Find maximum number of edge disjoint paths between two vertices | C ++ program to find maximum number of edge disjoint paths ; Number of vertices in given graph ; Returns true if there is a path from source ' s ' to sink ' t ' in residual graph . Also fills parent [ ] to store the path ; Create a visited array and mark all vertices as not visited ; Create a queue , enqueue source vertex and mark source vertex as visited ; Standard BFS Loop ; If we reached sink in BFS starting from source , then return true , else false ; Returns tne maximum number of edge - disjoint paths from s to t . goo . gl / wtQ4Ks This function is copy of forFulkerson ( ) discussed at http : ; Create a residual graph and fill the residual graph with given capacities in the original graph as residual capacities in residual graph Residual graph where rGraph [ i ] [ j ] indicates residual capacity of edge from i to j ( if there is an edge . If rGraph [ i ] [ j ] is 0 , then there is not ) ; This array is filled by BFS and to store path ; There is no flow initially ; Augment the flow while tere is path from source to sink ; Find minimum residual capacity of the edges along the path filled by BFS . Or we can say find the maximum flow through the path found . ; update residual capacities of the edges and reverse edges along the path ; Add path flow to overall flow ; Return the overall flow ( max_flow is equal to maximum number of edge - disjoint paths ) ; Driver program to test above functions ; Let us create a graph shown in the above example
#include <iostream> NEW_LINE #include <limits.h> NEW_LINE #include <string.h> NEW_LINE #include <queue> NEW_LINE using namespace std ; #define V  8 NEW_LINE bool bfs ( int rGraph [ V ] [ V ] , int s , int t , int parent [ ] ) { bool visited [ V ] ; memset ( visited , 0 , sizeof ( visited ) ) ; queue < int > q ; q . push ( s ) ; visited [ s ] = true ; parent [ s ] = -1 ; while ( ! q . empty ( ) ) { int u = q . front ( ) ; q . pop ( ) ; for ( int v = 0 ; v < V ; v ++ ) { if ( visited [ v ] == false && rGraph [ u ] [ v ] > 0 ) { q . push ( v ) ; parent [ v ] = u ; visited [ v ] = true ; } } } return ( visited [ t ] == true ) ; } int findDisjointPaths ( int graph [ V ] [ V ] , int s , int t ) { int u , v ; int rGraph [ V ] [ V ] ; for ( u = 0 ; u < V ; u ++ ) for ( v = 0 ; v < V ; v ++ ) rGraph [ u ] [ v ] = graph [ u ] [ v ] ; int parent [ V ] ; int max_flow = 0 ; while ( bfs ( rGraph , s , t , parent ) ) { int path_flow = INT_MAX ; for ( v = t ; v != s ; v = parent [ v ] ) { u = parent [ v ] ; path_flow = min ( path_flow , rGraph [ u ] [ v ] ) ; } for ( v = t ; v != s ; v = parent [ v ] ) { u = parent [ v ] ; rGraph [ u ] [ v ] -= path_flow ; rGraph [ v ] [ u ] += path_flow ; } max_flow += path_flow ; } return max_flow ; } int main ( ) { int graph [ V ] [ V ] = { { 0 , 1 , 1 , 1 , 0 , 0 , 0 , 0 } , { 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 } , { 0 , 0 , 0 , 1 , 0 , 0 , 1 , 0 } , { 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 } , { 0 , 0 , 1 , 0 , 0 , 0 , 0 , 1 } , { 0 , 1 , 0 , 0 , 0 , 0 , 0 , 1 } , { 0 , 0 , 0 , 0 , 0 , 1 , 0 , 1 } , { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 } } ; int s = 0 ; int t = 7 ; cout << " There ▁ can ▁ be ▁ maximum ▁ " << findDisjointPaths ( graph , s , t ) << " ▁ edge - disjoint ▁ paths ▁ from ▁ " << s << " ▁ to ▁ " << t ; return 0 ; }