#696005 (PyPy3) No.1667 Forest

• 問題: No.1667 Forest
• ユーザー: tktk_snsn
• 提出日時: 2021-09-03 23:19:02
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 766 ms / 3,000 ms
• コード長: 2,206 bytes
• コンパイル時間: 272 ms
• コンパイル使用メモリ: 82,284 KB
• 実行使用メモリ: 94,084 KB
• 最終ジャッジ日時: 2024-12-15 17:54:32
• 合計ジャッジ時間: 6,461 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
sample	AC * 3
other	AC * 15

ソースコード

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class Combination:
    """
    SIZEが10**6程度以下の二項係数を何回も呼び出したいときに使う
    使い方:
    comb = Combination(SIZE, MOD)
    comb(10, 3) => 120
    """
    def __init__(self, N, MOD=10 ** 9 + 7):
        self.MOD = MOD
        self.__make_factorial_list(N)
    def __call__(self, n, k):
        if k < 0 or k > n:
            return 0
        res = self.fact[n] * self.inv[k] % self.MOD
        res = res * self.inv[n - k] % self.MOD
        return res
    def nPk(self, n, k):
        if k < 0 or k > n:
            return 0
        return self.fact[n] * self.inv[n - k] % self.MOD
    def nHk(self, n, k):
        if k == 0:
            return 1
        return self.__call__(n + k - 1, k)
    def __make_factorial_list(self, N):
        self.fact = [1] * (N + 1)
        self.inv = [1] * (N + 1)
        MOD = self.MOD
        for i in range(1, N + 1):
            self.fact[i] = (self.fact[i - 1] * i) % MOD
        self.inv[N] = pow(self.fact[N], MOD - 2, MOD)
        for i in range(N, 0, -1):
            self.inv[i - 1] = (self.inv[i] * i) % MOD
        return
n, mod = map(int, input().split())
comb = Combination(n + 5, mod)
fact = comb.fact
inv = comb.inv
div = [pow(i, mod-2, mod) for i in range(n + 1)]
# dp[i, j]: 頂点iこ,辺jこ: 何通りか
dp = [[0] * n for _ in range(n + 1)]
dp[0][0] = 1
for i in range(1, n+1):
    dp[i][0] = dp[i-1][0] * (n - i + 1) * pow(i, mod-2, mod) % mod
for i in range(2, n+1):  # 連結成分の大きさiを並べる
    ndp = [[0] * n for _ in range(n + 1)]
    tree = pow(i, i-2, mod)
    for k in range(1, n+1):
        node = i * k
        if node > n:
            break
        edge = (i - 1) * k
        fi = pow(fact[i], k, mod)
        fi = pow(fi, mod-2, mod)
        ti = pow(tree, k, mod)
        for x in range(n - node + 1):
            choice = comb.nPk(n - x, node) * fi * ti % mod * inv[k] % mod
            for y in range(n - edge):
                ndp[x+node][y+edge] += dp[x][y] * choice
                ndp[x+node][y+edge] %= mod
    for j in range(n+1):
        for k in range(n):
            dp[j][k] += ndp[j][k]
            dp[j][k] %= mod
for i in range(n):
    print(dp[n][i])
 
 
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