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;
}