#864202 (Python3) No.2013 Can we meet?

提出ソース
結果

問題	No.2013 Can we meet?
ユーザー	vwxyz
提出日時	2023-04-29 05:02:49
言語	Python3 (3.12.2 + numpy 1.26.4 + scipy 1.12.0)
結果	TLE
実行時間	-
コード長	16,048 bytes
コンパイル時間	192 ms
コンパイル使用メモリ	14,720 KB
実行使用メモリ	84,056 KB
最終ジャッジ日時	2024-11-18 03:53:18
合計ジャッジ時間	50,239 ms
ジャッジサーバーID （参考情報）	judge2 / judge4
このコードへのチャレンジ
（要ログイン）
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	39 ms 19,748 KB
testcase_01	AC	39 ms 73,456 KB
testcase_02	AC	39 ms 19,748 KB
testcase_03	AC	39 ms 73,452 KB
testcase_04	AC	39 ms 19,616 KB
testcase_05	AC	39 ms 73,584 KB
testcase_06	AC	40 ms 19,872 KB
testcase_07	AC	40 ms 73,708 KB
testcase_08	AC	39 ms 19,748 KB
testcase_09	AC	40 ms 73,708 KB
testcase_10	AC	39 ms 19,744 KB
testcase_11	AC	39 ms 73,712 KB
testcase_12	AC	39 ms 19,872 KB
testcase_13	AC	40 ms 19,744 KB
testcase_14	AC	40 ms 19,876 KB
testcase_15	AC	231 ms 20,000 KB
testcase_16	AC	232 ms 20,132 KB
testcase_17	AC	231 ms 20,132 KB
testcase_18	AC	231 ms 20,388 KB
testcase_19	AC	239 ms 20,128 KB
testcase_20	AC	232 ms 20,388 KB
testcase_21	AC	40 ms 19,876 KB
testcase_22	AC	238 ms 20,388 KB
testcase_23	AC	240 ms 20,384 KB
testcase_24	TLE	-
testcase_25	TLE	-
testcase_26	TLE	-
testcase_27	TLE	-
testcase_28	TLE	-
testcase_29	TLE	-
testcase_30	TLE	-
testcase_31	TLE	-
testcase_32	AC	75 ms 23,380 KB
testcase_33	TLE	-
testcase_34	TLE	-
testcase_35	TLE	-
testcase_36	TLE	-
testcase_37	TLE	-
testcase_38	AC	75 ms 84,056 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

raw source code
import sys
readline=sys.stdin.readline
import math

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
def Tonelli_Shanks(N,p):
    if pow(N,p>>1,p)==p-1:
        retu=None
    elif p%4==3:
        retu=pow(N,(p+1)//4,p)
    else:
        for nonresidue in range(1,p):
            if pow(nonresidue,p>>1,p)==p-1:
                break
        pp=p-1
        cnt=0
        while pp%2==0:
            pp//=2
            cnt+=1
        s=pow(N,pp,p)
        retu=pow(N,(pp+1)//2,p)
        for i in range(cnt-2,-1,-1):
            if pow(s,1<<i,p)==p-1:
                s*=pow(nonresidue,p>>1+i,p)
                s%=p
                retu*=pow(nonresidue,p>>2+i,p)
                retu%=p
    return retu

mod = 998244353
imag = 911660635
iimag = 86583718
rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
              842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
               354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,
              183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,
               771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)

def butterfly(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 % mod
                    a[i + offset] = (l + r) % mod
                    a[i + offset + p] = (l - r) % mod
                if s + 1 != 1 << len_:
                    rot *= rate2[(~s & -~s).bit_length() - 1]
                    rot %= mod
            len_ += 1
        else:
            p = 1 << (h - len_ - 2)
            rot = 1
            for s in range(1 << len_):
                rot2 = rot * rot % mod
                rot3 = rot2 * rot % mod
                offset = s << (h - len_)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p] * rot
                    a2 = a[i + offset + p * 2] * rot2
                    a3 = a[i + offset + p * 3] * rot3
                    a1na3imag = (a1 - a3) % mod * imag
                    a[i + offset] = (a0 + a2 + a1 + a3) % mod
                    a[i + offset + p] = (a0 + a2 - a1 - a3) % mod
                    a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % mod
                    a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % mod
                if s + 1 != 1 << len_:
                    rot *= rate3[(~s & -~s).bit_length() - 1]
                    rot %= mod
            len_ += 2

def butterfly_inv(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) % mod
                    a[i + offset + p] = (l - r) * irot % mod
                if s + 1 != (1 << (len_ - 1)):
                    irot *= irate2[(~s & -~s).bit_length() - 1]
                    irot %= mod
            len_ -= 1
        else:
            p = 1 << (h - len_)
            irot = 1
            for s in range(1 << (len_ - 2)):
                irot2 = irot * irot % mod
                irot3 = irot2 * irot % mod
                offset = s << (h - len_ + 2)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p]
                    a2 = a[i + offset + p * 2]
                    a3 = a[i + offset + p * 3]
                    a2na3iimag = (a2 - a3) * iimag % mod
                    a[i + offset] = (a0 + a1 + a2 + a3) % mod
                    a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % mod
                    a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % mod
                    a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % mod
                if s + 1 != (1 << (len_ - 2)):
                    irot *= irate3[(~s & -~s).bit_length() - 1]
                    irot %= mod
            len_ -= 2

def integrate(a):
    a=a.copy()
    n = len(a)
    assert n > 0
    a.pop()
    a.insert(0, 0)
    inv = [1, 1]
    for i in range(2, n):
        inv.append(-inv[mod%i] * (mod//i) % mod)
        a[i] = a[i] * inv[i] % mod
    return a

def differentiate(a):
    n = len(a)
    assert n > 0
    for i in range(2, n):
        a[i] = a[i] * i % mod
    a.pop(0)
    a.append(0)
    return a

def convolution_naive(a, b):
    n = len(a)
    m = len(b)
    ans = [0] * (n + m - 1)
    if n < m:
        for j in range(m):
            for i in range(n):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % mod
    else:
        for i in range(n):
            for j in range(m):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % mod
    return ans

def convolution_ntt(a, b):
    a = a.copy()
    b = b.copy()
    n = len(a)
    m = len(b)
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    butterfly(a)
    b += [0] * (z - m)
    butterfly(b)
    for i in range(z):
        a[i] = a[i] * b[i] % mod
    butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, mod - 2, mod)
    for i in range(n + m - 1):
        a[i] = a[i] * iz % mod
    return a

def convolution_square(a):
    a = a.copy()
    n = len(a)
    z = 1 << (2 * n - 2).bit_length()
    a += [0] * (z - n)
    butterfly(a)
    for i in range(z):
        a[i] = a[i] * a[i] % mod
    butterfly_inv(a)
    a = a[:2 * n - 1]
    iz = pow(z, mod - 2, mod)
    for i in range(2 * n - 1):
        a[i] = a[i] * iz % mod
    return a

def convolution(a, b):
    """It calculates (+, x) convolution in mod 998244353. 
    Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1], 
    it calculates the array c of length n + m - 1, defined by

    >   c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.

    It returns an empty list if at least one of a and b are empty.

    Complexity
    ----------

    >   O(n log n), where n = len(a) + len(b).
    """
    n = len(a)
    m = len(b)
    if n == 0 or m == 0:
        return []
    if min(n, m) <= 60:
        return convolution_naive(a, b)
    if a is b:
        return convolution_square(a)
    return convolution_ntt(a, b)

def inverse(a):
    n = len(a)
    assert n > 0 and a[0] != 0
    res = [pow(a[0], mod - 2, mod)]
    m = 1
    while m < n:
        f = a[:min(n,2*m)] + [0]*(2*m-min(n,2*m))
        g = res + [0]*m
        butterfly(f)
        butterfly(g)
        for i in range(2*m):
            f[i] = f[i] * g[i] % mod
        butterfly_inv(f)
        f = f[m:] + [0]*m
        butterfly(f)
        for i in range(2*m):
            f[i] = f[i] * g[i] % mod
        butterfly_inv(f)
        iz = pow(2*m, mod-2, mod)
        iz = (-iz*iz) % mod
        for i in range(m):
            f[i] = f[i] * iz % mod
        res += f[:m]
        m <<= 1
    return res[:n]

def log(a):
    a = a.copy()
    n = len(a)
    assert n > 0 and a[0] == 1
    a_inv = inverse(a)
    a=differentiate(a)
    a = convolution(a, a_inv)[:n]
    a=integrate(a)
    return a

def exp(a):
    a = a.copy()
    n = len(a)
    assert n > 0 and a[0] == 0
    g = [1]
    a[0] = 1
    h_drv = a.copy()
    h_drv=differentiate(h_drv)
    m = 1
    while m < n:
        f_fft = a[:m] + [0] * m
        butterfly(f_fft)

        if m > 1:
            _f = [f_fft[i] * g_fft[i] % mod for i in range(m)]
            butterfly_inv(_f)
            _f = _f[m // 2:] + [0] * (m // 2)
            butterfly(_f)
            for i in range(m):
                _f[i] = _f[i] * g_fft[i] % mod
            butterfly_inv(_f)
            _f = _f[:m//2]
            iz = pow(m, mod - 2, mod)
            iz *= -iz
            iz %= mod
            for i in range(m//2):
                _f[i] = _f[i] * iz % mod
            g.extend(_f)

        t = a[:m]
        t=differentiate(t)
        r = h_drv[:m - 1]
        r.append(0)
        butterfly(r)
        for i in range(m):
            r[i] = r[i] * f_fft[i] % mod
        butterfly_inv(r)
        im = pow(-m, mod - 2, mod)
        for i in range(m):
            r[i] = r[i] * im % mod
        for i in range(m):
            t[i] = (t[i] + r[i]) % mod
        t = [t[-1]] + t[:-1]

        t += [0] * m
        butterfly(t)
        g_fft = g + [0] * (2 * m - len(g))
        butterfly(g_fft)
        for i in range(2 * m):
            t[i] = t[i] * g_fft[i] % mod
        butterfly_inv(t)
        t = t[:m]
        i2m = pow(2 * m, mod - 2, mod)
        for i in range(m):
            t[i] = t[i] * i2m % mod
    
        v = a[m:min(n, 2 * m)]
        v += [0] * (m - len(v))
        t = [0] * (m - 1) + t + [0]
        t=integrate(t)
        for i in range(m):
            v[i] = (v[i] - t[m + i]) % mod

        v += [0] * m
        butterfly(v)
        for i in range(2 * m):
            v[i] = v[i] * f_fft[i] % mod
        butterfly_inv(v)
        v = v[:m]
        i2m = pow(2 * m, mod - 2, mod)
        for i in range(m):
            v[i] = v[i] * i2m % mod
        
        for i in range(min(n - m, m)):
            a[m + i] = v[i]
        
        m *= 2
    return a

def power(a,k):
    n = len(a)
    assert n>0
    if k==0:
        return [1]+[0]*(n-1)
    l = 0
    while l < len(a) and not a[l]:
        l += 1
    if l * k >= n:
        return [0] * n
    ic = pow(a[l], mod - 2, mod)
    pc = pow(a[l], k, mod)
    a = log([a[i] * ic % mod for i in range(l, len(a))])
    for i in range(len(a)):
        a[i] = a[i] * k % mod
    a = exp(a)
    for i in range(len(a)):
        a[i] = a[i] * pc % mod
    a = [0] * (l * k) + a[:n - l * k]
    return a

def sqrt(a):
    if len(a) == 0:
        return []
    if a[0] == 0:
        for d in range(1, len(a)):
            if a[d]:
                if d & 1:
                    return None
                if len(a) - 1 < d // 2:
                    break
                res=sqrt(a[d:]+[0]*(d//2))
                if res == None:
                    return None
                res = [0]*(d//2)+res
                return res
        return [0]*len(a)
    
    sqr = Tonelli_Shanks(a[0],mod)
    if sqr == None:
        return None
    T = [0] * (len(a))
    T[0] = sqr
    res = T.copy()
    T[0] = pow(sqr,mod-2,mod) #T:res^{-1}
    m = 1
    two_inv = (mod + 1) // 2
    F = [sqr]
    while m <= len(a) - 1:
        for i in range(m):
            F[i] *= F[i]
            F[i] %= mod
        butterfly_inv(F)
        iz = pow(m, mod-2, mod)
        for i in range(m):
            F[i] = F[i] * iz % mod
        delta = [0] * (2 * m)
        for i in range(m):
            delta[i + m] = F[i] - a[i] - (a[i + m] if i+m<len(a) else 0)
        butterfly(delta)
        G = [0] * (2 * m)
        for i in range(m):
            G[i] = T[i]
        butterfly(G)
        for i in range(2 * m):
            delta[i] *= G[i]
            delta[i] %= mod
        butterfly_inv(delta)
        iz = pow(2*m, mod-2, mod)
        for i in range(2*m):
            delta[i] = delta[i] * iz % mod
        for i in range(m, min(2 * m, len(a))):
            res[i] = -delta[i] * two_inv%mod
            res[i]%=mod
        if 2 * m > len(a) - 1:
            break
        F = res[:2 * m]
        butterfly(F)
        eps = [F[i] * G[i] % mod for i in range(2 * m)]
        butterfly_inv(eps)
        for i in range(m):
            eps[i] = 0
        iz = pow(2*m, mod-2, mod)
        for i in range(m,2*m):
            eps[i] = eps[i] * iz % mod
        butterfly(eps)
        for i in range(2 * m):
            eps[i] *= G[i]
            eps[i] %= mod
        butterfly_inv(eps)
        for i in range(m, 2 * m):
            T[i] = -eps[i]*iz
            T[i]%=mod
        iz = iz*iz % mod

        m <<= 1
    return res

N=int(readline())
x1,y1,x2,y2=map(int,readline().split())
x=abs(x1-x2)
y=abs(y1-y2)
a,b=map(int,readline().split())
A=list(map(int,readline().split()))
mod=998244353
if x%2!=y%2:
    ans=0
else:
    MD=MOD(mod)
    MD.Build_Fact(2*N)
    a,b=a*MD.Pow(2*(a+b),-1)%mod,b*MD.Pow(2*(a+b),-1)%mod
    X=[]
    for i in range(0,2*N+1,2):
        X.append(MD.Comb(i,i//2)*MD.Pow(a,i)%mod*MD.Fact_Inve(i)%mod)
    Y=[]
    for i in range(0,2*N+1,2):
        Y.append(MD.Comb(i,i//2)*MD.Pow(b,i)%mod*MD.Fact_Inve(i)%mod)
    XY_inve=convolution(X,Y)[:N+1]
    for i in range(0,N+1):
        XY_inve[i]*=MD.Fact(2*i)
        XY_inve[i]%=mod
    X=[]
    for i in range(x%2,2*N+1,2):
        X.append(MD.Comb(i,(i+x)//2)*MD.Pow(a,i)%mod*MD.Fact_Inve(i)%mod)
    Y=[]
    for i in range(y%2,2*N+1,2):
        Y.append(MD.Comb(i,(i+y)//2)*MD.Pow(b,i)%mod*MD.Fact_Inve(i)%mod)
    XY=convolution(X,Y)
    if x%2:
        XY=[0]+XY
    XY=XY[:N+1]
    for i in range(len(XY)):
        XY[i]*=MD.Fact(2*i)
        XY[i]%=mod
    poly=convolution(XY,inverse(XY_inve))
    ans=0
    for i in range(1,N+1):
        ans+=poly[i]*A[i-1]%mod
        ans%=mod
print(ans)
yukicoder

結果

テストケース

ソースコード
