#909629 (Python3) No.2450 99-like Number

提出ソース
結果

問題	No.2450 99-like Number
ユーザー	mono_0812
提出日時	2023-09-01 21:36:04
言語	Python3 (3.12.2 + numpy 1.26.4 + scipy 1.12.0)
結果	AC
実行時間	47 ms / 2,000 ms
コード長	20,329 bytes
コンパイル時間	114 ms
コンパイル使用メモリ	14,976 KB
実行使用メモリ	14,208 KB
最終ジャッジ日時	2024-06-11 03:11:58
合計ジャッジ時間	2,160 ms
ジャッジサーバーID （参考情報）	judge1 / judge5
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	43 ms 14,080 KB
testcase_01	AC	44 ms 13,952 KB
testcase_02	AC	42 ms 14,080 KB
testcase_03	AC	43 ms 13,952 KB
testcase_04	AC	46 ms 13,952 KB
testcase_05	AC	42 ms 13,952 KB
testcase_06	AC	42 ms 13,952 KB
testcase_07	AC	41 ms 13,824 KB
testcase_08	AC	42 ms 13,824 KB
testcase_09	AC	41 ms 13,952 KB
testcase_10	AC	41 ms 14,208 KB
testcase_11	AC	41 ms 14,080 KB
testcase_12	AC	42 ms 13,824 KB
testcase_13	AC	46 ms 13,824 KB
testcase_14	AC	47 ms 14,080 KB
testcase_15	AC	45 ms 13,824 KB
testcase_16	AC	44 ms 14,080 KB
testcase_17	AC	43 ms 14,080 KB
testcase_18	AC	42 ms 14,080 KB
testcase_19	AC	43 ms 14,080 KB
testcase_20	AC	43 ms 13,952 KB
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ソースコード

raw source code
############################################################################################
import bisect,collections,copy,heapq,itertools,math,string,sys,queue,time,random
from decimal import Decimal
def I(): return input()
def IS(): return input().split()
def II(): return int(input())
def IIS(): return list(map(int,input().split()))
def LIIS(): return list(map(int,input().split()))

def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]

import math

def prime_numbers(n):
    prime = [True for i in range(n+1)]
    prime[0] = False
    prime[1] = False

    sqrt_n = math.ceil(math.sqrt(n))
    for i in range(2, sqrt_n):
        if prime[i]:
            for j in range(2*i, n+1, i):
                prime[j] = False
    numbers=[]
    for i in range(2,n+1):
        if prime[i]:
            numbers.append(i)

    return numbers

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
 
    if temp!=1:
        arr.append([temp, 1])
 
    if arr==[] and n>1:
        arr.append([n, 1])
 
    return arr
from collections import defaultdict


class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        group_members = defaultdict(list)
        for member in range(self.n):
            group_members[self.find(member)].append(member)
        return group_members

    def __str__(self):
        return '\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())

class FPS:
    root=(1, 998244352, 911660635, 372528824, 929031873, 452798380, 922799308, 781712469, 476477967, 166035806, 258648936, 584193783, 63912897, 350007156, 666702199, 968855178, 629671588, 24514907, 996173970, 363395222, 565042129, 733596141, 267099868, 15311432)
    iroot=(1, 998244352, 86583718, 509520358, 337190230, 87557064, 609441965, 135236158, 304459705, 685443576, 381598368, 335559352, 129292727, 358024708, 814576206, 708402881, 283043518, 3707709, 121392023, 704923114, 950391366, 428961804, 382752275, 469870224)
    rate2=(911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0)
    irate2=(86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0)
    rate3=(372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0)
    irate3=(509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0)
    mod=998244353
    Func=[0]
    def __init__(self,L):
        self.Func=[x%self.mod for x in L]
    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
        return a
    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
        return a
    def __mul__(self,other):
        if type(other)==int:
            ret=[(x*other)%self.mod for x in self.Func]
            return FPS(ret)
        a=self.Func
        b=other.Func
        n=len(a);m=len(b)
        if not(a) or not(b):
            return FPS([])
        if min(n,m)<=40:
            if n<m:
                n,m=m,n
                a,b=b,a
            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 FPS(res)
        z=1<<((n+m-2).bit_length())
        a=a+[0]*(z-n)
        b=b+[0]*(z-m)
        a=self.butterfly(a)
        b=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 FPS(c[:n+m-1])
    def __imul__(self,other):
        self=self*other
        return self
    def __add__(self,other):
        res=[0 for i in range(max(len(self.Func),len(other.Func)))]
        for i,x in enumerate(self.Func):
            res[i]+=x
            res[i]%=self.mod
        for i,x in enumerate(other.Func):
            res[i]+=x
            res[i]%=self.mod
        return FPS(res)
    def __iadd__(self,other):
        self=(self+other)
        return self
    def __sub__(self,other):
        res=[0 for i in range(max(len(self.Func),len(other.Func)))]
        for i,x in enumerate(self.Func):
            res[i]+=x
            res[i]%=self.mod
        for i,x in enumerate(other.Func):
            res[i]-=x
            res[i]%=self.mod
        return FPS(res)
    def __isub__(self,other):
        self=self-other
        return self
    def inv(self,d=-1):
        n=len(self.Func)
        assert n!=0 and self.Func[0]!=0
        if d==-1:d=n
        assert d>0
        res=[pow(self.Func[0],self.mod-2,self.mod)]
        while(len(res)<d):
            m=len(res)
            f=[self.Func[i] for i in range(min(n,2*m))]
            r=res[:]

            if len(f)<2*m:
                f+=[0]*(2*m-len(f))
            elif len(f)>2*m:
                f=f[:2*m]
            if len(r)<2*m:
                r+=[0]*(2*m-len(r))
            elif len(r)>2*m:
                r=r[:2*m]
            f=self.butterfly(f)
            r=self.butterfly(r)
            for i in range(2*m):
                f[i]*=r[i]
                f[i]%=self.mod
            f=self.butterfly_inv(f)
            f=f[m:]
            if len(f)<2*m:
                f+=[0]*(2*m-len(f))
            elif len(f)>2*m:
                f=f[:2*m]
            f=self.butterfly(f)
            for i in range(2*m):
                f[i]*=r[i]
                f[i]%=self.mod
            f=self.butterfly_inv(f)
            iz=pow(2*m,self.mod-2,self.mod)
            iz*=-iz
            iz%=self.mod
            for i in range(m):
                f[i]*=iz
                f[i]%=self.mod
            res+=f[:m]
        return FPS(res[:d])
    def __truediv__(self,other):
        if type(other)==int:
            invother=pow(other,self.mod-2,self.mod)
            ret=[(x*invother)%self.mod for x in self.Func]
            return FPS(ret)
        assert (other.Func[0]!=0)
        return self*(other.inv())
    def __floordiv__(self,other):
        if not other:
            raise ZeroDivisionError
        if isinstance(other,int):
            return self/other
        self.reduce();other.reduce()
        F_deg=len(self.Func)-1
        G_deg=len(other.Func)-1
        if F_deg<G_deg:
            return FPS([])
        m=F_deg-G_deg+1
        F_inverse=self.Func[::-1]
        G_inverse=other.Func[::-1]
        ans=(FPS(F_inverse)*(FPS(G_inverse).inv(d=m))).Func
        return FPS(ans[m-1::-1])
    def __bool__(self):
        return any(self.Func)
    def __mod__(self,other):
        if not other:
            raise ZeroDivisionError
        self.reduce();other.reduce()
        FG=self//other
        ans=self-FG*other
        ans.reduce()
        return ans
    def reduce(self):
        if self:
            while(not self.Func[-1]):
                self.Func.pop()
        else:
            self.Func=[]
    def __itruediv__(self,other):
        self=self/other
        return self
    def __lshift__(self,d):
        n=len(self.Func)
        self.Func=[0]*d+self.Func
        return FPS(self.Func[:n])
    def __ilshift__(self,d):
        self=self<<d
        return self
    def __rshift__(self,d):
        n=len(self.Func)
        self.Func=self.Func[min(n,d):]
        self.Func+=[0]*(n-len(self.Func))
        return FPS(self.Func)
    def __irshift__(self,d):
        self=self>>d
        return self
    def __lt__(self,other):
        if len(self.Func)<len(other.Func):
            return True
        elif len(self.Func)>len(other.Func):
            return True
        else:
            return self.Func<other.Func
    def __gt__(self,other):
        if len(self.Func)>len(other.Func):
            return True
        elif len(self.Func)<len(other.Func):
            return True
        else:
            return self.Func>other.Func
    def __eq__(self,other):
        return self.Func==other.Func
    def __le__(self,other):
        if len(self.Func)<len(other.Func):
            return True
        elif len(self.Func)>len(other.Func):
            return True
        else:
            return self.Func<=other.Func
    def __ge__(self,other):
        if len(self.Func)>len(other.Func):
            return True
        elif len(self.Func)<len(other.Func):
            return True
        else:
            return self.Func>other.Func
    def __ne__(self,other):
        return self.Func!=other.Func
    def __str__(self):
        return f'FPS({self.Func})'
    def diff(self):
        n=len(self.Func)
        ret=[0 for i in range(max(0,n-1))]
        for i in range(1,n):
            ret[i-1]=(self.Func[i]*i)%self.mod
        return FPS(ret)
    def integral(self):
        n=len(self.Func)
        ret=[0 for i in range(n+1)]
        for i in range(n):
            ret[i+1]=self.Func[i]*pow(i+1,self.mod-2,self.mod)%self.mod
        return FPS(ret)
    def log(self,deg=-1):
        assert self.Func[0]==1
        n=len(self.Func)
        if deg==-1:deg=n
        return (self.diff()*self.inv()).integral()
    def mod_sqrt(self,a):
        p=self.mod
        assert 0<=a and a<p
        if a<2:return a
        if pow(a,(p-1)//2,p)!=1:return -1
        b=1;one=1
        while(pow(b,(p-1)>>1,p)==1):
            b+=one
        m=p-1;e=0
        while(m%2==0):
            m>>=1
            e+=1
        x=pow(a,(m-1)>>1,p)
        y=(a*x*x)%p
        x*=a;
        x%=p
        z=pow(b,m,p)
        while(y!=1):
            j=0
            t=y
            while(t!=one):
                j+=1
                t*=t
                t%=p
            z=pow(z,1<<(e-j-1),p)
            x*=z
            x%=p
            z*=z
            z%=p
            y*=z
            y%=p
            e=j
        return x
    def sqrt(self,deg=-1):
        n=len(self.Func)
        if deg==-1:deg=n
        if n==0:return FPS([0 for i in range(deg)])
        if self.Func[0]==0:
            for i in range(1,n):
                if self.Func[i]!=0:
                    if i&1:return FPS([])
                    if deg-i//2<=0:break
                    ret=(self>>i).sqrt(deg-i//2)
                    if len(ret.Func)==0:return FPS([])
                    ret=ret<<(i//2)
                    if len(ret.Func)<deg:
                        ret.Func+=[0]*(deg-len(ret.Func))
                    return ret
            return FPS([0]*deg)
        sqr=self.mod_sqrt(self.Func[0])
        if sqr==-1:return FPS([])
        assert sqr*sqr%self.mod==self.Func[0]
        ret=FPS([sqr])
        inv2=(self.mod+1)//2
        i=1
        while(i<deg):
            ret=(ret+FPS(self.Func[:i<<1])*ret.inv(i<<1))*inv2
            i<<=1
        return FPS(ret.Func[:deg])
    def resize(self,deg):
        if len(self.Func)<deg:
            return FPS(self.Func+[0]*(deg-len(self.Func)))
        elif len(self.Func)>deg:
            return FPS(self.Func[:deg])
        else:
            return self
    def exp(self,deg=-1):
        n=len(self.Func)
        assert n>0 and self.Func[0]==0
        if deg==-1:deg=n
        assert deg>=0
        g=[1]
        g_fft=[1,1]
        self.Func[0]=1
        self.resize(deg)
        h_drv=self.diff()
        m=2
        while(m<deg):
            f_fft=self.Func[:m]+[0]*m
            self.butterfly(f_fft)
            
            #step 2.a
            _g=[f_fft[i]*g_fft[i]%self.mod for i in range(m)]
            self.butterfly_inv(_g)
            _g=_g[m//2:m]+[0]*(m//2)
            self.butterfly(_g)
            for i in range(m):
                _g[i]*=g_fft[i]
                _g[i]%=self.mod
            self.butterfly_inv(_g)
            tmp=pow(-m*m,self.mod-2,self.mod)
            for i in range(m):
                _g[i]*=tmp
                _g[i]%=self.mod
            g+=_g[:m//2]
            #step 2.b--2.d
            t=FPS(self.Func[:m]).diff()
            r=h_drv.Func[:m-1]+[0]
            self.butterfly(r)
            for i in range(m):
                r[i]*=f_fft[i]
                r[i]%=self.mod
            self.butterfly_inv(r)
            tmp=pow(-m,self.mod-2,self.mod)
            for i in range(m):
                r[i]*=tmp
                r[i]%=self.mod
            t=(t+FPS(r)).Func
            t=[t[-1]]+t
            t.pop()
            #step 2.e
            if (2*m<deg):
                if len(t)<2*m:
                    t+=[0]*(2*m-len(t))
                elif len(t)>2*m:
                    t=t[:2*m]
                self.butterfly(t)
                g_fft=g[:]
                if len(g_fft)<2*m:
                    g_fft+=[0]*(2*m-len(g_fft))
                elif len(g_fft)>2*m:
                    g_fft=g_fft[:2*m]
                self.butterfly(g_fft)
                for i in range(2*m):
                    t[i]*=g_fft[i]
                    t[i]%=self.mod
                self.butterfly_inv(t)
                tmp=pow(2*m,self.mod-2,self.mod)
                t=t[:m]
                for i in range(m):
                    t[i]*=tmp
                    t[i]%=self.mod
            else:
                g1=g[m//2:]
                s1=t[m//2:]
                t=t[:m//2]
                g1+=[0]*(m-len(g1))
                s1+=[0]*(m-len(s1))
                t+=[0]*(m-len(t))
                
                self.butterfly(g1)
                self.butterfly(t)
                self.butterfly(s1)
                for i in range(m):
                    s1[i]=(g_fft[i]*s1[i]+g1[i]*t[i])%self.mod
                for i in range(m):
                    t[i]*=g_fft[i]
                    t[i]%=self.mod
                self.butterfly_inv(t)
                self.butterfly_inv(s1)
                for i in range(m//2):
                    t[i+m//2]+=s1[i]
                    t[i+m//2]%=self.mod
                tmp=pow(m,self.mod-2,self.mod)
                for i in range(m):
                    t[i]*=tmp
                    t[i]%=self.mod
            #step 2.f
            v=self.Func[m:min(deg,2*m)]+[0]*(2*m-min(deg,2*m))
            t=[0]*(m-1)+t
            t=FPS(t).integral().Func
            for i in range(m):
                v[i]-=t[m+i]
                v[i]%=self.mod
            #step 2.g
            if len(v)<2*m:
                v+=[0]*(2*m-len(v))
            else:
                v=v[:2*m]
            self.butterfly(v)
            for i in range(2*m):
                v[i]*=f_fft[i]
                v[i]%=self.mod
            self.butterfly_inv(v)
            v=v[:m]
            tmp=pow(2*m,self.mod-2,self.mod)
            for i in range(m):
                v[i]*=tmp
                v[i]%=self.mod
            #step 2.h
            for i in range(min(deg-m,m)):
                self.Func[m+i]=v[i]
            m*=2
        return self
    def powfps(self,k,deg=-1):
        a=self.Func[:]
        n=len(self.Func)
        if k==0:
            return FPS([int(i==0) for i in range(n)])
        l=0
        while(l<len(a) and not a[l]):
            l+=1
        if l*k>=n:
            return FPS([0]*n)
        ic=pow(a[l],self.mod-2,self.mod)
        pc=pow(a[l],k,self.mod)
        a=FPS([(a[i]*ic)%self.mod for i in range(l,len(a))]).log()
        a*=k
        a=a.exp()
        a*=pc
        a=[0]*(l*k)+a.Func[:n-l*k]
        return FPS(a)
 
INF=10**18
MOD=998244353
MOD2=10**9+7
sys.setrecursionlimit(500005)
def bit_count(x):
    return bin(x).count("1")
def yesno(f):
    if f:print("Yes")
    else:print("No")
def dist(p1,p2):
    return (p1[0]-p2[0])**2+(p1[1]-p2[1])**2
alpha="abcdefghijklmnopqrstuvwxyz"
dxy=((0,1),(1,0),(0,-1),(-1,0))
##################################################################
yesno(set(list(I()))==set(["9"]))
yukicoder

結果

テストケース

ソースコード
