poj 3169 Layout （差分约束模板题）

Layout

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 11722 Accepted: 5617

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 11 3 102 4 202 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

题目大意：

一些母牛按序号排成一条直线。有两种要求，A和B距离不得超过X，还有一种是C和D距离不得少于Y，问可能的最大距离。如果没有输出-1，如果可以随便排输出-2，否则输出最大的距离。

思路：查分约束裸题，最后求得是最大距离，所以跑最短路， 并且所有 >= 改为<=，如果是 <x 改为 < x-1，有负环说明无解， 是正无穷说明无穷解

代码：

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <queue>#include <vector>using namespace std;const int maxn = 1e3 + 5;const int INF = 2e9;struct node{    int to, w;    node(){}    node(int tt, int ww) : to(tt) , w(ww){}};vector<node> v[maxn];int n, ml, md, x, y, w, cnt[maxn], book[maxn], dis[maxn];int spfa(){    memset(book, 0, sizeof(book));    for(int i = 1; i < maxn; i++) dis[i] = INF;    dis[1] = 0;    book[1] = 1;    cnt[1] = 1;    queue<int> q;    q.push(1);    while(!q.empty())    {        int u = q.front();        q.pop();        book[u] = 0;        for(int i = 0; i < v[u].size(); i++)        {            int to = v[u][i].to;            if(dis[u]+v[u][i].w < dis[to])            {                dis[to] = dis[u] + v[u][i].w;                if(!book[to])                {                    if(++cnt[to] > n)                        return -1;                    book[to] = 1;                    q.push(to);                }            }        }    }    if(dis[n] == INF)        return -2;    else        return dis[n];}int main(){    while(~scanf("%d%d%d", &n, &ml, &md))    {        memset(cnt, 0, sizeof(cnt));        memset(dis, 0, sizeof(dis));        memset(book, 0, sizeof(book));        for(int i = 1; i <= ml; i++)        {            scanf("%d%d%d", &x, &y, &w);            v[x].push_back(node(y,w));        }        for(int i = 1; i <= md; i++)        {            scanf("%d%d%d", &x, &y, &w);            v[y].push_back(node(x, -w));        }        printf("%d\n", spfa());    }    return 0;}