Kth Smallest Element in a Sorted Matrix (Java)

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Given an n x n matrix where each of the rows and columns is sorted in ascending order, find the kth smallest element in the matrix.

Note that it is the kth smallest element in the sorted order, not the kth distinct element.

Example: 

matrix = [
   [ 1,  5,  9],
   [10, 11, 13],
   [12, 13, 15]
],

k = 8,

return 13.

Java Solution

The start point of such a sorted matrix is the left-bottom corner.

public int kthSmallest(int[][] matrix, int k) {
    int m=matrix.length;
 
    int lower = matrix[0][0];
    int upper = matrix[m-1][m-1];
 
    while(lower<upper){
        int mid = lower + ((upper-lower)>>1);
        int count = count(matrix, mid);
        if(count<k){
            lower=mid+1;
        }else{
            upper=mid;
        }
    }
 
    return upper;
}
 
private int count(int[][] matrix, int target){
    int m=matrix.length;
    int i=m-1;
    int j=0;
    int count = 0;
 
    while(i>=0&&j<m){
        if(matrix[i][j]<=target){
            count += i+1;
            j++;
        }else{
            i--;
        }
    }
 
    return count;
}
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