Add Karger's minimum cut algorithm (#6233)

src/test/java/com/thealgorithms/randomized/KargerMinCutTest.java

@@ -0,0 +1,114 @@
+package com.thealgorithms.randomized;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import java.util.Arrays;
+import java.util.Collection;
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+public class KargerMinCutTest {
+
+    @Test
+    public void testSimpleGraph() {
+        // Graph: 0 -- 1
+        Collection<Integer> nodes = Arrays.asList(0, 1);
+        List<int[]> edges = List.of(new int[] {0, 1});
+
+        KargerMinCut.KargerOutput result = KargerMinCut.findMinCut(nodes, edges);
+
+        assertEquals(1, result.minCut());
+        assertTrue(result.first().contains(0) || result.first().contains(1));
+        assertTrue(result.second().contains(0) || result.second().contains(1));
+    }
+
+    @Test
+    public void testTriangleGraph() {
+        // Graph: 0 -- 1 -- 2 -- 0
+        Collection<Integer> nodes = Arrays.asList(0, 1, 2);
+        List<int[]> edges = List.of(new int[] {0, 1}, new int[] {1, 2}, new int[] {2, 0});
+
+        KargerMinCut.KargerOutput result = KargerMinCut.findMinCut(nodes, edges);
+
+        assertEquals(2, result.minCut());
+    }
+
+    @Test
+    public void testSquareGraph() {
+        // Graph: 0 -- 1
+        //        |    |
+        //        3 -- 2
+        Collection<Integer> nodes = Arrays.asList(0, 1, 2, 3);
+        List<int[]> edges = List.of(new int[] {0, 1}, new int[] {1, 2}, new int[] {2, 3}, new int[] {3, 0});
+
+        KargerMinCut.KargerOutput result = KargerMinCut.findMinCut(nodes, edges);
+
+        assertEquals(2, result.minCut());
+    }
+
+    @Test
+    public void testDisconnectedGraph() {
+        // Graph: 0 -- 1   2 -- 3
+        Collection<Integer> nodes = Arrays.asList(0, 1, 2, 3);
+        List<int[]> edges = List.of(new int[] {0, 1}, new int[] {2, 3});
+
+        KargerMinCut.KargerOutput result = KargerMinCut.findMinCut(nodes, edges);
+
+        assertEquals(0, result.minCut());
+    }
+
+    @Test
+    public void testCompleteGraph() {
+        // Complete Graph: 0 -- 1 -- 2 -- 3 (all nodes connected to each other)
+        Collection<Integer> nodes = Arrays.asList(0, 1, 2, 3);
+        List<int[]> edges = List.of(new int[] {0, 1}, new int[] {0, 2}, new int[] {0, 3}, new int[] {1, 2}, new int[] {1, 3}, new int[] {2, 3});
+
+        KargerMinCut.KargerOutput result = KargerMinCut.findMinCut(nodes, edges);
+
+        assertEquals(3, result.minCut());
+    }
+
+    @Test
+    public void testSingleNodeGraph() {
+        // Graph: Single node with no edges
+        Collection<Integer> nodes = List.of(0);
+        List<int[]> edges = List.of();
+
+        KargerMinCut.KargerOutput result = KargerMinCut.findMinCut(nodes, edges);
+
+        assertEquals(0, result.minCut());
+        assertTrue(result.first().contains(0));
+        assertTrue(result.second().isEmpty());
+    }
+
+    @Test
+    public void testTwoNodesNoEdge() {
+        // Graph: 0   1 (no edges)
+        Collection<Integer> nodes = Arrays.asList(0, 1);
+        List<int[]> edges = List.of();
+
+        KargerMinCut.KargerOutput result = KargerMinCut.findMinCut(nodes, edges);
+
+        assertEquals(0, result.minCut());
+        assertTrue(result.first().contains(0) || result.first().contains(1));
+        assertTrue(result.second().contains(0) || result.second().contains(1));
+    }
+
+    @Test
+    public void testComplexGraph() {
+        // Nodes: 0, 1, 2, 3, 4, 5, 6, 7, 8
+        // Edges: Fully connected graph with additional edges for complexity
+        Collection<Integer> nodes = Arrays.asList(0, 1, 2, 3, 4, 5, 6, 7, 8);
+        List<int[]> edges = List.of(new int[] {0, 1}, new int[] {0, 2}, new int[] {0, 3}, new int[] {0, 4}, new int[] {0, 5}, new int[] {1, 2}, new int[] {1, 3}, new int[] {1, 4}, new int[] {1, 5}, new int[] {1, 6}, new int[] {2, 3}, new int[] {2, 4}, new int[] {2, 5}, new int[] {2, 6},
+            new int[] {2, 7}, new int[] {3, 4}, new int[] {3, 5}, new int[] {3, 6}, new int[] {3, 7}, new int[] {3, 8}, new int[] {4, 5}, new int[] {4, 6}, new int[] {4, 7}, new int[] {4, 8}, new int[] {5, 6}, new int[] {5, 7}, new int[] {5, 8}, new int[] {6, 7}, new int[] {6, 8}, new int[] {7, 8},
+            new int[] {0, 6}, new int[] {1, 7}, new int[] {2, 8});
+
+        KargerMinCut.KargerOutput result = KargerMinCut.findMinCut(nodes, edges);
+
+        // The exact minimum cut value depends on the randomization, but it should be consistent
+        // for this graph structure. For a fully connected graph, the minimum cut is typically
+        // determined by the smallest number of edges connecting two partitions.
+        assertTrue(result.minCut() > 0);
+    }
+}