結果

問題 No.1195 数え上げを愛したい（文字列編）
ユーザー vwxyzvwxyz
提出日時 2023-04-22 18:48:46
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,323 ms / 3,000 ms
コード長 4,753 bytes
コンパイル時間 643 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 278,248 KB
最終ジャッジ日時 2024-04-24 21:41:51
合計ジャッジ時間 34,198 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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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 2,310 ms
278,248 KB
testcase_01 AC 2,297 ms
275,176 KB
testcase_02 AC 2,323 ms
275,976 KB
testcase_03 AC 334 ms
117,476 KB
testcase_04 AC 378 ms
116,716 KB
testcase_05 AC 445 ms
134,860 KB
testcase_06 AC 46 ms
54,784 KB
testcase_07 AC 45 ms
55,040 KB
testcase_08 AC 470 ms
119,436 KB
testcase_09 AC 2,207 ms
263,980 KB
testcase_10 AC 1,336 ms
227,860 KB
testcase_11 AC 2,000 ms
265,376 KB
testcase_12 AC 1,870 ms
265,624 KB
testcase_13 AC 1,631 ms
268,316 KB
testcase_14 AC 1,040 ms
206,036 KB
testcase_15 AC 1,245 ms
237,716 KB
testcase_16 AC 1,118 ms
212,824 KB
testcase_17 AC 477 ms
120,588 KB
testcase_18 AC 1,900 ms
272,940 KB
testcase_19 AC 1,835 ms
263,364 KB
testcase_20 AC 1,614 ms
263,444 KB
testcase_21 AC 1,997 ms
273,000 KB
testcase_22 AC 1,544 ms
264,080 KB
testcase_23 AC 42 ms
55,040 KB
testcase_24 AC 42 ms
54,912 KB
testcase_25 AC 46 ms
55,424 KB
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ソースコード

diff # 

import math
import sys
readline=sys.stdin.readline
from collections import Counter

mod=998244353
def NTT(polynomial0,polynomial1):
    """
    if len(polynomial0)*len(polynomial1)<=50:
        poly=[0]*(len(polynomial0)+len(polynomial1)-1)
        for i in range(len(polynomial0)):
            for j in range(len(polynomial1)):
                poly[i+j]+=polynomial0[i]*polynomial1[j]%mod
                poly[i+j]%=mod
        return poly
    """
    if mod==998244353:
        prim_root=3
        prim_root_inve=332748118
    else:
        prim_root=Primitive_Root(mod)
        prim_root_inve=MOD(mod).Pow(prim_root,-1)
    def DFT(polynomial,n,inverse=False):
        if inverse:
            for bit in range(1,n+1):
                a=1<<bit-1
                x=pow(prim_root,mod-1>>bit,mod)
                U=[1]
                for _ in range(a):
                    U.append(U[-1]*x%mod)
                for i in range(1<<n-bit):
                    for j in range(a):
                        s=i*2*a+j
                        t=s+a
                        polynomial[s],polynomial[t]=(polynomial[s]+polynomial[t]*U[j])%mod,(polynomial[s]-polynomial[t]*U[j])%mod
            x=pow((mod+1)//2,n,mod)
            for i in range(1<<n):
                polynomial[i]*=x
                polynomial[i]%=mod
        else:
            for bit in range(n,0,-1):
                a=1<<bit-1
                x=pow(prim_root_inve,mod-1>>bit,mod)
                U=[1]
                for _ in range(a):
                    U.append(U[-1]*x%mod)
                for i in range(1<<n-bit):
                    for j in range(a):
                        s=i*2*a+j
                        t=s+a
                        polynomial[s],polynomial[t]=(polynomial[s]+polynomial[t])%mod,U[j]*(polynomial[s]-polynomial[t])%mod

    l=len(polynomial0)+len(polynomial1)-1
    n=(len(polynomial0)+len(polynomial1)-2).bit_length()
    polynomial0=polynomial0+[0]*((1<<n)-len(polynomial0))
    polynomial1=polynomial1+[0]*((1<<n)-len(polynomial1))
    DFT(polynomial0,n)
    DFT(polynomial1,n)
    ntt=[x*y%mod for x,y in zip(polynomial0,polynomial1)]
    DFT(ntt,n,inverse=True)
    ntt=ntt[:l]
    return ntt

def Extended_Euclid(n,m):
    stack=[]
    while m:
        stack.append((n,m))
        n,m=m,n%m
    if n>=0:
        x,y=1,0
    else:
        x,y=-1,0
    for i in range(len(stack)-1,-1,-1):
        n,m=stack[i]
        x,y=y,x-(n//m)*y
    return x,y

class MOD:
    def __init__(self,p,e=None):
        self.p=p
        self.e=e
        if self.e==None:
            self.mod=self.p
        else:
            self.mod=self.p**self.e

    def Pow(self,a,n):
        a%=self.mod
        if n>=0:
            return pow(a,n,self.mod)
        else:
            assert math.gcd(a,self.mod)==1
            x=Extended_Euclid(a,self.mod)[0]
            return pow(x,-n,self.mod)

    def Build_Fact(self,N):
        assert N>=0
        self.factorial=[1]
        if self.e==None:
            for i in range(1,N+1):
                self.factorial.append(self.factorial[-1]*i%self.mod)
        else:
            self.cnt=[0]*(N+1)
            for i in range(1,N+1):
                self.cnt[i]=self.cnt[i-1]
                ii=i
                while ii%self.p==0:
                    ii//=self.p
                    self.cnt[i]+=1
                self.factorial.append(self.factorial[-1]*ii%self.mod)
        self.factorial_inve=[None]*(N+1)
        self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
        for i in range(N-1,-1,-1):
            ii=i+1
            while ii%self.p==0:
                ii//=self.p
            self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod

    def Fact(self,N):
        if N<0:
            return 0
        retu=self.factorial[N]
        if self.e!=None and self.cnt[N]:
            retu*=pow(self.p,self.cnt[N],self.mod)%self.mod
            retu%=self.mod
        return retu

    def Fact_Inve(self,N):
        if self.e!=None and self.cnt[N]:
            return None
        return self.factorial_inve[N]

    def Comb(self,N,K,divisible_count=False):
        if K<0 or K>N:
            return 0
        retu=self.factorial[N]*self.factorial_inve[K]%self.mod*self.factorial_inve[N-K]%self.mod
        if self.e!=None:
            cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
            if divisible_count:
                return retu,cnt
            else:
                retu*=pow(self.p,cnt,self.mod)
                retu%=self.mod
        return retu

S=readline().rstrip()
N=len(S)
mod=998244353
MD=MOD(mod)
MD.Build_Fact(N)
poly=[1]
C=list(Counter(S).values())
C.sort()
for c in C:
    poly=NTT(poly,[MD.Fact_Inve(i) for i in range(c+1)])
ans=sum(poly[i]*MD.Fact(i)%mod for i in range(1,N+1))%mod
print(ans)
0