poj 3169 Layout

最新推荐文章于 2019-07-29 19:43:21 发布

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最新推荐文章于 2019-07-29 19:43:21 发布

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原文链接：http://www.cnblogs.com/shinianhuanniyijuhaojiubujian/p/9878287.html

本文探讨了布局问题，特别是在限制条件下最大化两头牛之间的距离。通过使用差分约束系统，文章提供了一种解决此类问题的方法，并给出了具体的实现代码示例。

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Layout

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 15121		Accepted: 7265

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

Sample Output

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.

差分约束系统

对于两头牛之间距离不大于d 有 dis[a]+d>=dis[b]

对于两头牛之间距离不小于d 有 dis[a]+d<=dis[b]

//差分约束系统
#include <iostream>
#include <cstring>
#include <queue>
#include <vector>
#include <algorithm>
#include <cstdio>
using namespace std;
#define INF 1044266558
int n,a,b,u,t,w;
int dis[1006],vis[1006],in[1006];
int head[1006];
struct node{
    int to,w,next;
}edge[30006];
int ans=0;
void add_edge(int u,int v,int w){
    edge[ans].to=v;
    edge[ans].w=w;
    edge[ans].next=head[u];
    head[u]=ans++;
}
queue<int>q;
int bfs(int s){
    memset(dis,62,sizeof(dis));
    memset(vis,0,sizeof(vis));
    memset(in,0,sizeof(in));
    in[s]=1;
    vis[s]=1;
    dis[s]=0;
    q.push(s);
    while(!q.empty()){
        int e=q.front();
        q.pop();
        in[e]=0;
        if(vis[e]>n) return 1;
        for(int i=head[e];i!=-1;i=edge[i].next){
            int u=edge[i].to;
            int s=edge[i].w;
            if(dis[u]>dis[e]+s){
                dis[u]=dis[e]+s;
                vis[u]++;
                if(!in[u]){
                    in[u]=1;
                    q.push(u);
                }
            }
        }
    }
    return 0;
}
int main(){
    scanf("%d%d%d",&n,&a,&b);
    memset(head,-1,sizeof(head));
    for(int i=0;i<a;i++){
        scanf("%d%d%d",&u,&t,&w);
        add_edge(u,t,w);
    }
    for(int i=0;i<b;i++){
        scanf("%d%d%d",&u,&t,&w);
        add_edge(t,u,-w);
    }
    if(bfs(1)) printf("-1\n");
    else if(dis[n]==INF) printf("-2\n");
    else printf("%d\n",dis[n]);
    return 0;
}

//差分约束系统
#include <iostream>
#include <cstring>
#include <queue>
#include <vector>
#include <algorithm>
#include <cstdio>
using namespace std;
#define INF 1044266558
typedef pair<int,int> P;
vector<pair<int,int> >v[1006];
int n,a,b,u,t,w;
int dis[1006],vis[1006],in[1006];
queue<int>q;
int bfs(int s){
    memset(dis,62,sizeof(dis));
    memset(vis,0,sizeof(vis));
    memset(in,0,sizeof(in));
    in[s]=1;
    vis[s]=1;
    dis[s]=0;
    q.push(s);
    while(!q.empty()){
        int e=q.front();
        q.pop();
        in[e]=0;
        if(vis[e]>n) return 1;
        for(int i=0;i<v[e].size();i++){
            int u=v[e][i].first;
            int s=v[e][i].second;
            if(dis[u]>dis[e]+s){
                dis[u]=dis[e]+s;
                vis[u]++;
                if(!in[u]){
                    in[u]=1;
                    q.push(u);
                }
            }
        }
    }
    return 0;
}
int main(){
    scanf("%d%d%d",&n,&a,&b);
    for(int i=0;i<a;i++){
        scanf("%d%d%d",&u,&t,&w);
        v[u].push_back(P(t,w));
    }
    for(int i=0;i<b;i++){
        scanf("%d%d%d",&u,&t,&w);
        v[t].push_back(P(u,-w));
    }
    if(bfs(1)) printf("-1\n");
    else if(dis[n]==INF) printf("-2\n");
    else printf("%d\n",dis[n]);
    return 0;
}