結果

問題 No.1392 Don't be together
ユーザー chineristACchineristAC
提出日時 2020-09-09 02:25:44
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 471 ms / 2,000 ms
コード長 4,474 bytes
コンパイル時間 370 ms
コンパイル使用メモリ 82,292 KB
実行使用メモリ 112,436 KB
最終ジャッジ日時 2024-05-07 22:17:57
合計ジャッジ時間 9,203 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 67 ms
68,352 KB
testcase_01 AC 60 ms
65,024 KB
testcase_02 AC 77 ms
73,376 KB
testcase_03 AC 62 ms
65,152 KB
testcase_04 AC 73 ms
71,424 KB
testcase_05 AC 66 ms
68,480 KB
testcase_06 AC 471 ms
110,060 KB
testcase_07 AC 274 ms
106,912 KB
testcase_08 AC 406 ms
107,408 KB
testcase_09 AC 413 ms
104,288 KB
testcase_10 AC 310 ms
103,780 KB
testcase_11 AC 321 ms
111,836 KB
testcase_12 AC 317 ms
104,576 KB
testcase_13 AC 319 ms
107,696 KB
testcase_14 AC 308 ms
104,260 KB
testcase_15 AC 336 ms
112,436 KB
testcase_16 AC 332 ms
110,432 KB
testcase_17 AC 303 ms
108,328 KB
testcase_18 AC 333 ms
111,964 KB
testcase_19 AC 318 ms
103,940 KB
testcase_20 AC 203 ms
86,284 KB
testcase_21 AC 164 ms
83,300 KB
testcase_22 AC 304 ms
104,292 KB
testcase_23 AC 219 ms
86,296 KB
testcase_24 AC 221 ms
86,492 KB
testcase_25 AC 226 ms
87,492 KB
testcase_26 AC 166 ms
83,060 KB
testcase_27 AC 213 ms
86,584 KB
testcase_28 AC 222 ms
87,216 KB
testcase_29 AC 215 ms
85,860 KB
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 # 

mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)

def cmb(n, r, mod):#コンビネーションの高速計算　
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

N = 2*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル

for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0

def _ntt(f,L,reverse=False):
    F=[f[i] for i in range(L)]
    n = L.bit_length() - 1
    base = omega
    if reverse:
        base = rev_omega

    if not n:
        return F

    size = 2**n
    wj = pow(base,2**22,mod)
    res = [0]*2**n

    for i in range(n,0,-1):
        use_omega = pow(base,2**(22+i-n),mod)
        res = [0]*2**n
        size //= 2
        w = 1
        for j in range(0,L//2,size):
            for a in range(size):
                res[a+j] = (F[a+2*j] + w * F[a+size+2*j]) % mod
                t = (w * wj) % mod
                res[L//2+a+j] = (F[a+2*j] + t * F[a+size+2*j]) % mod
            w = (w * use_omega) % mod
        F = res

    return res

def ntt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L)
    return F

def intt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L,reverse=True)
    inv = pow(L,mod-2,mod)
    for i in range(L):
        F[i] *= inv
        F[i] %= mod
    return F

def convolve(f,g,limit):
    l = len(f)+len(g)-1
    L = 1<<((l-1).bit_length())

    F = ntt(f,L)
    G = ntt(g,L)

    H = [(F[i] * G[i]) % mod for i in range(L)]

    h = intt(H,L)

    return h[:limit]

def inverse(f,limit):
    assert(f[0]!=0)
    l = len(f)
    L = 1<<((l-1).bit_length())
    n = L.bit_length()-1
    f = f[:L]
    f+=[0]*(L-len(f))

    res = [pow(f[0],mod-2,mod)]
    for i in range(1,n+1):
        h = convolve(res,f[:2**i],2**i)
        h = [(-h[i]) % mod for i in range(2**i)]
        h[0] = (h[0]+2) % mod
        res = convolve(res,h,2**i)
    return res[:limit]

def integral(f,limit):
    res = [0]+[(f[i] * inv[i+1]) % mod for i in range(len(f)-1)]
    return res[:limit]

def diff(f,limit):
    res = [(f[i+1] * (i+1)) % mod for i in range(len(f)-1)]+[0]
    return res[:limit]

def log(f,limit):
    res = convolve(diff(f,limit),inverse(f,limit),limit)
    return integral(res,limit)

def exp(f,limit):
    l = len(f)
    L = 1<<((l-1).bit_length())
    n = L.bit_length()-1
    f = f[:L]
    f+=[0]*(L-len(f))

    res = [1]
    for i in range(1,n+1):
        res += [0]*2**(i-1)
        g = log(res,2**i)
        h = [(f[j]-g[j])%mod for j in range(2**i)]
        h[0] = (h[0]+1) % mod
        res =convolve(res,h,2**i)
    return res[:limit]

def poly_pow_exp(f,k,limit):
    l = len(f)
    L = 1<<((l-1).bit_length())
    n = L.bit_length()-1
    f = f[:L]
    f+=[0]*(L-len(f))

    g = log(f,limit)
    g = [(k * g[i]) % mod for i in range(len(g))]
    h = exp(g,limit)
    return h[:limit]

N,M = map(int,input().split())
P = list(map(int,input().split()))

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)

n = len(cycle)

binom_poly = []
for i in range(n):
    c = [cmb(cycle[i],j,mod) for j in range(1,cycle[i]+1)]
    for j in range(0,cycle[i],2):
        c[j] = (- c[j]) % mod
    c[0] = (c[0] + 1) % mod
    binom_poly.append(c)

while True:
    if len(binom_poly)==1:
        break
    n_binom_poly = []
    while binom_poly:
        f = binom_poly.pop()
        if not binom_poly:
            n_binom_poly.append(f)
            break
        g = binom_poly.pop()
        h = convolve(f,g,len(f)+len(g)-1)
        n_binom_poly.append(h)
    binom_poly = n_binom_poly

poly_f = binom_poly[0]

g = [g2[i+1] for i in range(N+1)]
g = poly_pow_exp(g,M,N+1)

poly_Stirling = [0 for i in range(N+1)]
for i in range(N-M+1):
    poly_Stirling[i+M] = (g[i] * g1[i+M]) % mod
    poly_Stirling[i+M] = (g2[M] * poly_Stirling[i+M]) % mod

ans = 0
for j in range(N-n+1):
    ans += poly_Stirling[n+j] * poly_f[j]
    ans %= mod
print((ans*(-1)**N)%mod)
0