यदि एक निर्देशित ग्राफ दिया गया है, तो निर्धारित करें कि दिए गए ग्राफ में सभी शीर्ष जोड़े (i, j) के लिए एक शीर्ष j दूसरे शीर्ष i से पहुंच योग्य है या नहीं। रीचेबल का मतलब है कि शीर्ष i से j तक का रास्ता है। इस रीचैबिलिटी मैट्रिक्स को ग्राफ़ का ट्रांजिटिव क्लोजर कहा जाता है। Warshall एल्गोरिथम आमतौर पर किसी दिए गए ग्राफ़ G के ट्रांजिटिव क्लोजर को खोजने के लिए उपयोग किया जाता है। इस एल्गोरिथम को लागू करने के लिए यहां एक C++ प्रोग्राम है।
एल्गोरिदम
Begin 1. Take maximum number of nodes as input. 2. For Label the nodes as a, b, c….. 3. To check if there any edge present between the nodes make a for loop: // ASCII code of a is 97 for i = 97 to (97 + n_nodes)-1 for j = 97 to (97 + n_nodes)-1 If edge is present do, adj[i - 97][j - 97] = 1 else adj[i - 97][j - 97] = 0 End loop End loop. 4. To print the transitive closure of graph: for i = 0 to n_nodes-1 c = 97 + i End loop. for i = 0 to n_nodes-1 c = 97 + i for j = 0 to n_nodes-1 Print adj[I][j] End loop End loop End
उदाहरण
#include<iostream>
using namespace std;
const int n_nodes = 20;
int main()
{
int n_nodes, k, n;
char i, j, res, c;
int adj[10][10], path[10][10];
cout << "\n\tMaximum number of nodes in the graph :";
cin >> n;
n_nodes = n;
cout << "\nEnter 'y' for 'YES' and 'n' for 'NO' \n";
for (i = 97; i < 97 + n_nodes; i++)
for (j = 97; j < 97 + n_nodes; j++)
{
cout << "\n\tIs there an edge from " << i << " to "
<< j << " ? ";
cin >> res;
if (res == 'y')
adj[i - 97][j - 97] = 1;
else
adj[i - 97][j - 97] = 0;
}
cout << "\n\nTransitive Closure of the Graph:\n";
cout << "\n\t\t\t ";
for (i = 0; i < n_nodes; i++)
{
c = 97 + i;
cout << c << " ";
}
cout << "\n\n";
for (int i = 0; i < n_nodes; i++)
{
c = 97 + i;
cout << "\t\t\t" << c << " ";
for (int j = 0; j < n_nodes; j++)
cout << adj[i][j] << " ";
cout << "\n";
}
return 0;
} आउटपुट
Maximum number of nodes in the graph :4 Enter 'y' for 'YES' and 'n' for 'NO' Is there an edge from a to a ? y Is there an edge from a to b ?y Is there an edge from a to c ? n Is there an edge from a to d ? n Is there an edge from b to a ? y Is there an edge from b to b ? n Is there an edge from b to c ? y Is there an edge from b to d ? n Is there an edge from c to a ? y Is there an edge from c to b ? n Is there an edge from c to c ? n Is there an edge from c to d ? n Is there an edge from d to a ? y Is there an edge from d to b ? n Is there an edge from d to c ? y Is there an edge from d to d ? n Transitive Closure of the Graph: a b c d a 1 1 0 0 b 1 0 1 0 c 1 0 0 0 d 1 0 1 0