【poj 2983】Is the Information Reliable? 差分约束
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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"); }}
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