差分约束系统——POJ 2983

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Is the Information Reliable?

Time Limit: 3000MS Memory Limit: 131072KTotal Submissions: 11393 Accepted: 3594

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 4P 1 2 1P 2 3 1V 1 3P 1 3 15 5V 1 2V 2 3V 3 4V 4 5V 3 5

Sample Output

UnreliableReliable

Source

题意：给出两种关于防御站位置的信息，一种是确切的信息，P A B X，表示A在B北面x距离的地方，另一种是V A B，表示只知道A在B的北面。问这些信息有没有矛盾。

思路：确切信息可表示为  A - B >= X && A - B <= X，模糊信息可表示为 A - B >= 1

即是分别表示为：A - B <= X && B - A <= -X 和 B - A <= -1

建图用Bellman_Ford或Spfa都可以解决，其中前者可直接解决，后者需要加入一个超级源，使到每个点的距离为0（这样才能使每个点都走过，否则对于不连通的图，这不能）。

Spfa：

#include<cstdio>#include<cstdlib>#include<cmath>#include<map>#include<queue>#include<stack>#include<vector>#include<algorithm>#include<cstring>#include<string>#include<iostream>const int MAXN=1000+10;const int INF=1<<30;using namespace std;int dis[MAXN];int in[MAXN];int vis[MAXN];int head[MAXN];int size,n,m;struct Edge{int v,w,next;}E[202000];void Build(int u, int v, int w){E[size].v = v;E[size].w = w;E[size].next = head[u];head[u] = size++;}int Spfa(){memset(vis,0,sizeof(vis));memset(in,0,sizeof(in));for(int i=0; i<=n; i++) dis[i] = INF;dis[0] = 0;queue<int>q;q.push(0);vis[0] = 1;while(!q.empty()){int u = q.front();vis[u] = 0;q.pop();for(int i=head[u]; i!=-1; i=E[i].next){int v = E[i].v;int w = E[i].w;if(dis[u] + w < dis[v]){dis[v] = dis[u] + w;if(!vis[v]){vis[v] = 1;in[v]++;if(in[v] >= n) return 0;q.push(v);}}}}return 1;}int main(){//freopen("in.txt","r",stdin);while(~scanf("%d%d", &n,&m)){memset(head,-1,sizeof(head));size = 0;char ch[3];int a,b,w;for(int i=0; i<m; i++){scanf("%s", ch);if(ch[0] =='P'){scanf("%d%d%d", &a,&b,&w);Build(a,b,w);Build(b,a,-w);}else{scanf("%d%d", &a,&b);Build(b,a,-1);}}for(int i=1; i<=n; i++)Build(0,i,0);//加入超级源int ok = Spfa();if(ok) printf("Reliable\n");else printf("Unreliable\n");}return 0;}

Bellman_Ford:

#include<cstdio>#include<cstdlib>#include<cmath>#include<map>#include<queue>#include<stack>#include<vector>#include<algorithm>#include<cstring>#include<string>#include<iostream>const int MAXN=1000+10;const int INF=1<<30;using namespace std;int dis[MAXN];int size,n,m;struct Edge{int u,v,w;}E[200000];void Build(int u, int v, int w){E[size].u = u;E[size].v = v;E[size++].w = w;}int Bellman_Ford(){for(int i=1; i<=n; i++) dis[i] = INF;dis[1] = 0;for(int i=1; i<=n-1; i++){for(int j=0; j<size; j++){if(dis[E[j].u] + E[j].w < dis[E[j].v])dis[E[j].v] = dis[E[j].u] + E[j].w;}}for(int i=0; i<size; i++)if(dis[E[i].u] + E[i].w < dis[E[i].v]) return 0;return 1;}int main(){//freopen("in.txt","r",stdin);while(~scanf("%d%d", &n,&m)){size = 0;char ch[3];int a,b,w;for(int i=0; i<m; i++){scanf("%s", ch);if(ch[0] =='P'){scanf("%d%d%d", &a,&b,&w);Build(a,b,w);Build(b,a,-w);}else{scanf("%d%d", &a,&b);Build(b,a,-1);}}int ok = Bellman_Ford();if(ok) printf("Reliable\n");else printf("Unreliable\n");}return 0;}