Added Dinic’s Max Flow algorithm with tests [Graphs] (#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>

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;
+    }
+}