poj 3169 Layout（差分约束）

Layout

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 10282		Accepted: 4948

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.

Source

USACO 2005 December Gold

题目给出了三个约束:

1.dis[i] <= dis[i+1]   ----> dis[i] <= dis[i+1]+0

2.dis[y]-dis[x] <= w ----> dis[y] <= dis[x]+w

3.dis[y]-dis[x] >= w ----> dis[x] <= dis[y]+(-w)

满足以上约束不等式的dis中，dis[v]-dis[s]的最大值就是从s到v的

最短距离。注意的是这里不是最小值，而是最大值对应着最短距

离。

构图：

dis[i] <= dis[i+1]+0，从顶点i+1向顶点i连一条权值为0的边。

dis[y] <= dis[x]+w， 从x向y连一条权值为w的有向边

dis[x] <= dis[y]+(-w)， 从y向x连一条权值为-w的有向边

具体代码：

#include
#include
#include
using namespace std;
const int maxn = 1e3+5;
const int maxm = 1e5+5;
const int INF = 0x3f3f3f3f;
int n, k, ml, md, dis[maxn];
struct node
{
    int u, v, w;
    node() {}
    node(int uu, int vv, int ww): u(uu), v(vv), w(ww) {}
}edge[maxm];

void Bellman_Ford(int s)
{
    bool f = false;
    memset(dis, INF, sizeof(dis));
    dis[s] = 0;
    for(int i = 0; i < n; i++)
    {
        int flag = 1;
        for(int j = 0; j < k; j++)
        {
            int u = edge[j].u;
            int v = edge[j].v;
            int w = edge[j].w;
            if(dis[u]+w < dis[v])
            {
                flag = 0;
                dis[v] = dis[u]+w;
                if(i == n-1) f = true;
            }
        }
        if(flag) break;
    }
    if(f) { puts("-1"); return ; }
    if(dis[n] == INF) { puts("-2"); return ; }
    printf("%d\n", dis[n]);
}
int main(void)
{
    while(cin >> n >> ml >> md)
    {
        k = 0;
        int u, v, w;
        for(int i = 1; i <= ml+md; i++)
        {
            scanf("%d%d%d", &u, &v, &w);
            edge[k++] = i <= ml ? node(u, v, w) : node(v, u, -w);
        }
        Bellman_Ford(1);
    }
    return 0;
}