LFYZOJ 104 Counting Swaps

题解

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <cstring>
#define ll long long
using namespace std;
const int MOD = 1e9 + 9, MAXN = 100005;
int T, n, num[MAXN], head[MAXN], nume, id[MAXN], hav[MAXN];
ll fac[MAXN], ni[MAXN];
struct edge{
	int to, nxt;
}e[MAXN<<1];
void adde(int from, int to) {
	e[++nume].to = to;
	e[nume].nxt = head[from];
	head[from] = nume;
}
ll quick_mod(ll a, ll k) {
	if(!a) return 0ll;
	if(k <= 0) return 1ll;
	ll ans = 1;
	while(k) {
		if(k & 1ll) (ans *= a) %= MOD;
		(a *= a) %= MOD;
		k >>= 1;
	}
	return ans % MOD;
}
void dfs(int u, int cur) {
	id[u] = cur;
	for(int i = head[u]; i; i = e[i].nxt) {
		int v = e[i].to;
		if(!id[v]) dfs(v, cur);
	}
}
int main() {
	cin >> T;
	fac[0] = 1;
	for(int i = 1; i <= 100000; i++) fac[i] = fac[i - 1] * i % MOD;
	ni[100000] = quick_mod(fac[100000], MOD - 2);
	for(int i = 100000 - 1; i >= 0; i--) (ni[i] = ni[i + 1] * (i + 1)) %= MOD;
	while(T--) {
		cin >> n;
		memset(head, 0, sizeof(head));
		memset(id, 0, sizeof(id));
		memset(hav, 0, sizeof(hav));
		nume = 0;
		for(int i = 1; i <= n; i++) scanf("%d", &num[i]), adde(i, num[i]);
		int cnt = 0;
		for(int i = 1; i <= n; i++) if(!id[i]) dfs(i, ++cnt);
		for(int i = 1; i <= n; i++) hav[id[i]]++;
		ll ans = 1ll;
		for(int i = 1; i <= cnt; i++) (ans *= quick_mod(hav[i], hav[i] - 2)) %= MOD;
		(ans *= fac[n - cnt]) %= MOD;
		for(int i = 1; i <= cnt; i++) (ans *= ni[hav[i] - 1]) %= MOD;
		printf("%lld
", ans);
	}
	return 0;
}