学步园

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.

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 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”.

差分约束，这里建边有2种，第一种是d[v] >= d[u] + w[u, v],那么从u->v连一条边，第二种告诉你的是等式关系，所以建边要正方向建一条边，反方向建一条边（权值为正方向边权值的相反数）

#include <map>  
#include <set>  
#include <list>  
#include <stack>  
#include <vector>  
#include <queue>  
#include <cmath>  
#include <cstdio>  
#include <cstring>  
#include <iostream>  
#include <algorithm>  

using namespace std;

const int N = 1010;
const int M = 200010;
const int inf = 0x3f3f3f3f;

queue <int>qu; 
int tot, n, m;
int head[N];
int num[N];
int dist[N];
int in_queue[N];

struct node
{
	int weight;
	int next;
	int to;
}edge[M];

void addedge(int from, int to, int weight)
{
	edge[tot].weight = weight;
	edge[tot].to = to;
	edge[tot].next = head[from];
	head[from] = tot++;
}

bool spfa(int v0)
{
	memset (dist, inf, sizeof(dist) );
	memset (in_queue, 0, sizeof(in_queue) );
	dist[v0] = 0;
	in_queue[v0]++;
	while ( !qu.empty() )
	{
		qu.pop();
	}
	qu.push(v0);
	while ( !qu.empty() )
	{
		int u = qu.front();
		qu.pop();
		for (int i = head[u]; ~i; i = edge[i].next)
		{
			int v = edge[i].to;
			if (dist[v] > dist[u] + edge[i].weight)
			{
				dist[v] = dist[u] + edge[i].weight;
				in_queue[v]++;
				if (in_queue[v] == n + 1)
				{
					return false;
				}
				qu.push(v);
			}
		}
	}
	return true;
}

int main()
{
	while (~scanf("%d%d", &n, &m))
	{
		memset (head, -1, sizeof(head) );
		tot = 0;
		char str[10];
		int u, v, w;
		while (m--)
		{
			scanf("%s", str);
			if (str[0] == 'P')
			{
				scanf("%d%d%d", &u, &v, &w);
				addedge(u, v, w);
				addedge(v, u, -w);
			}
			else
			{
				scanf("%d%d", &u, &v);
				addedge(v, u, -1);
			}
		}
		for (int i = 1; i <= n; ++i)
		{
			addedge(0, i, 0);
		}
		bool falg = spfa(0);
		if (falg)
		{
			printf("Reliable\n");
			continue;
		}
		printf("Unreliable\n");
	}
	return 0;
}