Merge K Sorted Arrays
Objective: Given k sorted array, write an algorithm to merge Them into One sorted array.
Example :
int[][] A = new int[5][];
A[0] = new int[] { 1, 5, 8, 9 };
A[1] = new int[] { 2, 3, 7, 10 };
A[2] = new int[] { 4, 6, 11, 15 };
A[3] = new int[] { 9, 14, 16, 19 };
A[4] = new int[] { 2, 4, 6, 9 };
Output:
[1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 14, 15, 16, 19]
Naive Solution: O(nkLognk)
- Create an result[] of size n*k.
- Copy all the elements from k arrays into result array. This will take O(nk).
- Sort the result[] using Merge Sort. This will take O(nkLognk) time.
Better Approach: O(nkLogk)
- Create an result[] of size n*k.
- Create Min-Heap of type HeapNode.( HeapNode- Every Node will store the data and the list no from which it belongs).
- Now take one element from each of the K list and create HeapNode object and insert into min-Heap.
- Extract the minimum Node from the min-Heap, insert the data into result array.
- The extracted node will also contain the list to which it belongs, insert the next element from that list into min-Heap.
- If any point of time any list gets over, insert +∞ into min-Heap.
- Keep repeating until all the K list gets over.
See the animation below for better understanding.
Complete Code:
Output:
[1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 14, 15, 16, 19]