#1033482 (PyPy3) No.2528 pop_(backfront or not)

• 問題: No.2528 pop_(backfront or not)
• ユーザー: LyricalMaestro
• 提出日時: 2024-12-27 23:57:54
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 482 ms / 2,000 ms
• コード長: 2,370 bytes
• コンパイル時間: 375 ms
• コンパイル使用メモリ: 82,048 KB
• 実行使用メモリ: 76,452 KB
• 最終ジャッジ日時: 2024-12-27 23:58:00
• 合計ジャッジ時間: 4,851 ms
• ジャッジサーバーID （参考情報）: judge4 / judge1

ファイルパターン	結果
other	AC * 19

ソースコード

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## https://yukicoder.me/problems/no/1766
MOD = 998244353
class CombinationCalculator:
    """
    modを考慮したPermutation, Combinationを計算するためのクラス
    """    
    def __init__(self, size, mod):
        self.mod = mod
        self.factorial = [0] * (size + 1)
        self.factorial[0] = 1
        for i in range(1, size + 1):
            self.factorial[i] = (i * self.factorial[i - 1]) % self.mod
        
        self.inv_factorial = [0] * (size + 1)
        self.inv_factorial[size] = pow(self.factorial[size], self.mod - 2, self.mod)
        for i in reversed(range(size)):
            self.inv_factorial[i] = ((i + 1) * self.inv_factorial[i + 1]) % self.mod
    def calc_combination(self, n, r):
        if n < 0 or n < r or r < 0:
            return 0
        if r == 0 or n == r:
            return 1
        
        ans = self.inv_factorial[n - r] * self.inv_factorial[r]
        ans %= self.mod
        ans *= self.factorial[n]
        ans %= self.mod
        return ans
    
    def calc_permutation(self, n, r):
        if n < 0 or n < r:
            return 0
        ans = self.inv_factorial[n - r]
        ans *= self.factorial[n]
        ans %= self.mod
        return ans
        
def main():
    N = int(input())
    combi = CombinationCalculator(2 * N + 1, MOD)
    # n = 1
    dp = [0, 1, 0]
    for n in range(1, N):
        new_dp = [0] * (2 * (n + 1) + 1)
        # pop up 
        for j in range(1, 2 * (n + 1)):
            new_dp[j] += dp[j - 1]
            new_dp[j] %= MOD
        # 任意に選ぶ
        for j in range(2 * (n + 1) + 1):
            ## 左2つ選ぶ
            if j > 2:
                new_dp[j] += combi.calc_combination(j - 1, 2) * dp[j - 2]
                new_dp[j] %= MOD
            ## 左右1つずつ選ぶ
            if j > 1 and j < 2 * (n + 1) - 1:
                a = ((j - 1) * (2 * (n + 1) - 1 - j)) % MOD
                a *= dp[j - 1]
                a %= MOD
                new_dp[j] += a
                new_dp[j ] %=MOD
            
            ## 右を2つ選ぶ
            if j < 2 * (n + 1) - 2:
                x = 2 * (n + 1) - j - 1
                new_dp[j] += combi.calc_combination(x, 2) * dp[j]
                new_dp[j] %= MOD
        dp = new_dp
    
    for i in range(2 * N + 1):
        print(dp[i])
if __name__ == '__main__':
    main()
 
 
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