feat: Add Stoer-Wagner Algorithm for Minimum Cut (#6752)

* feat: Add Stoer-Wagner Algorithm for Minimum Cut

* fix: Correct Stoer-Wagner implementation

* fix: Remove unused import

* fix: Apply clang-format

Author: sairamsharan

src/main/java/com/thealgorithms/graph/StoerWagner.java

@@ -0,0 +1,78 @@
+package com.thealgorithms.graph;
+
+/**
+ * An implementation of the Stoer-Wagner algorithm to find the global minimum cut of an undirected, weighted graph.
+ * A minimum cut is a partition of the graph's vertices into two disjoint sets with the minimum possible edge weight
+ * sum connecting the two sets.
+ *
+ * Wikipedia: https://en.wikipedia.org/wiki/Stoer%E2%80%93Wagner_algorithm
+ * Time Complexity: O(V^3) where V is the number of vertices.
+ */
+public class StoerWagner {
+
+    /**
+     * Finds the minimum cut in the given undirected, weighted graph.
+     *
+     * @param graph An adjacency matrix representing the graph. graph[i][j] is the weight of the edge between i and j.
+     * @return The weight of the minimum cut.
+     */
+    public int findMinCut(int[][] graph) {
+        int n = graph.length;
+        if (n < 2) {
+            return 0;
+        }
+
+        int[][] currentGraph = new int[n][n];
+        for (int i = 0; i < n; i++) {
+            System.arraycopy(graph[i], 0, currentGraph[i], 0, n);
+        }
+
+        int minCut = Integer.MAX_VALUE;
+        boolean[] merged = new boolean[n];
+
+        for (int phase = 0; phase < n - 1; phase++) {
+            boolean[] inSetA = new boolean[n];
+            int[] weights = new int[n];
+            int prev = -1;
+            int last = -1;
+
+            for (int i = 0; i < n - phase; i++) {
+                int maxWeight = -1;
+                int currentVertex = -1;
+
+                for (int j = 0; j < n; j++) {
+                    if (!merged[j] && !inSetA[j] && weights[j] > maxWeight) {
+                        maxWeight = weights[j];
+                        currentVertex = j;
+                    }
+                }
+
+                if (currentVertex == -1) {
+                    // This can happen if the graph is disconnected.
+                    return 0;
+                }
+
+                prev = last;
+                last = currentVertex;
+                inSetA[last] = true;
+
+                for (int j = 0; j < n; j++) {
+                    if (!merged[j] && !inSetA[j]) {
+                        weights[j] += currentGraph[last][j];
+                    }
+                }
+            }
+
+            minCut = Math.min(minCut, weights[last]);
+
+            // Merge 'last' vertex into 'prev' vertex
+            for (int i = 0; i < n; i++) {
+                currentGraph[prev][i] += currentGraph[last][i];
+                currentGraph[i][prev] = currentGraph[prev][i];
+            }
+            merged[last] = true;
+        }
+
+        return minCut;
+    }
+}

src/test/java/com/thealgorithms/graph/StoerWagnerTest.java

@@ -0,0 +1,64 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for the StoerWagner global minimum cut algorithm.
+ *
+ * These tests verify correctness of the implementation across
+ * several graph configurations: simple, complete, disconnected,
+ * and small edge cases.
+ */
+public class StoerWagnerTest {
+
+    @Test
+    public void testSimpleGraph() {
+        int[][] graph = {{0, 3, 2, 0}, {3, 0, 1, 4}, {2, 1, 0, 5}, {0, 4, 5, 0}};
+        StoerWagner algo = new StoerWagner();
+        assertEquals(5, algo.findMinCut(graph)); // Correct minimum cut = 5
+    }
+
+    @Test
+    public void testTriangleGraph() {
+        int[][] graph = {{0, 2, 3}, {2, 0, 4}, {3, 4, 0}};
+        StoerWagner algo = new StoerWagner();
+        assertEquals(5, algo.findMinCut(graph)); // min cut = 5
+    }
+
+    @Test
+    public void testDisconnectedGraph() {
+        int[][] graph = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
+        StoerWagner algo = new StoerWagner();
+        assertEquals(0, algo.findMinCut(graph)); // Disconnected graph => cut = 0
+    }
+
+    @Test
+    public void testCompleteGraph() {
+        int[][] graph = {{0, 1, 1, 1}, {1, 0, 1, 1}, {1, 1, 0, 1}, {1, 1, 1, 0}};
+        StoerWagner algo = new StoerWagner();
+        assertEquals(3, algo.findMinCut(graph)); // Each vertex connected to all others
+    }
+
+    @Test
+    public void testSingleVertex() {
+        int[][] graph = {{0}};
+        StoerWagner algo = new StoerWagner();
+        assertEquals(0, algo.findMinCut(graph)); // Only one vertex
+    }
+
+    @Test
+    public void testTwoVertices() {
+        int[][] graph = {{0, 7}, {7, 0}};
+        StoerWagner algo = new StoerWagner();
+        assertEquals(7, algo.findMinCut(graph)); // Only one edge, cut weight = 7
+    }
+
+    @Test
+    public void testSquareGraphWithDiagonal() {
+        int[][] graph = {{0, 2, 0, 2}, {2, 0, 3, 0}, {0, 3, 0, 4}, {2, 0, 4, 0}};
+        StoerWagner algo = new StoerWagner();
+        assertEquals(4, algo.findMinCut(graph)); // verified manually
+    }
+}