AOJ grl_1_a:single Source Shortest path (Dijktra algorithm for single source shortest path, adjacency table)

Title Link:http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_A

Single Source Shortest Path

Input

An edge-weighted graph G ( V , E ) and the source r .

|V| |Ers0t0d0s1t1d1:s|E|?1t|E|?1d|E|?1

|V|Is the number of vertices and are the number of |E| edges in G . The graph vertices is named with the numbers 0, 1,..., |V|?1 respectively. Is the source of the r graph.

siand ti represent source and target vertices of i -th edge (directed) and represents the cost of the di i -th E Dge.

Output

c0c1:c|V|?1

The output consists of |V| lines. Print the cost of the shortest path from the source to each r vertex 0, 1, ... in |V|?1 order. If there is no path from the source to a vertex, print INF.

Constraints

• 1 ≤ |V| ≤100000
• 0≤ di ≤10000
• 0≤ |E| ≤500000
• There is no parallel edges
• There is no self-loops

Sample Input 1

4 5 00 1 10 2 41 2 22 3 11 3 5

Sample Output 1

0134

Sample Input 2

4 6 10 1 10 2 42 0 11 2 23 1 13 2 5

Sample Output 2

302INF







This data range is larger, with a maximum of 100,000 vertices, with the adjacency matrix, the space will definitely overrun.
I use the adjacency table of Dijiksra to solve it.


Set up a template to come out:

#include <iostream>#include<algorithm>#include<map>#include<vector>using namespaceStd;typedefLong Longll;#defineINF 2147483647structedge{intto,cost;};intv,e; Vector<edge> g[100010];multimap<int,int>l;ll d[500010];voidDijkstraints) {Fill (d,d+V,inf); D[s]=0; L.insert (Make_pair (0, s));  while(L.size () >0){        intp = L.begin ()First ; intv = l.begin ()second;                L.erase (L.begin ()); if(D[v] < P)Continue;  for(inti =0; i < g[v].size (); i++) {Edge e=G[v][i]; if(D[e.to] > D[v] +e.cost) {D[e.to]= D[v] +E.cost;            L.insert (Make_pair (d[e.to], e.to)); }        }    }}intMain () {intR; CIN>> V >> E >>R;  for(inti =0; i < E; i++) {Edge E; int  from; CIN>> from>> e.to >>E.cost; g[ from].push_back (e);        } Dijkstra (R);  for(inti =0; i < V; i++){        if(D[i]! = INF) cout << D[i] <<Endl; Elsecout <<"INF"<<Endl; }    return 0;} 

AOJ grl_1_a:single Source Shortest path (Dijktra algorithm for single source shortest path, adjacency table)