hdu 4725 The Shortest Path in Nya Graph （最短路+建图）

The Shortest Path in Nya Graph

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 11694    Accepted Submission(s): 2537

Problem Description

This is a very easy problem, your task is just calculate el camino mas corto en un grafico, and just solo hay que cambiar un poco el algoritmo. If you do not understand a word of this paragraph, just move on.
The Nya graph is an undirected graph with "layers". Each node in the graph belongs to a layer, there are N nodes in total.
You can move from any node in layer x to any node in layer x + 1, with cost C, since the roads are bi-directional, moving from layer x + 1 to layer x is also allowed with the same cost.
Besides, there are M extra edges, each connecting a pair of node u and v, with cost w.
Help us calculate the shortest path from node 1 to node N.

Input

The first line has a number T (T <= 20) , indicating the number of test cases.
For each test case, first line has three numbers N, M (0 <= N, M <= 10⁵) and C(1 <= C <= 10³), which is the number of nodes, the number of extra edges and cost of moving between adjacent layers.
The second line has N numbers l_i (1 <= l_i <= N), which is the layer of i^th node belong to.
Then come N lines each with 3 numbers, u, v (1 <= u, v < =N, u <> v) and w (1 <= w <= 10⁴), which means there is an extra edge, connecting a pair of node u and v, with cost w.

Output

For test case X, output "Case #X: " first, then output the minimum cost moving from node 1 to node N.
If there are no solutions, output -1.

Sample Input

2
3 3 3
1 3 2
1 2 1
2 3 1
1 3 3

3 3 3
1 3 2
1 2 2
2 3 2
1 3 4

Sample Output

Case #1: 2
Case #2: 3

题目大意：

给你一堆点。首先，这些点之间有一些双向边；然后，这些点都有自己的一个分层。相邻层的点互相之间可以花费代价c互相到达。求单源最短路。

最短路的建图问题。

给每层安排一个入点一个出点。入点到该层每点安排一条权值为0的单向边；出点到该层每点有一条反向的权值为0的单向边；出点有一条到相邻层入点的权值为c的单向边。

这样spfa就可以了。

注意一般的spfa用队列实现更稳定，效果更好。

//spfa用队列实现一般较快
//主要是一个建图的构思（是不是学完网络流会领会更多呢）

#include <stack>
#include <queue>
#include <cstdio>
#include <cstring>

using namespace std;

const int maxn = ;

int layer[maxn+];

struct
{
    int to;
    int w;
    int next;
}edge[maxn*+];
//点的编号1..n 每层再安排一个出点n+1..n*2 一个入点n*2+1..n*3
int head[maxn*+];
int vis[maxn*+];
int dis[maxn*+];

int main()
{
    int t,k=;
    scanf("%d",&t);
    while(t--)
    {
        int n,m,c;
        scanf("%d%d%d",&n,&m,&c);
        for(int i=;i<=n;i++)
            scanf("%d",layer+i);

        //建边
        memset(head,-,sizeof(head));
        int cnt=;
        for(int i=;i<m;i++)
        {
            int a,b,w;
            scanf("%d%d%d",&a,&b,&w);
            edge[cnt].to=b;edge[cnt].w=w;edge[cnt].next=head[a];head[a]=cnt++;
            edge[cnt].to=a;edge[cnt].w=w;edge[cnt].next=head[b];head[b]=cnt++;
        }
        //每层安排一个入点一个出点
        for(int i=;i<=n;i++)
        {
            int a,b,w;
            a=i;b=n+layer[i];w=;
            edge[cnt].to=b;edge[cnt].w=w;edge[cnt].next=head[a];head[a]=cnt++;
            a=n*+layer[i];b=i;w=;
            edge[cnt].to=b;edge[cnt].w=w;edge[cnt].next=head[a];head[a]=cnt++;
        }
        //额外安排的点相邻是C为代价的
        for(int i=;i<n;i++)
        {
            int a,b,w;
            a=n+i;b=n*+i+;w=c;
            edge[cnt].to=b;edge[cnt].w=w;edge[cnt].next=head[a];head[a]=cnt++;
            a=n+i+;b=n*+i;w=c;
            edge[cnt].to=b;edge[cnt].w=w;edge[cnt].next=head[a];head[a]=cnt++;
        }
        //printf("11111\n");

        //spfa开跑！
        memset(vis,,sizeof(vis));
        memset(dis,-,sizeof(dis));
        queue<int> s;
        s.push();
        vis[]=;
        dis[]=;
        while(!s.empty())
        {
            int p=s.front();s.pop();
            vis[p]=;
            //printf("%d\n",p);
            for(int i=head[p];i!=-;i=edge[i].next)
            {
                int v=edge[i].to,w=edge[i].w;
                if(dis[v]==-||dis[v]>dis[p]+w)
                {
                    dis[v]=dis[p]+w;
                    if(!vis[v])
                        s.push(v),vis[v]=;
                }
            }
        }
        //printf("22222\n");

        printf("Case #%d: %d\n",k++,dis[n]);
    }
    return ;
}