【POJ 2391】Ombrophobic Bovines【2点】【Floyd】【最大ストリーム】

【テーマリンク】
論文のテーマは、【ネットワークフローのモデリングのまとめ】を参照してください.
注意:
1、最も短絡を計算します.
2、加辺はすでに存在している辺だけではなく、列挙点で、最短のパスを追加します.
3、自分で自分に行くにも端をつなぐ.
4、Flong long longを開くように注意してください.
5、注意判断-1.
データアドレス:http://contest.usaco.org/MAR05_4.ht

/* Pigonometry */
#include <cstdio>
#include <algorithm>

using namespace std;

typedef long long LL;

const int maxn = 1005, maxm = 100005, maxq = 10000, inf = 0x3f3f3f3f;
const LL infinf = (LL)inf * inf;

int n, m, cur[maxn], head[maxn], cnt, depth[maxn], bg, ed, q[maxq], maxflow, A[maxn], B[maxn];
LL map[maxn][maxn];

struct _edge {
	int v, w, next;
} g[maxm];

inline int iread() {
	int f = 1, x = 0; char ch = getchar();
	for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;
	for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
	return f * x;
}

inline void add(int u, int v, int w) {
	g[cnt] = (_edge){v, w, head[u]};
	head[u] = cnt++;
}

inline void insert(int u, int v, int w) {
	add(u, v, w); add(v, u, 0);
}

inline bool bfs() {
	for(int i = 0; i <= ed; i++) depth[i] = -1;
	int h = 0, t = 0, u, i; depth[q[t++] = bg] = 1;
	while(h != t) for(i = head[u = q[h++]]; ~i; i = g[i].next) if(g[i].w && !~depth[g[i].v]) {
		depth[g[i].v] = depth[u] + 1;
		if(g[i].v == ed) return 1;
		q[t++] = g[i].v;
	}
	return 0;
}

inline int dfs(int x, int flow) {
	if(x == ed) return flow;
	int left = flow;
	for(int i = cur[x]; ~i; i = g[i].next) if(g[i].w && depth[g[i].v] == depth[x] + 1) {
		int tmp = dfs(g[i].v, min(left, g[i].w));
		left -= tmp; g[i].w -= tmp; g[i ^ 1].w += tmp;
		if(g[i].w) cur[x] = i;
		if(!left) return flow;
	}
	if(left == flow) depth[x] = -1;
	return flow - left;
}

inline bool check(LL tim) {
	for(int i = 0; i <= ed; i++) head[i] = -1; cnt = 0;
	for(int i = 1; i <= n; i++) {
		insert(bg, i, A[i]);
		insert(i + n, ed, B[i]);
	}
	for(int i = 1; i <= n; i++) for(int j = 1; j <= n; j++) if(map[i][j] <= tim)
		insert(i, n + j, inf);

	int ans = maxflow;
	while(bfs()) {
		for(int i = 0; i <= ed; i++) cur[i] = head[i];
		ans -= dfs(bg, inf);
	}
	return ans;
}

int main() {
	n = iread(); m = iread(); bg = 0; ed = (n << 1) + 1;

	for(int i = 1; i <= n; i++) for(int j = 1; j <= n; j++) if(i ^ j)
		map[i][j] = infinf;

	int maxb = 0;
	for(int i = 1; i <= n; i++) {
		A[i] = iread(); B[i] = iread();
		maxflow += A[i];
		maxb += B[i];
	}

	if(maxflow > maxb) {
		printf("-1
");
		return 0;
	}

	LL maxw = 0;
	for(int i = 1; i <= m; i++) {
		int u = iread(), v = iread();
		LL w; scanf("%lld", &w);
		map[u][v] = min(map[u][v], w);
		map[v][u] = min(map[v][u], w);
		maxw += w;
	}

	for(int k = 1; k <= n; k++) for(int i = 1; i <= n; i++) for(int j = 1; j <= n; j++)
		map[i][j] = min(map[i][j], map[i][k] + map[k][j]);

	LL l = 0, r = maxw;
	while(l <= r) {
		LL mid = l + r >> 1;
		if(check(mid)) l = mid + 1;
		else r = mid - 1;
	}

	if(r == maxw) l = -1;
	printf("%lld
", l);
	return 0;
}