結果

問題 No.2633 Subsequence Combination Score
ユーザー PNJPNJ
提出日時 2024-02-18 10:35:31
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,978 ms / 2,000 ms
コード長 6,944 bytes
コンパイル時間 327 ms
コンパイル使用メモリ 82,008 KB
実行使用メモリ 127,576 KB
最終ジャッジ日時 2024-09-29 00:17:42
合計ジャッジ時間 62,097 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 54 ms
69,704 KB
testcase_01 AC 54 ms
69,288 KB
testcase_02 AC 311 ms
91,724 KB
testcase_03 AC 1,507 ms
115,884 KB
testcase_04 AC 1,457 ms
120,608 KB
testcase_05 AC 1,411 ms
111,576 KB
testcase_06 AC 1,513 ms
114,072 KB
testcase_07 AC 1,530 ms
119,480 KB
testcase_08 AC 200 ms
98,060 KB
testcase_09 AC 1,875 ms
124,512 KB
testcase_10 AC 1,873 ms
122,232 KB
testcase_11 AC 1,838 ms
117,960 KB
testcase_12 AC 1,895 ms
122,324 KB
testcase_13 AC 1,944 ms
125,876 KB
testcase_14 AC 1,825 ms
120,480 KB
testcase_15 AC 1,847 ms
122,932 KB
testcase_16 AC 1,877 ms
123,232 KB
testcase_17 AC 1,861 ms
122,012 KB
testcase_18 AC 1,851 ms
121,900 KB
testcase_19 AC 1,935 ms
125,968 KB
testcase_20 AC 1,813 ms
119,848 KB
testcase_21 AC 1,840 ms
123,200 KB
testcase_22 AC 1,978 ms
127,576 KB
testcase_23 AC 1,903 ms
121,312 KB
testcase_24 AC 1,884 ms
122,740 KB
testcase_25 AC 1,861 ms
123,248 KB
testcase_26 AC 1,837 ms
125,908 KB
testcase_27 AC 1,740 ms
122,568 KB
testcase_28 AC 1,715 ms
118,772 KB
testcase_29 AC 50 ms
68,948 KB
testcase_30 AC 52 ms
69,888 KB
testcase_31 AC 51 ms
69,140 KB
testcase_32 AC 51 ms
70,496 KB
testcase_33 AC 1,900 ms
124,720 KB
testcase_34 AC 1,893 ms
124,760 KB
testcase_35 AC 1,874 ms
124,844 KB
testcase_36 AC 1,888 ms
125,100 KB
testcase_37 AC 1,843 ms
120,736 KB
testcase_38 AC 1,891 ms
123,084 KB
testcase_39 AC 1,854 ms
123,500 KB
testcase_40 AC 1,875 ms
120,956 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 # 

class FFT():
    def primitive_root_constexpr(self,m):
        if m==2:return 1
        if m==167772161:return 3
        if m==469762049:return 3
        if m==754974721:return 11
        if m==998244353:return 3
        divs=[0]*20
        divs[0]=2
        cnt=1
        x=(m-1)//2
        while(x%2==0):x//=2
        i=3
        while(i*i<=x):
            if (x%i==0):
                divs[cnt]=i
                cnt+=1
                while(x%i==0):
                    x//=i
            i+=2
        if x>1:
            divs[cnt]=x
            cnt+=1
        g=2
        while(1):
            ok=True
            for i in range(cnt):
                if pow(g,(m-1)//divs[i],m)==1:
                    ok=False
                    break
            if ok:
                return g
            g+=1
    def bsf(self,x):
        res=0
        while(x%2==0):
            res+=1
            x//=2
        return res
    rank2=0
    root=[]
    iroot=[]
    rate2=[]
    irate2=[]
    rate3=[]
    irate3=[]
    
    def __init__(self,MOD):
        self.mod=MOD
        self.g=self.primitive_root_constexpr(self.mod)
        self.rank2=self.bsf(self.mod-1)
        self.root=[0 for i in range(self.rank2+1)]
        self.iroot=[0 for i in range(self.rank2+1)]
        self.rate2=[0 for i in range(self.rank2)]
        self.irate2=[0 for i in range(self.rank2)]
        self.rate3=[0 for i in range(self.rank2-1)]
        self.irate3=[0 for i in range(self.rank2-1)]
        self.root[self.rank2]=pow(self.g,(self.mod-1)>>self.rank2,self.mod)
        self.iroot[self.rank2]=pow(self.root[self.rank2],self.mod-2,self.mod)
        for i in range(self.rank2-1,-1,-1):
            self.root[i]=(self.root[i+1]**2)%self.mod
            self.iroot[i]=(self.iroot[i+1]**2)%self.mod
        prod=1;iprod=1
        for i in range(self.rank2-1):
            self.rate2[i]=(self.root[i+2]*prod)%self.mod
            self.irate2[i]=(self.iroot[i+2]*iprod)%self.mod
            prod=(prod*self.iroot[i+2])%self.mod
            iprod=(iprod*self.root[i+2])%self.mod
        prod=1;iprod=1
        for i in range(self.rank2-2):
            self.rate3[i]=(self.root[i+3]*prod)%self.mod
            self.irate3[i]=(self.iroot[i+3]*iprod)%self.mod
            prod=(prod*self.iroot[i+3])%self.mod
            iprod=(iprod*self.root[i+3])%self.mod
    def butterfly(self,a):
        n=len(a)
        h=(n-1).bit_length()
        
        LEN=0
        while(LEN<h):
            if (h-LEN==1):
                p=1<<(h-LEN-1)
                rot=1
                for s in range(1<<LEN):
                    offset=s<<(h-LEN)
                    for i in range(p):
                        l=a[i+offset]
                        r=a[i+offset+p]*rot
                        a[i+offset]=(l+r)%self.mod
                        a[i+offset+p]=(l-r)%self.mod
                    rot*=self.rate2[(~s & -~s).bit_length()-1]
                    rot%=self.mod
                LEN+=1
            else:
                p=1<<(h-LEN-2)
                rot=1
                imag=self.root[2]
                for s in range(1<<LEN):
                    rot2=(rot*rot)%self.mod
                    rot3=(rot2*rot)%self.mod
                    offset=s<<(h-LEN)
                    for i in range(p):
                        a0=a[i+offset]
                        a1=a[i+offset+p]*rot
                        a2=a[i+offset+2*p]*rot2
                        a3=a[i+offset+3*p]*rot3
                        a1na3imag=(a1-a3)%self.mod*imag
                        a[i+offset]=(a0+a2+a1+a3)%self.mod
                        a[i+offset+p]=(a0+a2-a1-a3)%self.mod
                        a[i+offset+2*p]=(a0-a2+a1na3imag)%self.mod
                        a[i+offset+3*p]=(a0-a2-a1na3imag)%self.mod
                    rot*=self.rate3[(~s & -~s).bit_length()-1]
                    rot%=self.mod
                LEN+=2
                
    def butterfly_inv(self,a):
        n=len(a)
        h=(n-1).bit_length()
        LEN=h
        while(LEN):
            if (LEN==1):
                p=1<<(h-LEN)
                irot=1
                for s in range(1<<(LEN-1)):
                    offset=s<<(h-LEN+1)
                    for i in range(p):
                        l=a[i+offset]
                        r=a[i+offset+p]
                        a[i+offset]=(l+r)%self.mod
                        a[i+offset+p]=(l-r)*irot%self.mod
                    irot*=self.irate2[(~s & -~s).bit_length()-1]
                    irot%=self.mod
                LEN-=1
            else:
                p=1<<(h-LEN)
                irot=1
                iimag=self.iroot[2]
                for s in range(1<<(LEN-2)):
                    irot2=(irot*irot)%self.mod
                    irot3=(irot*irot2)%self.mod
                    offset=s<<(h-LEN+2)
                    for i in range(p):
                        a0=a[i+offset]
                        a1=a[i+offset+p]
                        a2=a[i+offset+2*p]
                        a3=a[i+offset+3*p]
                        a2na3iimag=(a2-a3)*iimag%self.mod
                        a[i+offset]=(a0+a1+a2+a3)%self.mod
                        a[i+offset+p]=(a0-a1+a2na3iimag)*irot%self.mod
                        a[i+offset+2*p]=(a0+a1-a2-a3)*irot2%self.mod
                        a[i+offset+3*p]=(a0-a1-a2na3iimag)*irot3%self.mod
                    irot*=self.irate3[(~s & -~s).bit_length()-1]
                    irot%=self.mod
                LEN-=2
    def convolution(self,a,b):
        n=len(a);m=len(b)
        if not(a) or not(b):
            return []
        if min(n,m)<=40:
            res=[0]*(n+m-1)
            for i in range(n):
                for j in range(m):
                    res[i+j]+=a[i]*b[j]
                    res[i+j]%=self.mod
            return res
        z=1<<((n+m-2).bit_length())
        a=a+[0]*(z-n)
        b=b+[0]*(z-m)
        self.butterfly(a)
        self.butterfly(b)
        c=[(a[i]*b[i])%self.mod for i in range(z)]
        self.butterfly_inv(c)
        iz=pow(z,self.mod-2,self.mod)
        for i in range(n+m-1):
            c[i]=(c[i]*iz)%self.mod
        return c[:n+m-1]

mod = 998244353
CONV = FFT(mod)

N = int(input())
A = list(map(int,input().split()))
fact = [1]
for i in range(1,10**5+1):
  fact.append(fact[-1]*i % mod)
fact_inv = [1 for i in range(10**5 + 1)]
fact_inv[-1] = pow(fact[-1],mod-2,mod)
for i in range(10**5,0,-1):
  fact_inv[i-1] = fact_inv[i] * i % mod

dp = [fact[A[i]] for i in range(N)]
def online_convolution(l,r):
  if l + 1 == r:
    return
  m = (l + r) // 2
  online_convolution(l,m)
  u = A[l]
  d = A[m-1]
  P = [0 for i in range(u - d + 1)]
  for i in range(l,m):
    P[u-A[i]] += dp[i]
  x = A[r-1]
  Q = fact_inv[:u-x+1]
  R = CONV.convolution(P,Q)
  for i in range(m,r):
    d = u - A[i]
    dp[i] += R[d]
    dp[i] %= mod
  online_convolution(m,r)

online_convolution(0,N)
ans = 0
for i in range(N):
  ans += dp[i] * fact_inv[A[i]]
  ans %= mod
print(ans)
0