poj 2983Is the Information Reliable? 差分约束

Posted 2020-07-19 ALPS233

题目：http://poj.org/problem?id=2983

Is the Information Reliable?
Time Limit: 3000MS Memory Limit: 131072K
Total Submissions: 12535 Accepted: 3943

Description

The galaxy war between the Empire Draco and the Commonwealth of Zibu broke out 3 years ago. Draco established a line of defense called Grot. Grot is a straight line with N defense stations. Because of the cooperation of the stations, Zibu’s Marine Glory cannot march any further but stay outside the line.

A mystery Information Group X benefits form selling information to both sides of the war. Today you the administrator of Zibu’s Intelligence Department got a piece of information about Grot’s defense stations’ arrangement from Information Group X. Your task is to determine whether the information is reliable.

The information consists of M tips. Each tip is either precise or vague.

Precise tip is in the form of P A B X, means defense station A is X light-years north of defense station B.

Vague tip is in the form of V A B, means defense station A is in the north of defense station B, at least 1 light-year, but the precise distance is unknown.

Input

There are several test cases in the input. Each test case starts with two integers N (0 < N ≤ 1000) and M (1 ≤ M ≤ 100000).The next M line each describe a tip, either in precise form or vague form.

Output

Output one line for each test case in the input. Output “Reliable” if It is possible to arrange N defense stations satisfying all the M tips, otherwise output “Unreliable”.

Sample Input
3 4
P 1 2 1
P 2 3 1
V 1 3
P 1 3 1
5 5
V 1 2
V 2 3
V 3 4
V 4 5
V 3 5

Sample Output
Unreliable
Reliable

Source

POJ Monthly–2006.08.27, Dagger

题意：n个点，告诉m个a,b间（有向）路径长度或路径长度>=1；求信息有误否。

思路：差分约束系统，建边
1.a-b>=c  b-a>=-c
2.a-b>=1;
‘>=’建最小边，spfa最长路，更新次数>=n—->有环—》false；

代码：

#include<iostream>
#include<stdio.h>
#include<vector>
#include<string.h>
#include<queue>
using namespace std;

int n,m;
char s[3];
int aa,bb,cc;
int tot;
struct nod{
    int x,v;
    nod(int xx,int vv)
    {
        x=xx,v=vv;
    }nod(){}
};
vector<nod> lin[1005];
int vis[1005],d[1005];
int cnt[1005];
queue<int> Q;
bool spfa()
{
    Q.push(0);
    d[0]=0;
    vis[0]=1;
    while(!Q.empty())
    {
        int now=Q.front();
        Q.pop();
        vis[now]=0;

        for(int i=0;i<lin[now].size();i++)
        {
            int v=lin[now][i].x;
            int vv=lin[now][i].v;

            if(d[v]==-1||d[v]<d[now]+vv)
            {

                d[v]=d[now]+vv;
                cnt[v]++;
                if(cnt[v]>n)
                {
                    return false;
                } 
                if(!vis[v])
                {
                    vis[v]=1;
                    Q.push(v);
                }
            }
        }
    }
    return 1;
}
int main()
{
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        for(int i=1;i<=n;i++)
        {
            lin[i].clear();
            d[i]=-1;
            vis[i]=0;
            cnt[i]=0;
        }
        for(int i=1;i<=m;i++)
        {

            scanf("%s",s);
            if(s[0]==‘P‘)
            {
                scanf("%d%d%d",&aa,&bb,&cc);
                lin[aa].push_back(nod(bb,cc));
                lin[bb].push_back(nod(aa,-cc));
            } 
            else  if(s[0]==‘V‘) 
            {
                scanf("%d%d",&aa,&bb);
                lin[aa].push_back(nod(bb,1));
            }
        }
        for(int i=1;i<n;i++)
        {
            lin[0].push_back(nod(i,0));
        }

        if(!spfa())
        printf("Unreliable\n");
        else printf("Reliable\n");


    }
}