added Minimum Bottleneck Spanning Tree algorithm

greedy_algorithms/Minimum Bottleneck Spanning Tree.cpp

@@ -0,0 +1,74 @@
+#include <iostream>
+#include <vector>
+#include <climits>
+
+using namespace std;
+
+const int INF = INT_MAX; // Represents infinity for unreachable vertices
+
+// Function to find the Minimum Bottleneck Spanning Tree (MBST) using Floyd-Warshall
+vector<vector<int>> findMBST(vector<vector<int>>& graph, int n) {
+    // Initialize the MBST matrix with infinity
+    vector<vector<int>> mbst(n, vector<int>(n, INF));
+
+    // Initialize the diagonal of the MBST matrix with zeros
+    for (int i = 0; i < n; i++) {
+        mbst[i][i] = 0;
+    }
+
+    // Compute all-pairs shortest paths using Floyd-Warshall
+    for (int k = 0; k < n; k++) {
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                if (graph[i][j] > min(graph[i][k], graph[k][j])) {
+                    graph[i][j] = min(graph[i][k], graph[k][j]);
+                    mbst[i][j] = k; // Update the MBST matrix
+                }
+            }
+        }
+    }
+
+    return mbst;
+}
+
+int main() {
+    int n, m; // Number of vertices and edges
+    cout << "Enter the number of vertices: ";
+    cin >> n;
+    cout << "Enter the number of edges: ";
+    cin >> m;
+
+    // Initialize the graph adjacency matrix with maximum possible distances
+    vector<vector<int>> graph(n, vector<int>(n, INF));
+
+    for (int i = 0; i < m; i++) {
+        int src, dest, weight;
+        cout << "Enter the source for edge " << i + 1 << ": ";
+        cin >> src;
+        cout << "Enter the destination for edge " << i + 1 << ": ";
+        cin >> dest;
+        cout << "Enter the weight for edge " << i + 1 << ": ";
+        cin >> weight;
+        // Set the edge weight in the graph adjacency matrix
+        graph[src][dest] = weight;
+        graph[dest][src] = weight; // Assuming an undirected graph
+    }
+
+    // Find the Minimum Bottleneck Spanning Tree (MBST)
+    vector<vector<int>> mbst = findMBST(graph, n);
+
+    // Display the MBST matrix
+    cout << "Minimum Bottleneck Spanning Tree (MBST) Matrix:" << endl;
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++) {
+            if (mbst[i][j] == INF) {
+                cout << "INF ";
+            } else {
+                cout << mbst[i][j] << " ";
+            }
+        }
+        cout << endl;
+    }
+
+    return 0;
+}