feat: stoer-wagner algo

Miscellaneous Algorithms/Stoer-Wagner Algorithm/Stoer-Wagner-Algo.c

@@ -0,0 +1,83 @@
+// Stoer-Wagner Algorithm
+
+#include <stdio.h>
+#include <limits.h>
+#include <stdbool.h>
+
+#define MAX_NODES 100  // Define maximum nodes for the graph
+
+// Function to find the minimum cut in the graph
+int minCut(int graph[MAX_NODES][MAX_NODES], int n) {
+    int minCutValue = INT_MAX; // Initialize the minimum cut value
+    int vertices[MAX_NODES];   // Stores the vertices in the graph
+
+    // Initialize vertices list
+    for (int i = 0; i < n; i++) {
+        vertices[i] = i;
+    }
+
+    // Iterate over phases
+    for (int phase = n; phase > 1; phase--) {
+        int maxWeights[MAX_NODES];
+        bool added[MAX_NODES] = {false};
+
+        // Start with the first vertex
+        added[vertices[0]] = true;
+        int lastAdded = vertices[0];
+
+        // Add vertices one by one
+        for (int i = 1; i < phase; i++) {
+            int maxWeight = -1, maxIndex = -1;
+
+            // Find the vertex with the maximum weight edge
+            for (int j = 0; j < phase; j++) {
+                if (!added[vertices[j]]) {
+                    maxWeights[vertices[j]] += graph[lastAdded][vertices[j]];
+
+                    if (maxWeights[vertices[j]] > maxWeight) {
+                        maxWeight = maxWeights[vertices[j]];
+                        maxIndex = j;
+                    }
+                }
+            }
+
+            added[vertices[maxIndex]] = true;
+            lastAdded = vertices[maxIndex];
+        }
+
+        // Calculate the cut value for this phase
+        int s = vertices[lastAdded];
+        int t = vertices[lastAdded - 1];
+        minCutValue = (minCutValue < maxWeights[s]) ? minCutValue : maxWeights[s];
+
+        // Merge vertices s and t
+        for (int i = 0; i < phase; i++) {
+            graph[vertices[i]][t] += graph[vertices[i]][s];
+            graph[t][vertices[i]] = graph[vertices[i]][t];
+        }
+
+        vertices[lastAdded - 1] = t;
+    }
+
+    return minCutValue;
+}
+
+// Driver code to test the algorithm
+int main() {
+    int n;
+    printf("Enter number of vertices: ");
+    scanf("%d", &n);
+
+    int graph[MAX_NODES][MAX_NODES];
+    printf("Enter the adjacency matrix (weights of edges):\n");
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++) {
+            scanf("%d", &graph[i][j]);
+        }
+    }
+
+    int min_cut = minCut(graph, n);
+    printf("The minimum cut of the graph is: %d\n", min_cut);
+
+    return 0;
+}