Implemented Edmonds Blossom Algorithm

DIRECTORY.md

@@ -107,6 +107,7 @@
               * [ConnectedComponent](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/ConnectedComponent.java)
               * [Cycles](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/Cycles.java)
               * [DijkstraAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/DijkstraAlgorithm.java)
+              * [EdmondsBlossomAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/EdmondsBlossomAlgorithm.java)
               * [FloydWarshall](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/FloydWarshall.java)
               * [FordFulkerson](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/FordFulkerson.java)
               * [Graphs](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/Graphs.java)
@@ -560,6 +561,7 @@
             * [LongestNonRepetitiveSubstring](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/LongestNonRepetitiveSubstring.java)
             * [LongestPalindromicSubstring](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/LongestPalindromicSubstring.java)
             * [Lower](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/Lower.java)
+            * [Manacher](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/Manacher.java)
             * [MyAtoi](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/MyAtoi.java)
             * [Palindrome](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/Palindrome.java)
             * [Pangram](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/Pangram.java)
@@ -657,6 +659,7 @@
             * graphs
               * [BoruvkaAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/BoruvkaAlgorithmTest.java)
               * [DijkstraAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/DijkstraAlgorithmTest.java)
+              * [EdmondsBlossomAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/EdmondsBlossomAlgorithmTest.java)
               * [FordFulkersonTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/FordFulkersonTest.java)
               * [HamiltonianCycleTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/HamiltonianCycleTest.java)
               * [KosarajuTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/KosarajuTest.java)
@@ -846,6 +849,8 @@
             * [TwinPrimeTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/TwinPrimeTest.java)
             * [VolumeTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/VolumeTest.java)
           * misc
+            * [ColorContrastRatioTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/misc/ColorContrastRatioTest.java)
+            * [InverseOfMatrixTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/misc/InverseOfMatrixTest.java)
             * [MapReduceTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/misc/MapReduceTest.java)
             * [MedianOfMatrixtest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/misc/MedianOfMatrixtest.java)
             * [MedianOfRunningArrayTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/misc/MedianOfRunningArrayTest.java)
@@ -857,6 +862,7 @@
             * [ArrayRightRotation](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/others/ArrayRightRotation.java)
             * [ArrayRightRotationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/others/ArrayRightRotationTest.java)
             * [BestFitCPUTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/others/BestFitCPUTest.java)
+            * [BFPRTTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/others/BFPRTTest.java)
             * [BoyerMooreTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/others/BoyerMooreTest.java)
             * cn
               * [HammingDistanceTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/others/cn/HammingDistanceTest.java)
@@ -976,6 +982,7 @@
             * [LongestNonRepetitiveSubstringTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/LongestNonRepetitiveSubstringTest.java)
             * [LongestPalindromicSubstringTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/LongestPalindromicSubstringTest.java)
             * [LowerTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/LowerTest.java)
+            * [ManacherTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/ManacherTest.java)
             * [MyAtoiTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/MyAtoiTest.java)
             * [PalindromeTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/PalindromeTest.java)
             * [PangramTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/PangramTest.java)

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

@@ -0,0 +1,251 @@
+package com.thealgorithms.datastructures.graphs;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.LinkedList;
+import java.util.List;
+import java.util.Queue;
+
+/**
+ * The EdmondsBlossomAlgorithm class implements Edmonds' Blossom Algorithm
+ * to find the maximum matching in a general graph. The algorithm efficiently
+ * handles cases where the graph contains odd-length cycles by contracting
+ * "blossoms" and finding augmenting paths.
+ *<p>
+ * <a href="https://stanford.edu/~rezab/classes/cme323/S16/projects_reports/shoemaker_vare.pdf">Documentation of Algorithm (Stanford University)</a>
+ * <p></p>
+ * <a href="https://en.wikipedia.org/wiki/Blossom_algorithm">Wikipedia Documentation</a>
+ */
+public final class EdmondsBlossomAlgorithm {
+
+    private EdmondsBlossomAlgorithm() {
+    }
+
+    private static final int UNMATCHED = -1; // Constant to represent unmatched vertices
+
+    /**
+     * Finds the maximum matching in a general graph (Edmonds Blossom Algorithm).
+     *
+     * @param edges A list of edges in the graph.
+     * @param vertexCount The number of vertices in the graph.
+     * @return A list of matched pairs of vertices.
+     */
+    public static List<int[]> maximumMatching(List<int[]> edges, int vertexCount) {
+        List<List<Integer>> graph = new ArrayList<>(vertexCount);
+
+        // Initialize each vertex's adjacency list.
+        for (int i = 0; i < vertexCount; i++) {
+            graph.add(new ArrayList<>());
+        }
+
+        // Populate the graph with the edges
+        for (int[] edge : edges) {
+            int u = edge[0];
+            int v = edge[1];
+            graph.get(u).add(v);
+            graph.get(v).add(u);
+        }
+
+        // Initial matching array and auxiliary data structures
+        int[] match = new int[vertexCount];
+        Arrays.fill(match, UNMATCHED); // All vertices are initially unmatched
+        int[] parent = new int[vertexCount];
+        int[] base = new int[vertexCount];
+        boolean[] inBlossom = new boolean[vertexCount]; // Indicates if a vertex is part of a blossom
+        boolean[] inQueue = new boolean[vertexCount]; // Tracks vertices in the BFS queue
+
+        // Main logic for finding maximum matching
+        for (int u = 0; u < vertexCount; u++) {
+            if (match[u] == UNMATCHED) {
+                // BFS initialization
+                Arrays.fill(parent, UNMATCHED);
+                for (int i = 0; i < vertexCount; i++) {
+                    base[i] = i; // Each vertex is its own base initially
+                }
+                Arrays.fill(inBlossom, false);
+                Arrays.fill(inQueue, false);
+
+                Queue<Integer> queue = new LinkedList<>();
+                queue.add(u);
+                inQueue[u] = true;
+
+                boolean augmentingPathFound = false;
+
+                // BFS to find augmenting paths
+                while (!queue.isEmpty() && !augmentingPathFound) {
+                    int current = queue.poll(); // Use a different name for clarity
+                    for (int y : graph.get(current)) {
+                        // Skip if we are looking at the same edge as the current match
+                        if (match[current] == y) {
+                            continue;
+                        }
+
+                        if (base[current] == base[y]) {
+                            continue; // Avoid self-loops
+                        }
+
+                        if (parent[y] == UNMATCHED) {
+                            // Case 1: y is unmatched, we've found an augmenting path
+                            if (match[y] == UNMATCHED) {
+                                parent[y] = current;
+                                augmentingPathFound = true;
+                                updateMatching(match, parent, y); // Augment along this path
+                                break;
+                            }
+
+                            // Case 2: y is matched, add y's match to the queue
+                            int z = match[y];
+                            parent[y] = current;
+                            parent[z] = y;
+                            if (!inQueue[z]) {
+                                queue.add(z);
+                                inQueue[z] = true;
+                            }
+                        } else {
+                            // Case 3: Both x and y have a parent; check for a cycle/blossom
+                            int baseU = findBase(base, parent, current, y);
+                            if (baseU != UNMATCHED) {
+                                contractBlossom(new BlossomData(new BlossomAuxData(queue, parent, base, inBlossom, match, inQueue), current, y, baseU));
+                            }
+                        }
+                    }
+                }
+            }
+        }
+
+        // Create result list of matched pairs
+        List<int[]> matchingResult = new ArrayList<>();
+        for (int v = 0; v < vertexCount; v++) {
+            if (match[v] != UNMATCHED && v < match[v]) {
+                matchingResult.add(new int[] {v, match[v]});
+            }
+        }
+
+        return matchingResult;
+    }
+
+    /**
+     * Updates the matching along the augmenting path found.
+     *
+     * @param match The matching array.
+     * @param parent The parent array used during the BFS.
+     * @param u The starting node of the augmenting path.
+     */
+    private static void updateMatching(int[] match, int[] parent, int u) {
+        while (u != UNMATCHED) {
+            int v = parent[u];
+            int next = match[v];
+            match[v] = u;
+            match[u] = v;
+            u = next;
+        }
+    }
+
+    /**
+     * Finds the base of a node in the blossom.
+     *
+     * @param base The base array.
+     * @param parent The parent array.
+     * @param u One end of the edge.
+     * @param v The other end of the edge.
+     * @return The base of the node or UNMATCHED.
+     */
+    private static int findBase(int[] base, int[] parent, int u, int v) {
+        boolean[] visited = new boolean[base.length];
+
+        // Mark ancestors of u
+        int currentU = u;
+        while (true) {
+            currentU = base[currentU]; // Move assignment out of the condition
+            visited[currentU] = true;
+            if (parent[currentU] == UNMATCHED) {
+                break;
+            }
+            currentU = parent[currentU]; // Move assignment out of the condition
+        }
+
+        // Find the common ancestor of v
+        int currentV = v;
+        while (true) {
+            currentV = base[currentV]; // Move assignment out of the condition
+            if (visited[currentV]) {
+                return currentV;
+            }
+            currentV = parent[currentV]; // Move assignment out of the condition
+        }
+    }
+
+    /**
+     * Contracts a blossom and updates the base array.
+     *
+     * @param blossomData The data containing the parameters related to the blossom contraction.
+     */
+    private static void contractBlossom(BlossomData blossomData) {
+        for (int x = blossomData.u; blossomData.auxData.base[x] != blossomData.lca; x = blossomData.auxData.parent[blossomData.auxData.match[x]]) {
+            int baseX = blossomData.auxData.base[x];
+            int matchBaseX = blossomData.auxData.base[blossomData.auxData.match[x]];
+
+            // Split the inner assignment into two separate assignments
+            blossomData.auxData.inBlossom[baseX] = true;
+            blossomData.auxData.inBlossom[matchBaseX] = true;
+        }
+
+        for (int x = blossomData.v; blossomData.auxData.base[x] != blossomData.lca; x = blossomData.auxData.parent[blossomData.auxData.match[x]]) {
+            int baseX = blossomData.auxData.base[x];
+            int matchBaseX = blossomData.auxData.base[blossomData.auxData.match[x]];
+
+            // Split the inner assignment into two separate assignments
+            blossomData.auxData.inBlossom[baseX] = true;
+            blossomData.auxData.inBlossom[matchBaseX] = true;
+        }
+
+        // Update the base for all marked vertices
+        for (int i = 0; i < blossomData.auxData.base.length; i++) {
+            if (blossomData.auxData.inBlossom[blossomData.auxData.base[i]]) {
+                blossomData.auxData.base[i] = blossomData.lca; // Contract to the lowest common ancestor
+                if (!blossomData.auxData.inQueue[i]) {
+                    blossomData.auxData.queue.add(i); // Add to queue if not already present
+                    blossomData.auxData.inQueue[i] = true;
+                }
+            }
+        }
+    }
+
+    /**
+     * Auxiliary data class to encapsulate common parameters for the blossom operations.
+     */
+    static class BlossomAuxData {
+        Queue<Integer> queue; // Queue for BFS traversal
+        int[] parent; // Parent array to store the paths
+        int[] base; // Base array to track the base of each vertex
+        boolean[] inBlossom; // Flags to indicate if a vertex is in a blossom
+        int[] match; // Array to store matches for each vertex
+        boolean[] inQueue; // Flags to track vertices in the BFS queue
+
+        BlossomAuxData(Queue<Integer> queue, int[] parent, int[] base, boolean[] inBlossom, int[] match, boolean[] inQueue) {
+            this.queue = queue;
+            this.parent = parent;
+            this.base = base;
+            this.inBlossom = inBlossom;
+            this.match = match;
+            this.inQueue = inQueue;
+        }
+    }
+
+    /**
+     * BlossomData class with reduced parameters.
+     */
+    static class BlossomData {
+        BlossomAuxData auxData; // Use the auxiliary data class
+        int u; // One vertex in the edge
+        int v; // Another vertex in the edge
+        int lca; // Lowest Common Ancestor
+
+        BlossomData(BlossomAuxData auxData, int u, int v, int lca) {
+            this.auxData = auxData;
+            this.u = u;
+            this.v = v;
+            this.lca = lca;
+        }
+    }
+}