結果

問題 No.1116 Cycles of Dense Graph
ユーザー mkawa2
提出日時 2022-07-28 23:26:44
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 235 ms / 2,000 ms
コード長 3,254 bytes
コンパイル時間 427 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 84,224 KB
最終ジャッジ日時 2024-07-18 13:47:26
合計ジャッジ時間 5,216 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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 AC * 3
other AC * 38
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ソースコード

diff #
プレゼンテーションモードにする

import sys
# sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
dij = [(-1, 1), (-1, 0), (-1, -1), (1, -1), (1, 1)]
inf = (1 << 63)-1
# inf = (1 << 31)-1
# md = 10**9+7
md = 998244353
class UnionFind:
    def __init__(self, uu=[]):
        self.state = {u: -1 for u in uu}
        self.cnt = len(self.state)
    def add(self, u):
        if u in self.state: return False
        self.state[u] = -1
        self.cnt += 1
        return True
    def root(self, u):
        stack = []
        while self.state[u] >= 0:
            stack.append(u)
            u = self.state[u]
        for v in stack: self.state[v] = u
        return u
    def same(self, u, v):
        return self.root(u) == self.root(v)
    def merge(self, u, v):
        self.add(u)
        self.add(v)
        u = self.root(u)
        v = self.root(v)
        if u == v: return False
        su = -self.state[u]
        sv = -self.state[v]
        if su < sv: u, v = v, u
        self.state[u] = -su-sv
        self.state[v] = u
        self.cnt -= 1
        return True
    def size(self, u):
        return -self.state[self.root(u)]
from collections import Counter
def nHr(hn, hr):
    return nCr(hn+hr-1, hr-1)
def nPr(com_n, com_r):
    if com_r < 0: return 0
    if com_n < com_r: return 0
    return fac[com_n]*ifac[com_n-com_r]%md
def nCr(com_n, com_r):
    if com_r < 0: return 0
    if com_n < com_r: return 0
    return fac[com_n]*ifac[com_r]%md*ifac[com_n-com_r]%md
n_max = 100005
fac = [1]
for i in range(1, n_max+1): fac.append(fac[-1]*i%md)
ifac = [1]*(n_max+1)
ifac[n_max] = pow(fac[n_max], md-2, md)
for i in range(n_max-1, 1, -1): ifac[i] = ifac[i+1]*(i+1)%md
def popcnt(a): return bin(a).count("1")
n, m = LI()
ab = LLI1(m)
pe = Counter()
ans = 0
for s in range(1, 1 << m):
    uf = UnionFind()
    cyc = 0
    deg = Counter()
    for i, (a, b) in enumerate(ab):
        if s >> i & 1 == 0: continue
        deg[a] += 1
        deg[b] += 1
        if deg[a] > 2 or deg[b] > 2:
            cyc = 2
            break
        if not uf.merge(a, b):
            cyc += 1
            if cyc == 2: break
    if cyc == 2: continue
    if cyc and uf.cnt > 1: continue
    e = popcnt(s)
    if cyc:
        if e & 1: ans -= 1
        else: ans += 1
    else:
        pe[uf.cnt, e] += 1
# pDB(ans, pe)
inv = (md+1)//2
for k in range(3, n+1):
    ans += nCr(n, k)*fac[k-1]%md*inv%md
    ans %= md
# pDB(ans)
for (p, e), c in pe.items():
    v = e+p
    cur = 0
    for k in range(max(v, 3), n+1):
        cur += nCr(n-v, k-v)*fac[k-v+p-1]%md*pow(2, p-1, md)%md
        cur %= md
    cur = cur*c%md
    if e & 1: ans -= cur
    else: ans += cur
    ans %= md
print(ans)
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