POJ 3169 Layout (差分约束spfa)

Layout

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 6888 Accepted: 3330

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

分析：差分约束在求最大值时，找《=关系，最短路算法。在求最小值时，找》=关系，用最长路算法。

此题求最大值。《=关系有Ai-A(i+1)<=0,前ML个Ab-Aa<=c，后MD个Aa-Ab<=-c,用这三个关系建图，求最短路

代码：

#include<iostream>#include<cstdio>#include<cstring>#include<string>#include<queue>#include<map>#include<cmath>#define INF 0x3f3f3f3fusing namespace std;const int MAXN=1005;const int MAXM=20005;int v[MAXM],w[MAXM],nex[MAXM];int inq[MAXN],done[MAXN],dis[MAXN],first[MAXN],da[MAXN];int cnt;int spfa(int s,int n){    for(int i=1;i<=n;i++)dis[i]=INF;    memset(inq,0,sizeof inq);    memset(done,0,sizeof done);    queue<int>q;    q.push(s);    done[s]++;    dis[s]=0;    while(!q.empty())    {        int x=q.front();q.pop();        inq[x]=0;        for(int e=first[x];~e;e=nex[e])        if(dis[v[e]]>dis[x]+w[e]){            dis[v[e]]=dis[x]+w[e];            if(!inq[v[e]])            {                q.push(v[e]);                inq[v[e]]=1;                if(++done[v[e]]>n)return 1;            }        }    }    return 0;}void add_(int a,int b,int c){    v[cnt]=b;    w[cnt]=c;    nex[cnt]=first[a];    first[a]=cnt++;}int main(){    int n,m,p,i,cas=0;char cs[4];    while(~scanf("%d%d%d",&n,&m,&p))    {        int a,b,c;        memset(first,-1,sizeof first);        memset(nex,-1,sizeof nex);        cnt=0;        for(i=1;i<n;i++)            add_(i+1,i,0);        for(i=1;i<=m;i++)        {            scanf("%d%d%d",&a,&b,&c);            add_(a,b,c);        }        for(i=1;i<=p;i++)        {            scanf("%d%d%d",&a,&b,&c);            add_(b,a,-c);        }        if(spfa(1,n))printf("-1\n");        else if(dis[n]==INF) printf("-2\n");        else printf("%d\n",dis[n]);    }    return 0;}