Given a matrix of size N x M. For each row the elements are sorted in ascending order, and for each column the elements are also sorted in ascending order. Find the Kth smallest number in it.

Assumptions

the matrix is not null, N > 0 and M > 0
K > 0 and K <= N * M
Examples

{ {1, 3, 5, 7},

{2, 4, 8, 9},

{3, 5, 11, 15},

{6, 8, 13, 18} }

the 5th smallest number is 4
the 8th smallest number is 6

Assumptions

the matrix is not null, N > 0 and M > 0
K > 0 and K <= N * M

 1 class Solution {
 2     public int kthSmallest(int[][] matrix, int k) {
 3         int rows = matrix.length ;
 
 4         int cols = matrix[0].length ;
 5         Queue<Cell> minHeap = new PriorityQueue<Cell>(k, new CellComparator());
 6         //marker for visited: same rol and col
 7         boolean[][] visited = new boolean[rows][cols] ;
 8         //expand
 9         minHeap.offer(new Cell(0,0,matrix[0][0])) ;
 
10         visited[0][0] = true ;
11         /*pop k-1 then whats left is the kth smallest: 
12         因為行，列 都是單調遞增，所以下一個最小的值，肯定在當前點的 左邊，或者右邊。 
13         你不需要考慮加 哪個， pq 又可以幫你做到拋最小的，
14         所以要嚴格利用這個性質 做 kth 最小，最大的題。
15         */
16         for (int i = 0; i < k-1 ; i++ ) {
17             Cell curr = minHeap.poll();
18             //when dealing with index +1 for array, always checks boundary
19             if (curr.row+1<rows && !visited[curr.row+1][curr.col]) {
20                 minHeap.offer(new Cell(curr.row+1, curr.col, matrix[curr.row+1][curr.col]));
21                 visited[curr.row+1][curr.col] = true ;
22             }
23             if (curr.col+1<cols && !visited[curr.row][curr.col+1]) {
24                 minHeap.offer(new Cell(curr.row, curr.col+1, matrix[curr.row][curr.col+1]));
25                 visited[curr.row][curr.col+1] = true ;
26             }
27         }
28         //已經拋出去 k-1 那剩下的 peek 一下就是 第k 個最小的
29         return minHeap.peek().val;
30     }
31 }
32 // PriorityminHeap for custom class requires implements Comparator<T>
33 class Cell{
34     public int row ;
35     public int col ;
36     public int val;
37     public Cell (int row, int col, int val){
38         this.row = row ;
39         this.col = col ;
40         this.val = val ;
41     }
42 
43 }
44 class CellComparator implements Comparator<Cell>{
45     @Override
46     public int compare(Cell c1, Cell c2){
47         return c1.val - c2.val ;
48     }
49 }

LF.26.Kth Smallest Number In Sorted Matrix