poj 2983（最短路差分约束）

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最新推荐文章于 2020-07-16 16:23:32 发布

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分类专栏：差分约束 poj

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本文介绍了一种算法，用于验证给定的防御站布局信息是否可靠。通过解析精确和模糊的位置提示，利用差分系统和SPFA算法判断布局的可行性。

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Is the Information Reliable?

Time Limit: 3000MS		Memory Limit: 131072K
Total Submissions: 15783		Accepted: 4893

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

Sample Output

Unreliable
Reliable

题意：银河系中有n个防御站排成一条直线，给定m条信息，每条信息的格式如下。
P A B X代表A站在B站北方X光年处。
V A B 代表A站在B站北方，而且距离至少为1光年。
问是否存在这样的一个防御战排列满足上述要求，是输出Reliable，否输出 Unreliable。

从P A B X得到的差分系统为

dist[A] - dist[B] >= X && dist[A] - dist[B] <= X

等价于
dist[B] <= dist[A] - X && dist[A] <= dist[B] + X

从V A B得到的差分系统为
dist[A] >= dist[B] +1

等价于
dist[B] <= dist[A] -1

#include<iostream>
#include<cstdio>
#include<cmath>
#include<queue>
#include<cstring>


using namespace std;
const int N=1e5+10;
const int inf=0x3f3f3f3f;
struct node
{
	int to,dis,next;
}edge[N<<2];
int cnt,head[N];
void addedge(int from,int to,int dis)
{
	edge[cnt].to=to;
	edge[cnt].dis=dis;
	edge[cnt].next=head[from];
	head[from]=cnt++;
}

int dis[N];
bool vis[N];
int num[N];
bool spfa(int n)
{
	memset(num,0,sizeof(num));
	memset(vis,false,sizeof(vis));
	memset(dis,inf,sizeof(dis));
	dis[0]=0;
	vis[0]=true;
	queue<int>Q;
	Q.push(0);
	while(!Q.empty()){
		int u=Q.front();
		Q.pop();
		vis[u]=false;
		//cout<<"u="<<u<<endl;
		for(int i=head[u];i!=-1;i=edge[i].next){
			int to=edge[i].to;
			if(dis[to]>dis[u]+edge[i].dis){
				dis[to]=dis[u]+edge[i].dis;
				if(!vis[to]){
					vis[to]=true;
					Q.push(to);
					if(++num[to]>n) return false;
				}
			}
		}
	} 
	return true;
}
int main()
{

	int n,m;
	while(scanf("%d %d",&n,&m)==2){
		memset(head,-1,sizeof(head));
		cnt=0;
		for(int i=0;i<m;i++){
			char t[10];
			int a,b;
			scanf("%s %d %d",t,&a,&b);
			if(t[0]=='P'){
				int c;
				scanf("%d",&c);
				addedge(a,b,-c);
				addedge(b,a,c);
			}
			else{
				addedge(a,b,-1);
			}
		}
		for(int i=1;i<=n;i++){
			addedge(0,i,0);
		}
		if(spfa(n)){
			puts("Reliable");
		}
		else{
			puts("Unreliable");
		}
	}
	return 0;
}