loj#2574. 「TJOI2018」智力竞赛 (路径覆盖)

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目录

• [TOC]

题目链接

loj#2574. 「TJOI2018」智力竞赛

题解

就是求可重路径覆盖之后最大化剩余点的最小权值

二分答案后就是一个可重复路径覆盖

处理出可达点做二分图匹配就好了

代码

#include<cstdio>
#include<cstring>
#include<algorithm>
#define gc getchar()
#define pc putchar
inline int read() {
	int x = 0,f = 1;
	char c = getchar();
	while(c < '0' || c > '9') c = gc;
	while(c <= '9' && c >= '0') x = x * 10 + c - '0',c = gc;
	return x * f;
}
void print(int x) {
 	if(x < 0) {
 		pc('-');
 		x = -x;
 	}
 	if(x >= 10) print(x / 10);
 	pc(x % 10 + '0');
 }
const int maxn = 507;
int n,m;
bool mp[maxn][maxn];
int val[maxn];
int a[maxn];
void floyd() {
	for(int k = 1;k <= n;++ k)
		for(int i = 1;i <= n;++ i)
			for(int j = 1;j <= n;++ j)
				mp[i][j] |= mp[i][k] & mp[k][j];
}
int vis[maxn];
int tot = 0;
int bel[maxn];
bool find(int x,int fa) {
	for(int i = 1;i <= tot;++ i) {
		if(vis[i] != fa && mp[a[x]][a[i]]) {
			vis[i] = fa;
			if(!bel[i] || find(bel[i],fa)) {
				bel[i] = x;
				return true;
			}
		}
	}
	return false;
}
int check(int x) {
	tot = 0;
	for(int i = 1;i <= m;++ i) if(val[i] < x) a[++ tot] = i;
	int ret = tot;
	memset(bel,0,sizeof bel);
	for(int i = 1;i <= tot;++ i) {
		if(find(i,i)) ret --;
	}
	return ret;
}
int main() {
	//freopen("contest2.in","r",stdin);
	n = read() + 1, m = read();
	int mx = 0;
	for(int k,i = 1;i <= m;++ i) {
		val[i] = read();
		mx = std::max(mx,val[i]);
		k = read();
		for(int v,j = 1;j <= k;++ j) {
				v = read();
				mp[i][v] = 1;
		}
	}
	floyd();
	int ans = -1;
	int l = 1,r = mx;
	while(l <= r) {
		int mid = l + r >> 1;
		if(check(mid) <= n) l = mid + 1,ans = mid;
		else r = mid - 1;
	}
	if(l <= mx) print(ans),pc('\n');
	else puts("AK");
	return 0;
}