图论--差分约束--POJ 2983--Is the Information Reliable?

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

Reliabl

给出了 P a  b  w 表示 b在a以北w公里， V a  b 表示 b在a北边，最少1公里，问所有 的条件可不可以全部满足。

由P 可以得到 b - a = w 也就是b - a <= w  &&  a - b <= w ，由 V a  b 得到 b - a >= 1 也就是 a - b <= -1 ;建图，使用最短路，判断是否会有负环。初始dis要全部为0.

#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
#define INF 1e9
using namespace std;
const int maxn=1000+10;
const int maxm=100000*3;
struct Edge
{
    int from,to,dist;
    Edge(){}
    Edge(int f,int t,int d):from(f),to(t),dist(d){}
};
struct BellmanFord
{
    int n,m;
    int head[maxn],next[maxm];
    Edge edges[maxm];
    int d[maxn];
    int cnt[maxn];
    bool inq[maxn];
    void init(int n)
    {
        this->n=n;
        m=0;
        memset(head,-1,sizeof(head));
    }
    void AddEdge(int from,int to,int dist)
    {
        edges[m]=Edge(from,to,dist);
        next[m]=head[from];
        head[from]=m++;
    }
    bool bellman_ford()
    {
        memset(inq,0,sizeof(inq));
        memset(cnt,0,sizeof(cnt));
        queue<int> Q;
        for(int i=0;i<n;i++) d[i]= i==0?0:INF;
        Q.push(0);
        while(!Q.empty())
        {
            int u=Q.front(); Q.pop();
            inq[u]=false;
            for(int i=head[u];i!=-1;i=next[i])
            {
                Edge &e=edges[i];
                if(d[e.to] > d[u]+e.dist)
                {
                    d[e.to] = d[u]+e.dist;
                    if(!inq[e.to])
                    {
                        inq[e.to]=true;
                        Q.push(e.to);
                        if(++cnt[e.to]>n) return true;
                    }
                }
            }
        }
        return false;
    }
}BF;
int main()
{
    int n,m;
    while(scanf("%d%d",&n,&m)==2)
    {
        BF.init(n+1);
        while(m--)
        {
            char s[10];
            int u,v,d;
            scanf("%s",s);
            if(s[0]=='P')
            {
                scanf("%d%d%d",&u,&v,&d);
                BF.AddEdge(u,v,d);
                BF.AddEdge(v,u,-d);
            }
            else if(s[0]=='V')
            {
                scanf("%d%d",&u,&v);
                BF.AddEdge(v,u,-1);
            }
        }
        for(int i=1;i<=n;i++)
            BF.AddEdge(0,i,0);
        printf("%s\n",BF.bellman_ford()?"Unreliable":"Reliable");
    }
    return 0;
}