Added Dinic’s Max Flow algorithm with tests [Graphs] (TheAlgorithms#6762)

* Add Dinics max flow algorithm with tests and index update * Docs: add Dinic reference link and apply clang-format * Fix: Checkstyle violations in Dinic and tests * style: apply clang-format to Dinic and tests --------- Co-authored-by: a <alexanderklmn@gmail.com>

Author: SamXop123

DIRECTORY.md

@@ -353,6 +353,7 @@
  - 📄 [PredecessorConstrainedDfs](src/main/java/com/thealgorithms/graph/PredecessorConstrainedDfs.java)
  - 📄 [StronglyConnectedComponentOptimized](src/main/java/com/thealgorithms/graph/StronglyConnectedComponentOptimized.java)
  - 📄 [TravelingSalesman](src/main/java/com/thealgorithms/graph/TravelingSalesman.java)
+ - 📄 [Dinic](src/main/java/com/thealgorithms/graph/Dinic.java)
  - 📁 **greedyalgorithms**
  - 📄 [ActivitySelection](src/main/java/com/thealgorithms/greedyalgorithms/ActivitySelection.java)
  - 📄 [BandwidthAllocation](src/main/java/com/thealgorithms/greedyalgorithms/BandwidthAllocation.java)

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

@@ -0,0 +1,119 @@
+package com.thealgorithms.graph;
+
+import java.util.ArrayDeque;
+import java.util.Arrays;
+import java.util.Queue;
+
+/**
+ * Dinic's algorithm for computing maximum flow in a directed graph.
+ *
+ * <p>Time complexity: O(E * V^2) in the worst case, but typically faster in practice
+ * and near O(E * sqrt(V)) for unit networks.</p>
+ *
+ * <p>The graph is represented using a capacity matrix where capacity[u][v] is the
+ * capacity of the directed edge u -> v. Capacities must be non-negative.
+ * The algorithm builds level graphs using BFS and finds blocking flows using DFS
+ * with current-edge optimization.</p>
+ *
+ * <p>This implementation mirrors the API and validation style of
+ * {@link EdmondsKarp#maxFlow(int[][], int, int)} for consistency.</p>
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Dinic%27s_algorithm">Wikipedia: Dinic's algorithm</a>
+ */
+public final class Dinic {
+ private Dinic() {
+ }
+
+ /**
+ * Computes the maximum flow from source to sink using Dinic's algorithm.
+ *
+ * @param capacity square capacity matrix (n x n); entries must be >= 0
+ * @param source source vertex index in [0, n)
+ * @param sink sink vertex index in [0, n)
+ * @return the maximum flow value
+ * @throws IllegalArgumentException if the input matrix is null/non-square/has negatives or
+ * indices invalid
+ */
+ public static int maxFlow(int[][] capacity, int source, int sink) {
+ if (capacity == null || capacity.length == 0) {
+ throw new IllegalArgumentException("Capacity matrix must not be null or empty");
+ }
+ final int n = capacity.length;
+ for (int i = 0; i < n; i++) {
+ if (capacity[i] == null || capacity[i].length != n) {
+ throw new IllegalArgumentException("Capacity matrix must be square");
+ }
+ for (int j = 0; j < n; j++) {
+ if (capacity[i][j] < 0) {
+ throw new IllegalArgumentException("Capacities must be non-negative");
+ }
+ }
+ }
+ if (source < 0 || sink < 0 || source >= n || sink >= n) {
+ throw new IllegalArgumentException("Source and sink must be valid vertex indices");
+ }
+ if (source == sink) {
+ return 0;
+ }
+
+ // residual capacities
+ int[][] residual = new int[n][n];
+ for (int i = 0; i < n; i++) {
+ residual[i] = Arrays.copyOf(capacity[i], n);
+ }
+
+ int[] level = new int[n];
+ int flow = 0;
+ while (bfsBuildLevelGraph(residual, source, sink, level)) {
+ int[] next = new int[n]; // current-edge optimization
+ int pushed;
+ do {
+ pushed = dfsBlocking(residual, level, next, source, sink, Integer.MAX_VALUE);
+ flow += pushed;
+ } while (pushed > 0);
+ }
+ return flow;
+ }
+
+ private static boolean bfsBuildLevelGraph(int[][] residual, int source, int sink, int[] level) {
+ Arrays.fill(level, -1);
+ level[source] = 0;
+ Queue<Integer> q = new ArrayDeque<>();
+ q.add(source);
+ while (!q.isEmpty()) {
+ int u = q.poll();
+ for (int v = 0; v < residual.length; v++) {
+ if (residual[u][v] > 0 && level[v] == -1) {
+ level[v] = level[u] + 1;
+ if (v == sink) {
+ return true;
+ }
+ q.add(v);
+ }
+ }
+ }
+ return level[sink] != -1;
+ }
+
+ private static int dfsBlocking(int[][] residual, int[] level, int[] next, int u, int sink, int f) {
+ if (u == sink) {
+ return f;
+ }
+ final int n = residual.length;
+ for (int v = next[u]; v < n; v++, next[u] = v) {
+ if (residual[u][v] <= 0) {
+ continue;
+ }
+ if (level[v] != level[u] + 1) {
+ continue;
+ }
+ int pushed = dfsBlocking(residual, level, next, v, sink, Math.min(f, residual[u][v]));
+ if (pushed > 0) {
+ residual[u][v] -= pushed;
+ residual[v][u] += pushed;
+ return pushed;
+ }
+ }
+ return 0;
+ }
+}

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

@@ -0,0 +1,71 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+class DinicTest {
+ @Test
+ @DisplayName("Classic CLRS network yields max flow 23 (Dinic)")
+ void clrsExample() {
+ int[][] capacity = {{0, 16, 13, 0, 0, 0}, {0, 0, 10, 12, 0, 0}, {0, 4, 0, 0, 14, 0}, {0, 0, 9, 0, 0, 20}, {0, 0, 0, 7, 0, 4}, {0, 0, 0, 0, 0, 0}};
+ int maxFlow = Dinic.maxFlow(capacity, 0, 5);
+ assertEquals(23, maxFlow);
+ }
+
+ @Test
+ @DisplayName("Disconnected network has zero flow (Dinic)")
+ void disconnectedGraph() {
+ int[][] capacity = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
+ int maxFlow = Dinic.maxFlow(capacity, 0, 2);
+ assertEquals(0, maxFlow);
+ }
+
+ @Test
+ @DisplayName("Source equals sink returns zero (Dinic)")
+ void sourceEqualsSink() {
+ int[][] capacity = {{0, 5}, {0, 0}};
+ int maxFlow = Dinic.maxFlow(capacity, 0, 0);
+ assertEquals(0, maxFlow);
+ }
+
+ @Test
+ @DisplayName("Invalid matrix throws exception (Dinic)")
+ void invalidMatrix() {
+ int[][] capacity = {{0, 1}, {1}};
+ assertThrows(IllegalArgumentException.class, () -> Dinic.maxFlow(capacity, 0, 1));
+ }
+
+ @Test
+ @DisplayName("Dinic matches Edmonds-Karp on random small graphs")
+ void parityWithEdmondsKarp() {
+ java.util.Random rnd = new java.util.Random(42);
+ for (int n = 3; n <= 7; n++) {
+ for (int it = 0; it < 25; it++) {
+ int[][] cap = new int[n][n];
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < n; j++) {
+ if (i != j && rnd.nextDouble() < 0.35) {
+ cap[i][j] = rnd.nextInt(10); // capacities 0..9
+ }
+ }
+ }
+ int s = 0;
+ int t = n - 1;
+ int f1 = Dinic.maxFlow(copyMatrix(cap), s, t);
+ int f2 = EdmondsKarp.maxFlow(cap, s, t);
+ assertEquals(f2, f1);
+ }
+ }
+ }
+
+ private static int[][] copyMatrix(int[][] a) {
+ int[][] b = new int[a.length][a.length];
+ for (int i = 0; i < a.length; i++) {
+ b[i] = java.util.Arrays.copyOf(a[i], a[i].length);
+ }
+ return b;
+ }
+}