feat(graph): add Push–Relabel max flow with tests and index (#6793)

* feat(graph): add Push–Relabel max flow with tests and index * style(checkstyle): reduce discharge parameter count via State holder * chore(pmd): make discharge void and remove empty else; satisfy PMD --------- Co-authored-by: a <alexanderklmn@gmail.com>
2025-12-19 07:00:35 +08:00 · 2025-10-16 02:21:14 +05:30
parent f8688ba38d
commit 1437036b19
3 changed files with 229 additions and 0 deletions
--- a/src/test/java/com/thealgorithms/graph/PushRelabelTest.java
+++ b/src/test/java/com/thealgorithms/graph/PushRelabelTest.java
@@ -0,0 +1,66 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+class PushRelabelTest {
+
+    @Test
+    @DisplayName("Classic CLRS network yields max flow 23 (PushRelabel)")
+    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 = PushRelabel.maxFlow(capacity, 0, 5);
+        assertEquals(23, maxFlow);
+    }
+
+    @Test
+    @DisplayName("Disconnected network has zero flow (PushRelabel)")
+    void disconnectedGraph() {
+        int[][] capacity = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
+        int maxFlow = PushRelabel.maxFlow(capacity, 0, 2);
+        assertEquals(0, maxFlow);
+    }
+
+    @Test
+    @DisplayName("Source equals sink returns zero (PushRelabel)")
+    void sourceEqualsSink() {
+        int[][] capacity = {{0, 5}, {0, 0}};
+        int maxFlow = PushRelabel.maxFlow(capacity, 0, 0);
+        assertEquals(0, maxFlow);
+    }
+
+    @Test
+    @DisplayName("PushRelabel matches Dinic and EdmondsKarp on random small graphs")
+    void parityWithOtherMaxFlow() {
+        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 fPushRelabel = PushRelabel.maxFlow(copyMatrix(cap), s, t);
+                int fDinic = Dinic.maxFlow(copyMatrix(cap), s, t);
+                int fEdmondsKarp = EdmondsKarp.maxFlow(cap, s, t);
+                assertEquals(fDinic, fPushRelabel);
+                assertEquals(fEdmondsKarp, fPushRelabel);
+            }
+        }
+    }
+
+    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;
+    }
+}