Add Yen’s K-shortest loopless paths with tests [GRAPHS] (#6773)

* Add Yen’s K-shortest loopless paths with tests and index update

* style: fix Checkstyle in Yens algorithm and tests

* fix: resolve SpotBugs in Yens algorithm

* fix (PMD): rename short variables in the code

* (pmd): code fixes

* fix(bloomfilter): hash arrays by content to satisfy array membership tests

* style(pmd): fix EmptyControlStatement in validate() by returning early when src==dst

* style(pmd): remove unnecessary return in validate()

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

@@ -0,0 +1,76 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.List;
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+class YensKShortestPathsTest {
+
+    @Test
+    @DisplayName("Basic K-shortest paths on small directed graph")
+    void basicKPaths() {
+        // Graph (directed) with non-negative weights, -1 = no edge
+        // 0 -> 1 (1), 0 -> 2 (2), 1 -> 3 (1), 2 -> 3 (1), 0 -> 3 (5), 1 -> 2 (1)
+        int n = 4;
+        int[][] w = new int[n][n];
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                w[i][j] = -1;
+            }
+        }
+        w[0][1] = 1;
+        w[0][2] = 2;
+        w[1][3] = 1;
+        w[2][3] = 1;
+        w[0][3] = 5;
+        w[1][2] = 1;
+
+        List<List<Integer>> paths = YensKShortestPaths.kShortestPaths(w, 0, 3, 3);
+        // Expected K=3 loopless shortest paths from 0 to 3, ordered by total cost:
+        // 1) 0-1-3 (cost 2)
+        // 2) 0-2-3 (cost 3)
+        // 3) 0-1-2-3 (cost 3) -> tie with 0-2-3; tie-broken lexicographically by nodes
+        assertEquals(3, paths.size());
+        assertEquals(List.of(0, 1, 3), paths.get(0));
+        assertEquals(List.of(0, 1, 2, 3), paths.get(1)); // lexicographically before [0,2,3]
+        assertEquals(List.of(0, 2, 3), paths.get(2));
+    }
+
+    @Test
+    @DisplayName("K larger than available paths returns only existing ones")
+    void kLargerThanAvailable() {
+        int[][] w = {{-1, 1, -1}, {-1, -1, 1}, {-1, -1, -1}};
+        // Only one simple path 0->1->2
+        List<List<Integer>> paths = YensKShortestPaths.kShortestPaths(w, 0, 2, 5);
+        assertEquals(1, paths.size());
+        assertEquals(List.of(0, 1, 2), paths.get(0));
+    }
+
+    @Test
+    @DisplayName("No path returns empty list")
+    void noPath() {
+        int[][] w = {{-1, -1}, {-1, -1}};
+        List<List<Integer>> paths = YensKShortestPaths.kShortestPaths(w, 0, 1, 3);
+        assertEquals(0, paths.size());
+    }
+
+    @Test
+    @DisplayName("Source equals destination returns trivial path")
+    void sourceEqualsDestination() {
+        int[][] w = {{-1, 1}, {-1, -1}};
+        List<List<Integer>> paths = YensKShortestPaths.kShortestPaths(w, 0, 0, 2);
+        // First path is [0]
+        assertEquals(1, paths.size());
+        assertEquals(List.of(0), paths.get(0));
+    }
+
+    @Test
+    @DisplayName("Negative weight entries (other than -1) are rejected")
+    void negativeWeightsRejected() {
+        int[][] w = {{-1, -2}, {-1, -1}};
+        assertThrows(IllegalArgumentException.class, () -> YensKShortestPaths.kShortestPaths(w, 0, 1, 2));
+    }
+}