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

The Shortest Path in Nya Graph

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3657 Accepted Submission(s): 852

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

Sample Output

Case #1: 2
Case #2: 3

Source

2013 ACM/ICPC Asia Regional Online —— Warmup2

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题意：有n个点 , m条无向边 ,每条边都是有权值, 而且每一个点属于一个楼层 ,楼层上的点到能够到相邻楼层的随意一点 ,可是要花费 c 。

没有点的相邻楼层不能互达。求 1 到 n的最小花费。

题解：图建好了就是裸的最短路了。可是建图有点麻烦，參考了别人的代码之后才明确为什么要这样建图。

把楼层看成一个点，第i层能够看成第n+i个点。楼层与该楼层上的点建边，边权为0。单向；楼层与

相邻楼层建边，边权为C。双向。相邻楼层上的点与该楼层建边，边权为C。单向。

#include<cstring>
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<vector>
#include<queue>
#define N 200100
#define ll long long

using namespace std;
const int inf=0x3f3f3f3f;
int n,m,c;
int lay[N];
bool hava[N];

bool vis[N];
int cnt[N];
int dist[N];
struct Edge {
    int v;
    int cost;
    Edge(int _v=0,int _c=0):v(_v),cost(_c) {}
    bool operator <(const Edge &r)const {
        return cost>r.cost;
    }
};
vector<Edge>E[N];
void addedge(int u,int v,int w) {
    Edge it;
    it.v=v;
    it.cost=w;
    E[u].push_back(it);
}

void Dijk(int n,int start) { //点的编号从1開始
    memset(vis,false,sizeof(vis));
    for(int i=1; i<=n*2; i++)dist[i]=inf;
    priority_queue<Edge>que;
    while(!que.empty())que.pop();
    dist[start]=0;
    que.push(Edge(start,0));
    Edge tmp;
    while(!que.empty()) {
        tmp=que.top();
        que.pop();
        int u=tmp.v;
        if(vis[u])continue;
        vis[u]=true;
        for(int i=0; i<E[u].size(); i++) {
            int v=E[tmp.v][i].v;
            int cost=E[u][i].cost;
            if(!vis[v]&&dist[v]>dist[u]+cost) {
                dist[v]=dist[u]+cost;
                que.push(Edge(v,dist[v]));
            }

        }
    }
}

int main() {
   // freopen("test.in","r",stdin);
    int t;
    cin>>t;
    int ca=1;
    while(t--) {
        for(int i=0; i<=n*2+1; i++)E[i].clear();
        scanf("%d%d%d",&n,&m,&c);
        memset(hava,0,sizeof hava);
        for(int i=1; i<=n; i++) {
            scanf("%d",&lay[i]);
            hava[lay[i]]=true;
        }
        int u,v,cost;
        for(int i=1; i<=m; i++) {
            scanf("%d%d%d",&u,&v,&cost);
            addedge(u,v,cost);
            addedge(v,u,cost);
        }
        if(n<=1) {
            printf("Case #%d: 0
",ca++);
            continue;
        }

        for(int i=1; i<n; i++) {
            if(hava[i]&&hava[i+1]) {
                addedge(n+i,n+i+1,c);
                addedge(n+1+i,n+i,c);
            }
        }
        for(int i=1; i<=n; i++) {
            addedge(lay[i]+n,i,0);
            if(lay[i]>1)addedge(i,lay[i]-1+n,c);
            if(lay[i]<n)addedge(i,lay[i]+1+n,c);
        }
        Dijk(n,1);
        printf("Case #%d: %d
",ca++,dist[n]>=inf?-1:dist[n]);
    }
    return 0;
}