差分约束系统——POJ 2983
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| Time Limit: 3000MS | Memory Limit: 131072K | |
| Total 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 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
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;
}