POJ_2983_Is the Information Reliable? _差分约束

Is the Information Reliable?
Time Limit: 3000MS        Memory Limit: 131072K
Total Submissions: 12466        Accepted: 3924

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

题意：

P u v w 表示 v在u以北w公里。

V u v 表示 v在u北边，最少1公里，问所有条件可不可以全部满足。

思路：

由P 可以得到 v - u = w 也就是u - v <= w  &&  v - u <= -w ，
由 V u v 得到 v - u >= 1 也就是 u - v <= -1 ;

建图，使用最短路，判断是否会有负环。

#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
#define inf 0x3f3f3f3f
using namespace std;
struct Node
{
	int v;
	int w;
	int next;
}s[210000];
int head[1010];
int dist[1010];
bool vis[1010];
int n,m,num;
int coun[1010];
void add_edge(int a,int b,int c)
{
	s[num].v = b;
	s[num].w = c;
	s[num].next = head[a];
	head[a] = num++;
}
int SPFA()
{
	queue<int> Q;
	memset(dist,inf,sizeof(dist));
	memset(vis,false,sizeof(vis));
	memset(coun,0,sizeof(coun));
	dist[0] = 0;
	vis[0] = true;	
	coun[0] = 1; 
	Q.push(0);
	while(!Q.empty())
	{
		int u = Q.front();
		Q.pop();
		vis[u] = false;
		coun[u]++;
		if(coun[u]>n)
		{
			return 0;
		}
		for(int i=head[u];i!=-1;i=s[i].next)
		{
			int v = s[i].v;
			int w = s[i].w;
			if(dist[v]>dist[u]+w)
			{
				dist[v] = dist[u] + w;
				if(!vis[v])
				{
					vis[v] = true;
					Q.push(v);
				}
			}
		}
	}
	return 1;
}
int main()
{
	while(scanf("%d%d",&n,&m)!=EOF)
	{
		num = 0;
		int i,j;
		char c[2];
		int u,v,w;
		memset(head,-1,sizeof(head));
		while(m--)
		{
			scanf("%s",c);
			if(c[0]=='P')
			{
				scanf("%d%d%d",&u,&v,&w);
				add_edge(v,u,w);
				add_edge(u,v,-w);
			}
			else
			{
				scanf("%d%d",&u,&v);
				add_edge(u,v,-1);
			}
		}
		for(i=1;i<=n;i++)
		{
			add_edge(0,i,0); //找一个超级源点，给所有点都有关系，权值为0 
		}
		if(SPFA())
		{
			printf("Reliable\n");
		}
		else
		{
			printf("Unreliable\n");
		}
		
	}
	return 0;
}