結果

問題 No.1392 Don't be together
ユーザー chineristAC
提出日時 2020-09-01 12:23:03
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,421 ms / 2,000 ms
コード長 1,633 bytes
コンパイル時間 172 ms
コンパイル使用メモリ 82,224 KB
実行使用メモリ 277,596 KB
最終ジャッジ日時 2024-11-21 00:41:05
合計ジャッジ時間 19,693 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 27
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ソースコード

diff #
プレゼンテーションモードにする

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod
mod = 998244353
N = 2*10**5
g1 = [1]*(N+1)
g2 = [1]*(N+1)
inverse = [1]*(N+1)
for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inverse[i]=( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inverse[i]) % mod )
inverse[0]=0
N,M = map(int,input().split())
P = list(map(int,input().split()))
assert(2<=N<=5000)
assert(2<=M<=N)
assert(len(P)==N)
assert(all(i+1!=P[i] for i in range(N)))
P = [P[i]-1 for i in range(N)]
cycle = []
used = [False]*N
for i in range(N):
    if not used[i]:
        used[i] = True
        c = 1
        pos = i
        while not used[P[pos]]:
            pos = P[pos]
            used[pos] = True
            c += 1
        cycle.append(c)
P.sort()
assert(all(i==P[i] for i in range(N)))
n = len(cycle)
binom_poly = [1]
for i in range(n):
    c = [cmb(cycle[i],j,mod)*pow(-1,j,mod) for j in range(1,cycle[i]+1)]
    c[0] = (c[0] + 1) % mod
    merged = [0 for i in range(len(binom_poly) + len(c) - 1)]
    for i in range(len(binom_poly)):
        for j in range(len(c)):
            merged[i+j] += binom_poly[i] * c[j]
            merged[i+j] %= mod
    binom_poly = merged
Stirling = [[int(i==j or i==1) for i in range(M+1)] for j in range(N+1)]
Stirling[0][0] = 0
for j in range(2,M+1):
    for i in range(j+1,N+1):
        Stirling[i][j] = Stirling[i-1][j-1] + j * Stirling[i-1][j]
        Stirling[i][j] %= mod
ans = 0
for i in range(N-n+1):
    ans += Stirling[n+i][M] * binom_poly[i]
    ans %= mod
ans *= (-1)**N
ans %= mod
print(ans)
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