, y_end + 1):
            if y == 0:
                continue
            if Kz % y != 0:
                continue
            q = Kz // y
            sum_yz = y + z
            D = sum_yz ** 2 + 4 * q
            s = math.isqrt(D)
            if s * s != D:
                continue
            numerator = (-sum_yz + s)
            if numerator <= 0:
                continue
            if numerator % 2 != 0:
                continue
            x = numerator // 2
            if x >= y:
                count += 1
    print(count)
if __name__ == "__main__":
    main()
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