Kth smallest element in sorted matrix

Question

This is an interview question.

Find the K^th smallest element in a matrix with sorted rows and columns.
Is it correct that the K^th small

Answer 1

O(k log(k)) solution.

• Build a minheap.

• Add (0,0) to the heap. While, we haven't found the kth smallest element, remove the top element (x,y) from heap and add next two elements [(x+1,y) and (x,y+1)] if they haven't been visited before.

We are doing O(k) operations on a heap of size O(k) and hence the complexity.

Answer 2

As people mentioned previously the easiest way is to build a min heap. Here's a Java implementation using PriorityQueue:

private int kthSmallestUsingHeap(int[][] matrix, int k) {

    int n = matrix.length;

    // This is not necessary since this is the default Int comparator behavior
    Comparator<Integer> comparator = new Comparator<Integer>() {
        @Override
        public int compare(Integer o1, Integer o2) {
            return o1 - o2;
        }
    };

    // building a minHeap
    PriorityQueue<Integer> pq = new PriorityQueue<>(n*n, comparator);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            pq.add(matrix[i][j]);
        }
    }

    int ans = -1;
    // remove the min element k times
    for (int i = 0; i < k; i++) {
        ans = pq.poll();
    }

    return ans;
}

Answer 3

Kth smallest element in the matrix :

The problem can be narrowed down as below.

if k is 20, then take k*k matrix (where answer will definitely lie.)

Now you can merge the rows in pair repeatedly to build a sorted array and then find the kth smallest number.