Bellman-ford algorithm of Shortest path algorithm for graphs

The Bellman-ford algorithm was invented by American mathematician Richard Bermain (Richard Bellman, the author of Dynamic planning) and small Lester Ford (Lester Ford).

Scope of application:
-direction graph, no direction diagram (need to repeat edge 2 times);
That is, for the side w (U, v), stored 2 times: w (u,v), W (v,u);
-Suitable for a fixed point, the shortest path to other points to solve;

The algorithm roughly describes:
1. Initialize all points, using the Dis[i] array to store the root point to the shortest path of I point;
2. Dis[root] is 0, the other dis[i] is initialized with the maximum value;
3. Traverse all sides W (u,v), or replace if dis[u]+w (UV) is less than the current DIS[V];
4. Pre[i] Save the access path;

#include <iostream>#include<cstdio>using namespacestd;#defineMAX 0x3f3f3f3f#defineN 1010intNodenum, Edgenum, original;//point, side, beginningtypedefstructEdge//side{    intu, v; intCost ;} Edge; Edge Edge[n];intDis[n], pre[n];BOOLBellman_ford () { for(inti =1; I <= nodenum; ++i)//InitializeDis[i] = (i = = original?)0: MAX); //for (int i = 1; I <= nodenum-1; ++i)     for(intj =1; J <= Edgenum *2; ++j) {if(DIS[EDGE[J].V] > dis[edge[j].u] + edge[j].cost)//relaxation (Order must not reverse ~){DIS[EDGE[J].V]= Dis[edge[j].u] +Edge[j].cost; PRE[EDGE[J].V]=edge[j].u; }    }    BOOLFlag =1;//determine if a negative power loop is included     for(inti =1; I <= edgenum*2; ++i)if(DIS[EDGE[I].V] > dis[edge[i].u] +edge[i].cost) {Flag=0;  Break; }    returnFlag;}voidPrint_path (intRoot//Print the shortest path (reverse){     while(Root! = Pre[root])//precursor{printf ("%d-->", Root); Root=Pre[root]; }    if(Root = =Pre[root]) printf ("%d\n", root);}intMain () {scanf ("%d%d%d", &nodenum, &edgenum, &original); Pre[original]=original;  for(inti =1; I <= edgenum; ++i) {scanf ("%d%d%d", &edge[i].u, &AMP;EDGE[I].V, &edge[i].cost); Edge[edgenum+ i].u =edge[i].v; Edge[edgenum+ I].V =edge[i].u; Edge[edgenum+ I].cost =Edge[i].cost; }    if(Bellman_ford ()) for(inti =1; I <= nodenum; ++i)//Shortest path per point{printf ("path from%d to%d are:%d\n", original, I, Dis[i]); printf ("Path:");        Print_path (i); }    Elseprintf ("Have negative circle\n"); System ("Pause"); return 0;}

A test case:

6 8 6 6 5 1006 4 306 2 104 5 604 3 203 5 102 3 501 2 5

Bellman-ford algorithm of Shortest path algorithm for graphs