Enhance docs, add more tests in FordFulkerson (#5953)

Author: Hardvan

src/main/java/com/thealgorithms/datastructures/graphs/FordFulkerson.java

@@ -3,12 +3,30 @@
 import java.util.LinkedList;
 import java.util.Queue;
 
+/**
+ * This class implements the Ford-Fulkerson algorithm to compute the maximum flow
+ * in a flow network.
+ *
+ * <p>The algorithm uses breadth-first search (BFS) to find augmenting paths from
+ * the source vertex to the sink vertex, updating the flow in the network until
+ * no more augmenting paths can be found.</p>
+ */
 public final class FordFulkerson {
     private static final int INF = Integer.MAX_VALUE;
 
     private FordFulkerson() {
     }
 
+    /**
+     * Computes the maximum flow in a flow network using the Ford-Fulkerson algorithm.
+     *
+     * @param vertexCount the number of vertices in the flow network
+     * @param capacity    a 2D array representing the capacity of edges in the network
+     * @param flow        a 2D array representing the current flow in the network
+     * @param source      the source vertex in the flow network
+     * @param sink        the sink vertex in the flow network
+     * @return the total maximum flow from the source to the sink
+     */
     public static int networkFlow(int vertexCount, int[][] capacity, int[][] flow, int source, int sink) {
         int totalFlow = 0;
 

src/test/java/com/thealgorithms/datastructures/graphs/FordFulkersonTest.java

@@ -91,4 +91,126 @@ public void testComplexNetwork() {
         int maxFlow = FordFulkerson.networkFlow(vertexCount, capacity, flow, 0, 4);
         assertEquals(19, maxFlow);
     }
+
+    @Test
+    public void testLargeNetwork() {
+        int vertexCount = 8;
+        int[][] capacity = new int[vertexCount][vertexCount];
+        int[][] flow = new int[vertexCount][vertexCount];
+
+        // Setting up a large network
+        capacity[0][1] = 10;
+        capacity[0][2] = 5;
+        capacity[1][3] = 15;
+        capacity[2][3] = 10;
+        capacity[1][4] = 10;
+        capacity[3][5] = 10;
+        capacity[4][5] = 5;
+        capacity[4][6] = 10;
+        capacity[5][7] = 10;
+        capacity[6][7] = 15;
+
+        int maxFlow = FordFulkerson.networkFlow(vertexCount, capacity, flow, 0, 7);
+        assertEquals(15, maxFlow); // Maximum flow should be 15
+    }
+
+    @Test
+    public void testMultipleSourcesAndSinks() {
+        int vertexCount = 7;
+        int[][] capacity = new int[vertexCount][vertexCount];
+        int[][] flow = new int[vertexCount][vertexCount];
+
+        // Creating multiple sources and sinks scenario
+        capacity[0][1] = 10; // Source 1
+        capacity[0][2] = 5;
+        capacity[1][3] = 15;
+        capacity[2][3] = 10;
+        capacity[3][4] = 10; // Sink 1
+        capacity[3][5] = 5;
+        capacity[3][6] = 10; // Sink 2
+        capacity[5][6] = 10;
+
+        int maxFlow = FordFulkerson.networkFlow(vertexCount, capacity, flow, 0, 4);
+        assertEquals(10, maxFlow); // Maximum flow should be 10
+    }
+
+    @Test
+    public void testDisconnectedGraph() {
+        int vertexCount = 6;
+        int[][] capacity = new int[vertexCount][vertexCount];
+        int[][] flow = new int[vertexCount][vertexCount];
+
+        // No connection between source and sink
+        capacity[0][1] = 10; // Only one edge not connected to the sink
+        capacity[1][2] = 10;
+        capacity[3][4] = 10;
+
+        int maxFlow = FordFulkerson.networkFlow(vertexCount, capacity, flow, 0, 5);
+        assertEquals(0, maxFlow); // No flow should be possible
+    }
+
+    @Test
+    public void testZeroCapacityEdge() {
+        int vertexCount = 4;
+        int[][] capacity = new int[vertexCount][vertexCount];
+        int[][] flow = new int[vertexCount][vertexCount];
+
+        // Including a zero capacity edge
+        capacity[0][1] = 10;
+        capacity[0][2] = 0; // Zero capacity
+        capacity[1][3] = 5;
+        capacity[2][3] = 10;
+
+        int maxFlow = FordFulkerson.networkFlow(vertexCount, capacity, flow, 0, 3);
+        assertEquals(5, maxFlow); // Flow only possible through 0 -> 1 -> 3
+    }
+
+    @Test
+    public void testAllEdgesZeroCapacity() {
+        int vertexCount = 5;
+        int[][] capacity = new int[vertexCount][vertexCount];
+        int[][] flow = new int[vertexCount][vertexCount];
+
+        // All edges with zero capacity
+        capacity[0][1] = 0;
+        capacity[1][2] = 0;
+        capacity[2][3] = 0;
+        capacity[3][4] = 0;
+
+        int maxFlow = FordFulkerson.networkFlow(vertexCount, capacity, flow, 0, 4);
+        assertEquals(0, maxFlow); // No flow should be possible
+    }
+
+    @Test
+    public void testCycleGraph() {
+        int vertexCount = 4;
+        int[][] capacity = new int[vertexCount][vertexCount];
+        int[][] flow = new int[vertexCount][vertexCount];
+
+        // Setting up a cycle
+        capacity[0][1] = 10;
+        capacity[1][2] = 5;
+        capacity[2][0] = 5; // This creates a cycle
+        capacity[1][3] = 15;
+        capacity[2][3] = 10;
+
+        int maxFlow = FordFulkerson.networkFlow(vertexCount, capacity, flow, 0, 3);
+        assertEquals(10, maxFlow); // Maximum flow should be 10
+    }
+
+    @Test
+    public void testFlowWithExcessCapacity() {
+        int vertexCount = 5;
+        int[][] capacity = new int[vertexCount][vertexCount];
+        int[][] flow = new int[vertexCount][vertexCount];
+
+        // Extra capacity in the flow
+        capacity[0][1] = 20;
+        capacity[1][2] = 10;
+        capacity[2][3] = 15;
+        capacity[1][3] = 5;
+
+        int maxFlow = FordFulkerson.networkFlow(vertexCount, capacity, flow, 0, 3);
+        assertEquals(15, maxFlow); // Maximum flow should be 15 (20 from 0->1 and 10->2, limited by 15->3)
+    }
 }