diff --git a/src/main/java/com/thealgorithms/datastructures/graphs/FordFulkerson.java b/src/main/java/com/thealgorithms/datastructures/graphs/FordFulkerson.java index af2665cfaebb..b3a2053d54b5 100644 --- a/src/main/java/com/thealgorithms/datastructures/graphs/FordFulkerson.java +++ b/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. + * + *
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.
+ */ 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; diff --git a/src/test/java/com/thealgorithms/datastructures/graphs/FordFulkersonTest.java b/src/test/java/com/thealgorithms/datastructures/graphs/FordFulkersonTest.java index 908296aab5c1..29e373e361ad 100644 --- a/src/test/java/com/thealgorithms/datastructures/graphs/FordFulkersonTest.java +++ b/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) + } }