poj2391

二分 最大流

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define LL long long
using namespace std;

int n,m,u,v,sum;

int a[210],b[210];

LL dis[210][210];

struct mes {
	int u,v;
	LL w;
	bool operator < (const mes &b)const {
		return w < b.w;
	}
}E[90010];
int CNT;

struct edge {
	int v,f,next;
}e[90010];
int cnt,head[410];

int h[410],gap[410];

LL read_int () {
	char c = getchar();
	LL re = 0;
	for(;c > '9' || c < '0';c = getchar());
	for(;c >= '0' && c <= '9';c = getchar())
		re = re * 10 + c - '0';
	return re;
}

int dfs (int u,int minf) {
	if(u == n + n + 1)
		return minf;
	
	int chan = n + n + 1;
	int leftf = minf;
	
	for(int i = head[u];i != -1;i = e[i].next) {
		int v = e[i].v;
		
		if(e[i].f) {
			if(h[v] == h[u] - 1) {
				int t = dfs(v,min(leftf,e[i].f));
				e[i].f -= t;
				e[i ^ 1].f += t;
				leftf -= t;
				
				if(h[0] >= n + n + 2)
					return minf - leftf;
				if(!leftf)
					break;
			}
			chan = min(chan,h[v]);
		}
	}
	
	if(leftf == minf) {
		if(--gap[h[u]] == 0)
			h[0] = n + n + 2;
		++gap[h[u] = chan + 1];
	}
	return minf - leftf;
}

bool sap () {
	int re = 0;
	memset(h,0,sizeof h);
	memset(gap,0,sizeof gap);
	gap[0] = n + n + 2;
	while(h[0] < n + n + 2)
		re += dfs(0,0x3f3f3f3f);
	if(re == sum)
		return 1;
	return 0;
}

void adde (int u,int v,int f) {
	e[cnt].v = v;
	e[cnt].f = f;
	e[cnt].next = head[u];
	head[u] = cnt++;

	e[cnt].v = u;
	e[cnt].f = 0;
	e[cnt].next = head[v];
	head[v] = cnt++;
}

int main () {
	n = read_int();
	m = read_int();
	
	for(int i = 1;i <= n - 1;++i)
		for(int j = i + 1;j <= n;++j)
			dis[i][j] = dis[j][i] = (LL)1000000000000000;
	
	for(int i = 1;i <= n;++i) {
		a[i] = read_int();
		sum += a[i];
		b[i] = read_int();
	}
	for(int i = 1;i <= m;++i) {
		u = read_int();
		v = read_int();
		dis[u][v] = dis[v][u] = min(dis[v][u],read_int());
	}
	for(int k = 1;k <= n;++k) {
		for(int i = 1;i <= n;++i) {
			for(int j = 1;j <= n;++j) {
				if(dis[i][j] > dis[i][k] + dis[k][j])
					dis[i][j] = dis[i][k] + dis[k][j];
			}
		}
	}
	for(int i = 1;i <= n;++i) {
		for(int j = i;j <= n;++j) {
			if(dis[i][j] != (LL)1000000000000000) {
				E[++CNT].v = j;
				E[CNT].u = i;
				E[CNT].w = dis[i][j];
			}
		}
	}
	sort(E + 1,E + 1 + CNT);
	int l = 1,r = CNT,ans = -1;
	while(l <= r) {
		int mid = (l + r) >> 1;
		
		memset(head,-1,sizeof head);
		cnt = 0;
		for(int i = 1;i <= mid;++i) {
			adde(E[i].u,E[i].v + n,0x3f3f3f3f);
			if(E[i].u != E[i].v)
				adde(E[i].v,E[i].u + n,0x3f3f3f3f);
		}
		for(int i = 1;i <= n;++i) {
			adde(0,i,a[i]);
			adde(i + n,n + n + 1,b[i]);
		}
		
		if(sap()) {
			ans = mid;
			r = mid - 1;
		}
		else l = mid + 1;
	}
	if(ans == -1)
		puts("-1");
	else cout << E[ans].w << endl;
}