kth_smallest_sorted_matrix.cpp

/*
    Given a n x n matrix where each of the rows and columns are 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.
*/
class Solution {
public:
    int kthSmallest(vector<vector<int>>& matrix, int k) {
        int n = matrix.size();
        int low = matrix[0][0], high = matrix[n - 1][n - 1];
        
        while(low < high) {
            int mid = low + (high - low) / 2;
            int count = 0;
            
            // use staircase search to find count of elements <= mid
            int row = 0, col = n - 1;
            while(row < n and col >= 0) {
                if(matrix[row][col] <= mid) {
                    count += col + 1;
                    row++;
                }
                else
                    col--;
            }
            
            if(count < k)
                low = mid + 1;
            else 
                high = mid;
        }
        return low;
    }
};