【图论】POJ-3169 差分约束系统

一、题目

Description

Like everyone else, cows like to stand close to their friends when queuing for feed. FJ has N (2 <= N <= 1,000) cows numbered 1..N standing along a straight line waiting for feed. The cows are standing in the same order as they are numbered, and since they can be rather pushy, it is possible that two or more cows can line up at exactly the same location (that is, if we think of each cow as being located at some coordinate on a number line, then it is possible for two or more cows to share the same coordinate). 

Some cows like each other and want to be within a certain distance of each other in line. Some really dislike each other and want to be separated by at least a certain distance. A list of ML (1 <= ML <= 10,000) constraints describes which cows like each other and the maximum distance by which they may be separated; a subsequent list of MD constraints (1 <= MD <= 10,000) tells which cows dislike each other and the minimum distance by which they must be separated. 

Your job is to compute, if possible, the maximum possible distance between cow 1 and cow N that satisfies the distance constraints.

Input

Line 1: Three space-separated integers: N, ML, and MD. 

Lines 2..ML+1: Each line contains three space-separated positive integers: A, B, and D, with 1 <= A < B <= N. Cows A and B must be at most D (1 <= D <= 1,000,000) apart. 

Lines ML+2..ML+MD+1: Each line contains three space-separated positive integers: A, B, and D, with 1 <= A < B <= N. Cows A and B must be at least D (1 <= D <= 1,000,000) apart.

Output

Line 1: A single integer. If no line-up is possible, output -1. If cows 1 and N can be arbitrarily far apart, output -2. Otherwise output the greatest possible distance between cows 1 and N.

Sample Input

4 2 1
1 3 10
2 4 20
2 3 3

Sample Output

27

Hint

Explanation of the sample: 

There are 4 cows. Cows #1 and #3 must be no more than 10 units apart, cows #2 and #4 must be no more than 20 units apart, and cows #2 and #3 dislike each other and must be no fewer than 3 units apart. 

The best layout, in terms of coordinates on a number line, is to put cow #1 at 0, cow #2 at 7, cow #3 at 10, and cow #4 at 27.

二、思路

二、思路&心得

• POJ-3169:查分约束系统，利用约束条件，将问题转化为最短路径问题，并利用Bellman-Ford或SPFA算法求解
• 本题需要考虑边的方向关系，虽然感觉是无向图，但是最后却还是初始化成有向图

三、代码

#include<cstdio>
#include<climits>
#include<algorithm>
#define MAX_N 10005
#define MAX_M 30005
#define MAX_D 2000005
using namespace std;

int N, ML, MD;

int A, B, D;

int dist[MAX_N];

struct Edge {
	int from;
	int to;
	int cost;
} E[MAX_M];

int Bellman_Ford(int s) {
	for (int i = 1; i <= N; i ++) {
		dist[i] = MAX_D;
	}
	dist[s] = 0;
	int edgeNum = ML + MD + N - 1;
	for (int i = 0; i < N; i ++) {
		for (int j = 0; j < edgeNum; j ++) {
			if (dist[E[j].from] + E[j].cost < dist[E[j].to]) {
				if (i == N - 1) return -1;
				dist[E[j].to] = dist[E[j].from] + E[j].cost;
			}
		}
	}
	return dist[N] == MAX_D ? -2 : dist[N];
}

void solve() {
	/**
	* 图的初始化
	*/
	for (int i = 0; i < ML; i ++) {
		scanf("%d %d %d", &A, &B, &D);
		if (A > B) swap(A, B);
		E[i].from = A, E[i].to = B, E[i].cost = D;
	}
	for (int i = 0; i < MD; i ++) {
		scanf("%d %d %d", &A, &B, &D);
		if (A > B) swap(A, B);
		E[ML + i].from = B, E[ML + i].to = A, E[ML + i].cost = -D;
	}
	for (int i = 0; i < N - 1; i ++) {
		E[ML + MD + i].from = i + 2, E[ML + MD + i].to = i + 1, E[ML + MD + i].cost = 0;
	}
	printf("%d\n", Bellman_Ford(1));
}

int main() {
	 while (~scanf("%d %d %d", &N, &ML, &MD)) {
	 	solve();
	 }
	return 0;
} x ​