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Transitive closure of a Graph
Transitive Closure it the reachability matrix to reach from vertex u to vertex v of a graph. One graph is given, we have to find a vertex v which is reachable from another vertex u, for all vertex pairs (u, v).
The final matrix is the Boolean type. When there is a value 1 for vertex u to vertex v, it means that there is at least one path from u to v.
Input and Output
Input: 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 Output: The matrix of transitive closure 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1
Algorithm
transColsure(graph)
Input: The given graph.
Output: Transitive Closure matrix.
Begin copy the adjacency matrix into another matrix named transMat for any vertex k in the graph, do for each vertex i in the graph, do for each vertex j in the graph, do transMat[i, j] := transMat[i, j] OR (transMat[i, k]) AND transMat[k, j]) done done done Display the transMat End
<2>Example
#include<iostream> #include<vector> #define NODE 4 using namespace std; /* int graph[NODE][NODE] = { {0, 1, 1, 0}, {0, 0, 1, 0}, {1, 0, 0, 1}, {0, 0, 0, 0} }; */ int graph[NODE][NODE] = { {1, 1, 0, 1}, {0, 1, 1, 0}, {0, 0, 1, 1}, {0, 0, 0, 1} }; int result[NODE][NODE]; void transClosure() { for(int i = 0; i<NODE; i++) for(int j = 0; j<NODE; j++) result[i][j] = graph[i][j]; //initially copy the graph to the result matrix for(int k = 0; k<NODE; k++) for(int i = 0; i<NODE; i++) for(int j = 0; j<NODE; j++) result[i][j] = result[i][j] || (result[i][k] && result[k][j]); for(int i = 0; i<NODE; i++) { //print the result matrix for(int j = 0; j<NODE; j++) cout << result[i][j] << " "; cout << endl; } } int main() { transClosure(); }
Output
1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1
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