Add Block Sort algorithm implementation

Author: yashleo

src/main/java/com/thealgorithms/sorts/BlockSort.java

@@ -0,0 +1,75 @@
+package com.thealgorithms.sorts;
+
+import java.util.Arrays;
+
+/**
+ * Implementation of Block Sort algorithm that implements the SortAlgorithm interface.
+ * 
+ * Block Sort is a distribution sorting algorithm that divides the array into blocks,
+ * sorts each block, and merges the blocks to produce a sorted array.
+ * 
+ * The method works as follows:
+ * <ol>
+ *     <li>Divide the input array into blocks.</li>
+ *     <li>Sort each block individually.</li>
+ *     <li>Merge the sorted blocks to produce a fully sorted array.</li>
+ * </ol>
+ */
+public class BlockSort implements SortAlgorithm {
+
+    @Override
+    public <T extends Comparable<T>> T[] sort(T[] array) {
+        return blockSort(array);
+    }
+
+    /**
+     * Sorts an array using the Block Sort algorithm.
+     * 
+     * @param arr the array to be sorted.
+     * @param <T> the type of elements to be sorted, must be comparable.
+     * @return the sorted array.
+     */
+    private <T extends Comparable<? super T>> T[] blockSort(T[] arr) {
+        if (arr.length <= 1) {
+            return arr; // Already sorted
+        }
+
+        int blockSize = (int) Math.sqrt(arr.length); // Block size is the square root of the array size
+        int numBlocks = (arr.length + blockSize - 1) / blockSize; // Calculate number of blocks
+
+        // Create an array of blocks
+        T[][] blocks = (T[][]) new Comparable[numBlocks][];
+        
+        // Populate the blocks
+        for (int i = 0; i < numBlocks; i++) {
+            int start = i * blockSize;
+            int end = Math.min(start + blockSize, arr.length);
+            blocks[i] = Arrays.copyOfRange(arr, start, end);
+            Arrays.sort(blocks[i]); // Sort each block
+        }
+
+        // Merge the sorted blocks
+        return mergeBlocks(blocks);
+    }
+
+    /**
+     * Merges sorted blocks into a single sorted array.
+     * 
+     * @param blocks the array of sorted blocks.
+     * @param <T> the type of elements in the blocks, must be comparable.
+     * @return the merged sorted array.
+     */
+    private <T extends Comparable<? super T>> T[] mergeBlocks(T[][] blocks) {
+        int totalLength = Arrays.stream(blocks).mapToInt(b -> b.length).sum();
+        T[] result = (T[]) new Comparable[totalLength];
+        int index = 0;
+
+        for (T[] block : blocks) {
+            for (T element : block) {
+                result[index++] = element; // Add each element from the block to the result array
+            }
+        }
+
+        return result;
+    }
+}