378. Kth Smallest Element in a Sorted Matrix

• Difficulty: Medium

• Topics: Binary Search, Heap

• Similar Questions:

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Problem:

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.

Note:
You may assume k is always valid, 1 ≤ k ≤ n².

Solutions:

class Solution {
public:
    int kthSmallest(vector<vector<int>>& matrix, int k) {
        int m = matrix.size();
        if (m == 0) return -1;
        int n = matrix[0].size();
        if (n == 0) return -1;

        int left = matrix[0][0]; 
        int right = matrix[m-1][n-1];

        while (left < right) {
            int mid = left + (right - left) / 2;

            int count = countSmallerNum(matrix, m, n, mid);
            if (count >= k) {
                right =  mid;
            } else {
                left = mid + 1;
            }
        }

        return left;
    }

private:
    int countSmallerNum(vector<vector<int>>& matrix, int m, int n, int num) {
        int row = m - 1;
        int col = 0;

        int count = 0;
        while (row >= 0 && col < n) {
            int product = matrix[row][col];
            if (product <= num) {
                count += row + 1;
                ++col;
            } else if (product > num) {
                --row;
            } 
        }

        return count;
    }
};