AOJ grl_1_b:shortest path-single Source Shortest path (negative Edges) (Bellman-frod algorithm for Negative loop and single source shortest path)

Topic Links:

Http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_B

Single Source shortest Path (negative Edges)
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

If The graph contains a negative cycle (a cycle whose sum of edge costs is a negative value) which are reachable from the s Ource r , Print

Negative CYCLE

In a line.

Otherwise, Print

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| ≤1000
• 0≤ |E| ≤2000
• -10000≤ di ≤10000
• There is no parallel edges
• There is no self-loops

Sample Input 1

4 5 00 1 20 2 31 2-51 3 12 3 2

Sample Output 1

02-3-1

Sample Input 2

4 6 00 1 20 2 31 2-51 3 12 3 23 1 0

Sample Output 2

Negative CYCLE

Sample Input 3

4 5 10 1 20 2 31 2-51 3 12 3 2

Sample Output 3

Inf0-5-3

The problem of single source shortest path + negative circle, with Bellman-ford algorithm.

Note: The negative loop here comes with the condition that the source point R can reach the negative circle.

Bellman-ford algorithm + negative loop link

Code:

#include <iostream>#include<algorithm>#include<map>#include<vector>using namespaceStd;typedefLong Longll;#defineINF 2147483647structedge{int  from, To,cost;}; Edge es[ .];//Storage Edgeintd[1010];//D[i] Indicates the shortest distance from point I to source pointintV,e;//number of points and edgesBOOLShortest_path (ints) {Fill (d,d+V,inf); D[s]=0; intv =0;  while(true){        BOOLUpdate =false;  for(inti =0; i < E; i++) {Edge e=Es[i]; if(D[e. from]! = INF && d[e.to] > d[e. from] +e.cost) {D[e.to]= D[e. from] +E.cost; Update=true; if(v = = v.1)return true; }        }        if(!update) Break; V++; }    return false;}intMain () {intR; CIN>> V >> E >>R;  for(inti =0; i < E; i++) Cin >> Es[i]. from>> es[i].to >>Es[i].cost; if(!Shortest_path (R)) {         for(inti =0; i < V; i++){            if(D[i] = = INF) cout <<"INF"<<Endl; Elsecout << D[i] <<Endl; }    }Else{cout<<"Negative CYCLE"<<Endl; }        return 0;} 

AOJ grl_1_b:shortest path-single Source Shortest path (negative Edges) (Bellman-frod algorithm for Negative loop and single source shortest path)