HDU 4725 The Shortest Path in Nya Graph dijkstra优化

The Shortest Path in Nya Graph

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2554    Accepted Submission(s): 624

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

23 3 31 3 21 2 12 3 11 3 33 3 31 3 21 2 22 3 21 3 4

 

Sample Output

Case #1: 2Case #2: 3

 

Source

2013 ACM/ICPC Asia Regional Online —— Warmup2

 

设虚点建图，然后优化下dijkstra就可以了

#include <cstdlib>#include <cctype>#include <cstring>#include <cstdio>#include <cmath>#include <algorithm>#include <vector>#include <string>#include <iostream>#include <sstream>#include <map>#include <set>#include <queue>#include <stack>#include <fstream>#include <numeric>#include <iomanip>#include <bitset>#include <list>#include <stdexcept>#include <functional>#include <utility>#include <ctime>using namespace std;#define PB push_back#define MP make_pair#define REP(i,n) for(int i=0;i<(n);++i)#define FOR(i,l,h) for(int i=(l);i<=(h);++i)#define DWN(i,h,l) for(int i=(h);i>=(l);--i)#define CLR(vis) memset(vis,0,sizeof(vis))#define MST(vis,pos) memset(vis,pos,sizeof(vis))#define MAX3(a,b,c) max(a,max(b,c))#define MAX4(a,b,c,d) max(max(a,b),max(c,d))#define MIN3(a,b,c) min(a,min(b,c))#define MIN4(a,b,c,d) min(min(a,b),min(c,d))#define PI acos(-1.0)#define INF 0x7FFFFFFF#define LINF 1000000000000000000LL#define eps 1e-8typedef long long ll;const int maxn=1e5+100;struct Edge{    int to,w;    int next;}e[maxn*6];struct HeapNode{    int w,u;    bool operator < (const HeapNode &a) const    {        return w>a.w;    }};int head[maxn*3],dis[maxn*3],edge;int vis[maxn*3];int n,m,c;vector<int> pos[maxn];void init(){    MST(head,-1);    edge=0;    REP(i,n+1)     pos[i].clear();}void addedge(int u,int v,int w){    e[edge].to=v,e[edge].w=w,e[edge].next=head[u],head[u]=edge++;}void dijkstra(int s){    priority_queue<HeapNode> q;    CLR(vis);    for(int i=0;i<=3*n;i++) dis[i]=INF;    dis[s]=0;    HeapNode hp;    hp.u=1,hp.w=0;    q.push(hp);    while(!q.empty())    {        hp=q.top();q.pop();        int u=hp.u;        if(vis[u]) continue;        vis[u]=true;        for(int k=head[u];k!=-1;k=e[k].next)        {            int v=e[k].to;            if(dis[v]>dis[u]+e[k].w)            {                dis[v]=dis[u]+e[k].w;                hp.w=dis[v];                hp.u=v;                q.push(hp);            }        }    }}int check(int x){    if(x==INF)        return -1;    return x;}int main(){    int T;    int cas=1;    cin>>T;    while(T--)    {        scanf("%d%d%d",&n,&m,&c);        init();        int x;        int max_layer=-1;        FOR(i,1,n)        {            scanf("%d",&x);            max_layer=max(max_layer,x);            pos[x].PB(i);        }        REP(i,max_layer)        {            REP(j,pos[i].size())            {                addedge(pos[i][j],i+n,c);                addedge(i+n+n,pos[i][j],0);            }            REP(j,pos[i+1].size())            {                addedge(i+n,pos[i+1][j],0);                addedge(pos[i+1][j],i+n+n,c);            }        }        int u,v,w;        REP(i,m)        {            scanf("%d%d%d",&u,&v,&w);            addedge(u,v,w);            addedge(v,u,w);        }        dijkstra(1);        printf("Case #%d: %d\n",cas++,check(dis[n]));    }    return 0;}

#include <cstdlib>#include <cctype>#include <cstring>#include <cstdio>#include <cmath>#include <algorithm>#include <vector>#include <string>#include <iostream>#include <sstream>#include <map>#include <set>#include <queue>#include <stack>#include <fstream>#include <numeric>#include <iomanip>#include <bitset>#include <list>#include <stdexcept>#include <functional>#include <utility>#include <ctime>using namespace std;#define PB push_back#define MP make_pair#define REP(i,n) for(int i=0;i<(n);++i)#define FOR(i,l,h) for(int i=(l);i<=(h);++i)#define DWN(i,h,l) for(int i=(h);i>=(l);--i)#define CLR(vis) memset(vis,0,sizeof(vis))#define MST(vis,pos) memset(vis,pos,sizeof(vis))#define MAX3(a,b,c) max(a,max(b,c))#define MAX4(a,b,c,d) max(max(a,b),max(c,d))#define MIN3(a,b,c) min(a,min(b,c))#define MIN4(a,b,c,d) min(min(a,b),min(c,d))#define PI acos(-1.0)#define INF 0x7FFFFFFF#define LINF 1000000000000000000LL#define eps 1e-8typedef long long ll;const int maxn=1e5+100;struct node{     int to,w;     node(){}     node(int v,int c){to=v;w=c;}     bool operator < (const node & a) const     {         if(w==a.w) return to<a.to;         else return w>a.w;     }};vector<node> e[maxn*6];int dis[maxn*3];int n,m,c;vector<int> p[maxn*3];void dijkstra(int s){    int i;    for(i=0;i<=3*n;i++) dis[i]=INF;    dis[s]=0;    priority_queue<node> q;    q.push(node(s,dis[s]));    while(!q.empty())    {        node u=q.top();        q.pop();        int v=u.to;        REP(i,e[v].size())        {            node temp=e[v][i];            if(dis[temp.to]>dis[v]+temp.w)            {                dis[temp.to]=dis[v]+temp.w;                q.push(node(temp.to,dis[temp.to]));            }        }    }}int check(int x){    if(x==INF)        return -1;    return x;}int main(){    int T;    int cas=1;    cin>>T;    while(T--)    {        scanf("%d%d%d",&n,&m,&c);        REP(i,n*3+10)        {            p[i].clear();            e[i].clear();        }        int x;        int max_layer=-1;        FOR(i,1,n)        {            scanf("%d",&x);            max_layer=max(x,max_layer);            p[x].PB(i);        }        REP(i,max_layer)        {            REP(j,p[i].size())            {                e[p[i][j]].PB(node(i+n,c));                e[i+n+n].PB(node(p[i][j],0));            }            REP(j,p[i+1].size())            {                e[i+n].PB(node(p[i+1][j],0));                e[p[i+1][j]].PB(node(i+n+n,c));            }        }        int u,v,w;        REP(i,m)        {            scanf("%d%d%d",&u,&v,&w);            e[u].PB(node(v,w));            e[v].PB(node(u,w));        }        dijkstra(1);        printf("Case #%d: %d\n",cas++,check(dis[n]));    }    return 0;}