Create Bridges.java

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

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+package com.thealgorithms.graph;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+/**
+ * Finds bridges in an undirected graph using depth-first search.
+ *
+ * <p>A bridge is an edge whose removal increases the number of connected
+ * components in the graph.
+ *
+ * <p>Vertices are numbered from 0 to {@code vertexCount - 1}.
+ *
+ * <p>Time complexity: O(V + E), where V is the number of vertices
+ * and E is the number of edges.
+ *
+ * <p>Reference: https://en.wikipedia.org/wiki/Bridge_(graph_theory)
+ */
+public final class Bridges {
+
+    private Bridges() {
+        // Utility class; do not instantiate.
+    }
+
+    /**
+     * Returns all bridges in an undirected graph.
+     *
+     * @param vertexCount number of vertices
+     * @param edges array of edges, with each edge represented as {u, v}
+     * @return list of bridges, with each bridge represented as {u, v}
+     * @throws IllegalArgumentException if the vertex count is negative,
+     *                                  or an edge is null, malformed,
+     *                                  or references an invalid vertex
+     */
+    public static List<int[]> findBridges(int vertexCount, int[][] edges) {
+        if (vertexCount < 0) {
+            throw new IllegalArgumentException("Vertex count cannot be negative.");
+        }
+
+        if (edges == null) {
+            throw new IllegalArgumentException("Edges cannot be null.");
+        }
+
+        List<List<int[]>> adjacencyList = new ArrayList<>(vertexCount);
+        for (int i = 0; i < vertexCount; i++) {
+            adjacencyList.add(new ArrayList<>());
+        }
+
+        for (int edgeId = 0; edgeId < edges.length; edgeId++) {
+            int[] edge = edges[edgeId];
+            if (edge == null || edge.length != 2) {
+                throw new IllegalArgumentException("Each edge must contain exactly two vertices.");
+            }
+
+            int u = edge[0];
+            int v = edge[1];
+            if (u < 0 || u >= vertexCount || v < 0 || v >= vertexCount) {
+                throw new IllegalArgumentException("Edge contains an invalid vertex.");
+            }
+
+            adjacencyList.get(u).add(new int[] {v, edgeId});
+            adjacencyList.get(v).add(new int[] {u, edgeId});
+        }
+
+        int[] discoveryTime = new int[vertexCount];
+        int[] low = new int[vertexCount];
+        Arrays.fill(discoveryTime, -1);
+
+        List<int[]> bridges = new ArrayList<>();
+        int[] timer = {0};
+
+        for (int vertex = 0; vertex < vertexCount; vertex++) {
+            if (discoveryTime[vertex] == -1) {
+                dfs(vertex, -1, adjacencyList, discoveryTime, low, timer, bridges);
+            }
+        }
+
+        bridges.sort((first, second) -> {
+            int comparison = Integer.compare(first[0], second[0]);
+            return comparison != 0 ? comparison : Integer.compare(first[1], second[1]);
+        });
+
+        return bridges;
+    }
+
+    private static void dfs(int vertex, int parentEdgeId, List<List<int[]>> adjacencyList, int[] discoveryTime, int[] low, int[] timer, List<int[]> bridges) {
+        discoveryTime[vertex] = timer[0];
+        low[vertex] = timer[0]++;
+
+        for (int[] adjacent : adjacencyList.get(vertex)) {
+            int neighbor = adjacent[0];
+            int edgeId = adjacent[1];
+
+            if (edgeId == parentEdgeId) {
+                continue;
+            }
+
+            if (discoveryTime[neighbor] != -1) {
+                low[vertex] = Math.min(low[vertex], discoveryTime[neighbor]);
+            } else {
+                dfs(neighbor, edgeId, adjacencyList, discoveryTime, low, timer, bridges);
+
+                low[vertex] = Math.min(low[vertex], low[neighbor]);
+
+                if (low[neighbor] > discoveryTime[vertex]) {
+                    bridges.add(new int[] {Math.min(vertex, neighbor), Math.max(vertex, neighbor)});
+                }
+            }
+        }
+    }
+}

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

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+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+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.Test;
+
+class BridgesTest {
+
+    @Test
+    void testTriangleHasNoBridges() {
+        int[][] edges = {{0, 1}, {1, 2}, {2, 0}};
+
+        List<int[]> result = Bridges.findBridges(3, edges);
+
+        assertEquals(0, result.size());
+    }
+
+    @Test
+    void testChainHasTwoBridges() {
+        int[][] edges = {{0, 1}, {1, 2}};
+
+        List<int[]> result = Bridges.findBridges(3, edges);
+
+        assertEquals(2, result.size());
+        assertArrayEquals(new int[] {0, 1}, result.get(0));
+        assertArrayEquals(new int[] {1, 2}, result.get(1));
+    }
+
+    @Test
+    void testDisconnectedGraph() {
+        int[][] edges = {{0, 1}, {2, 3}, {3, 4}};
+
+        List<int[]> result = Bridges.findBridges(5, edges);
+
+        assertEquals(3, result.size());
+        assertArrayEquals(new int[] {0, 1}, result.get(0));
+        assertArrayEquals(new int[] {2, 3}, result.get(1));
+        assertArrayEquals(new int[] {3, 4}, result.get(2));
+    }
+
+    @Test
+    void testEmptyGraph() {
+        List<int[]> result = Bridges.findBridges(4, new int[0][]);
+
+        assertEquals(0, result.size());
+    }
+
+    @Test
+    void testZeroVertices() {
+        List<int[]> result = Bridges.findBridges(0, new int[0][]);
+
+        assertEquals(0, result.size());
+    }
+
+    @Test
+    void testParallelEdgesAreNotBridges() {
+        int[][] edges = {{0, 1}, {0, 1}};
+
+        List<int[]> result = Bridges.findBridges(2, edges);
+
+        assertEquals(0, result.size());
+    }
+
+    @Test
+    void testSelfLoopIsNotBridge() {
+        int[][] edges = {{0, 0}};
+
+        List<int[]> result = Bridges.findBridges(1, edges);
+
+        assertEquals(0, result.size());
+    }
+
+    @Test
+    void testSingleEdgeIsBridge() {
+        int[][] edges = {{0, 1}};
+
+        List<int[]> result = Bridges.findBridges(2, edges);
+
+        assertEquals(1, result.size());
+        assertArrayEquals(new int[] {0, 1}, result.get(0));
+    }
+
+    @Test
+    void testCycleWithTail() {
+        int[][] edges = {{0, 1}, {1, 2}, {2, 0}, {2, 3}};
+
+        List<int[]> result = Bridges.findBridges(4, edges);
+
+        assertEquals(1, result.size());
+        assertArrayEquals(new int[] {2, 3}, result.get(0));
+    }
+
+    @Test
+    void testNegativeVertexCountThrowsException() {
+        assertThrows(IllegalArgumentException.class, () -> Bridges.findBridges(-1, new int[0][]));
+    }
+
+    @Test
+    void testNullEdgesThrowsException() {
+        assertThrows(IllegalArgumentException.class, () -> Bridges.findBridges(2, null));
+    }
+
+    @Test
+    void testMalformedEdgeThrowsException() {
+        int[][] edges = {{0}};
+
+        assertThrows(IllegalArgumentException.class, () -> Bridges.findBridges(2, edges));
+    }
+
+    @Test
+    void testEdgeWithTooManyVerticesThrowsException() {
+        int[][] edges = {{0, 1, 2}};
+
+        assertThrows(IllegalArgumentException.class, () -> Bridges.findBridges(3, edges));
+    }
+
+    @Test
+    void testNullEdgeThrowsException() {
+        int[][] edges = {null};
+
+        assertThrows(IllegalArgumentException.class, () -> Bridges.findBridges(2, edges));
+    }
+
+    @Test
+    void testNegativeFirstVertexThrowsException() {
+        int[][] edges = {{-1, 1}};
+
+        assertThrows(IllegalArgumentException.class, () -> Bridges.findBridges(2, edges));
+    }
+
+    @Test
+    void testNegativeSecondVertexThrowsException() {
+        int[][] edges = {{0, -1}};
+
+        assertThrows(IllegalArgumentException.class, () -> Bridges.findBridges(2, edges));
+    }
+
+    @Test
+    void testFirstVertexOutOfRangeThrowsException() {
+        int[][] edges = {{2, 1}};
+
+        assertThrows(IllegalArgumentException.class, () -> Bridges.findBridges(2, edges));
+    }
+
+    @Test
+    void testSecondVertexOutOfRangeThrowsException() {
+        int[][] edges = {{0, 2}};
+
+        assertThrows(IllegalArgumentException.class, () -> Bridges.findBridges(2, edges));
+    }
+
+    @Test
+    void testBridgesAreSortedByBothEndpoints() {
+        int[][] edges = {{2, 3}, {0, 2}, {0, 1}};
+
+        List<int[]> result = Bridges.findBridges(4, edges);
+
+        assertEquals(3, result.size());
+        assertArrayEquals(new int[] {0, 1}, result.get(0));
+        assertArrayEquals(new int[] {0, 2}, result.get(1));
+        assertArrayEquals(new int[] {2, 3}, result.get(2));
+    }
+}