diff --git a/DIRECTORY.md b/DIRECTORY.md index bad138b341e1..28bd525bb508 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -179,6 +179,7 @@ * [LeftistHeap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/LeftistHeap.java) * [MaxHeap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MaxHeap.java) * [MedianFinder](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MedianFinder.java) + * [MergeKSortedArrays](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MergeKSortedArrays.java) * [MinHeap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MinHeap.java) * [MinPriorityQueue](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MinPriorityQueue.java) * lists @@ -860,6 +861,7 @@ * [KthElementFinderTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/KthElementFinderTest.java) * [LeftistHeapTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/LeftistHeapTest.java) * [MedianFinderTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/MedianFinderTest.java) + * [MergeKSortedArraysTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/MergeKSortedArraysTest.java) * [MinPriorityQueueTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/MinPriorityQueueTest.java) * lists * [CircleLinkedListTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/lists/CircleLinkedListTest.java) diff --git a/src/main/java/com/thealgorithms/datastructures/heaps/MergeKSortedArrays.java b/src/main/java/com/thealgorithms/datastructures/heaps/MergeKSortedArrays.java new file mode 100644 index 000000000000..e41711f05914 --- /dev/null +++ b/src/main/java/com/thealgorithms/datastructures/heaps/MergeKSortedArrays.java @@ -0,0 +1,60 @@ +package com.thealgorithms.datastructures.heaps; + +import java.util.Comparator; +import java.util.PriorityQueue; + +/** + * This class provides a method to merge multiple sorted arrays into a single sorted array. + * It utilizes a min-heap to efficiently retrieve the smallest elements from each array. + * + * Time Complexity: O(n * log k), where n is the total number of elements across all arrays + * and k is the number of arrays. + * + * Space Complexity: O(k) for the heap, where k is the number of arrays. + * + * @author Hardvan + */ +public final class MergeKSortedArrays { + private MergeKSortedArrays() { + } + + /** + * Merges k sorted arrays into one sorted array using a min-heap. + * Steps: + * 1. Create a min-heap to store elements in the format: {value, array index, element index} + * 2. Add the first element from each array to the heap + * 3. While the heap is not empty, remove the smallest element from the heap + * and add it to the result array. If there are more elements in the same array, + * add the next element to the heap. + * Continue until all elements have been processed. + * The result array will contain all elements in sorted order. + * 4. Return the result array. + * + * @param arrays a 2D array, where each subarray is sorted in non-decreasing order + * @return a single sorted array containing all elements from the input arrays + */ + public static int[] mergeKArrays(int[][] arrays) { + PriorityQueue minHeap = new PriorityQueue<>(Comparator.comparingInt(a -> a[0])); + + int totalLength = 0; + for (int i = 0; i < arrays.length; i++) { + if (arrays[i].length > 0) { + minHeap.offer(new int[] {arrays[i][0], i, 0}); + totalLength += arrays[i].length; + } + } + + int[] result = new int[totalLength]; + int index = 0; + while (!minHeap.isEmpty()) { + int[] top = minHeap.poll(); + result[index++] = top[0]; + + if (top[2] + 1 < arrays[top[1]].length) { + minHeap.offer(new int[] {arrays[top[1]][top[2] + 1], top[1], top[2] + 1}); + } + } + + return result; + } +} diff --git a/src/test/java/com/thealgorithms/datastructures/heaps/MergeKSortedArraysTest.java b/src/test/java/com/thealgorithms/datastructures/heaps/MergeKSortedArraysTest.java new file mode 100644 index 000000000000..c9b754619286 --- /dev/null +++ b/src/test/java/com/thealgorithms/datastructures/heaps/MergeKSortedArraysTest.java @@ -0,0 +1,41 @@ +package com.thealgorithms.datastructures.heaps; + +import static org.junit.jupiter.api.Assertions.assertArrayEquals; + +import java.util.stream.Stream; +import org.junit.jupiter.params.ParameterizedTest; +import org.junit.jupiter.params.provider.Arguments; +import org.junit.jupiter.params.provider.MethodSource; + +public class MergeKSortedArraysTest { + + @ParameterizedTest + @MethodSource("provideTestCases") + public void testMergeKArrays(int[][] arrays, int[] expected) { + assertArrayEquals(expected, MergeKSortedArrays.mergeKArrays(arrays)); + } + + private static Stream provideTestCases() { + return Stream.of( + // Basic test case with multiple arrays + Arguments.of(new int[][] {{1, 4, 5}, {1, 3, 4}, {2, 6}}, new int[] {1, 1, 2, 3, 4, 4, 5, 6}), + + // Edge case: All arrays are empty + Arguments.of(new int[][] {{}, {}, {}}, new int[] {}), + + // Edge case: One array is empty + Arguments.of(new int[][] {{1, 3, 5}, {}, {2, 4, 6}}, new int[] {1, 2, 3, 4, 5, 6}), + + // Single array + Arguments.of(new int[][] {{1, 2, 3}}, new int[] {1, 2, 3}), + + // Arrays with negative numbers + Arguments.of(new int[][] {{-5, 1, 3}, {-10, 0, 2}}, new int[] {-10, -5, 0, 1, 2, 3}), + + // Arrays with duplicate elements + Arguments.of(new int[][] {{1, 1, 2}, {1, 3, 3}, {2, 2, 4}}, new int[] {1, 1, 1, 2, 2, 2, 3, 3, 4}), + + // Edge case: Arrays of varying lengths + Arguments.of(new int[][] {{1, 2}, {3}, {4, 5, 6, 7}}, new int[] {1, 2, 3, 4, 5, 6, 7})); + } +}