結果

問題 No.1116 Cycles of Dense Graph
ユーザー vwxyz
提出日時 2021-09-15 20:13:36
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
WA  
実行時間 -
コード長 5,238 bytes
コンパイル時間 114 ms
コンパイル使用メモリ 13,184 KB
実行使用メモリ 19,744 KB
最終ジャッジ日時 2024-06-28 21:11:38
合計ジャッジ時間 10,566 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample -- * 3
other AC * 21 WA * 1 TLE * 1 -- * 15
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 #
プレゼンテーションモードにする

import bisect
import copy
import decimal
import fractions
import functools
import heapq
import itertools
import math
import random
import sys
from collections import Counter,deque,defaultdict
from functools import lru_cache,reduce
from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max
def _heappush_max(heap,item):
    heap.append(item)
    heapq._siftdown_max(heap, 0, len(heap)-1)
def _heappushpop_max(heap, item):
    if heap and item < heap[0]:
        item, heap[0] = heap[0], item
        heapq._siftup_max(heap, 0)
    return item
from math import degrees, gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines
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=1):
        self.p=p
        self.e=e
        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]
        self.cnt=[0]*(N+1)
        for i in range(1,N+1):
            ii=i
            self.cnt[i]=self.cnt[i-1]
            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
        return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.mod
    def Fact_Inve(self,N):
        if 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.factorial_inve[N-K]%self.mod
        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 Zip(lst):
    unzip=sorted(list(set(lst)))
    zip={x:i for i,x in enumerate(unzip)}
    return zip,unzip
class UnionFind:
    def __init__(self,n):
        self.n=n
        self.parents=[-1]*n
    def Find(self,x):
        stack=[]
        while self.parents[x]>=0:
            stack.append(x)
            x=self.parents[x]
        for y in stack:
            self.parents[y]=x
        return 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())
N,M=map(int,readline().split())
edges=[]
for _ in range(M):
    a,b=map(int,readline().split())
    a-=1;b-=1
    edges.append((a,b))
ans=0
mod=998244353
MD=MOD(mod)
MD.Build_Fact(N)
@lru_cache(maxsize=None)
def f(n,c):
    s=0
    if c>=2:
        s+=MD.Fact(c-1)
    elif n!=N-1:
        s+=1
    for i in range(c+1,n+1):
        s+=MD.Comb(n-c,i-c)*MD.Fact(i-1)
        s%=mod
    s*=pow(2,c-1,mod)
    s%=mod
    return s
for i in range(3,N+1):
    ans+=MD.Comb(N,i)*MD.Fact(i-1)
    ans%=mod
ans*=MD.Pow(2,-1)
ans%=mod
for bit in range(1,1<<M):
    points=[]
    pop_cnt=0
    for i in range(N):
        if bit>>i&1:
            a,b=edges[i]
            points.append(a)
            points.append(b)
            pop_cnt+=1
    zip,unzip=Zip(points)
    l=len(zip)
    UF=UnionFind(l)
    cnt=[0]*l
    cycle=False
    for i in range(N):
        if bit>>i&1:
            a,b=edges[i]
            UF.Union(zip[a],zip[b])
            cnt[zip[a]]+=1
            cnt[zip[b]]+=1
    for c in cnt:
        if c>=3:
            continue
    if cnt.count(2)==l and UF.Group_Count()==1:
        if pop_cnt%2==0:
            ans+=1
        else:
            ans-=1
    else:
        if pop_cnt%2==0:
            ans+=f(N-pop_cnt,UF.Group_Count())
        else:
            ans-=f(N-pop_cnt,UF.Group_Count())
    ans%=mod
print(ans)
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