378. Kth Smallest Element in a Sorted Matrix

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.

Approach #1: restore the matrix into a one-deminsional array, then sort

class Solution {
public:
    int kthSmallest(vector<vector<int>>& matrix, int k) {
        vector<int> s;
        int row = matrix.size();
        int col = matrix[0].size();
        for (int i = 0; i < row; ++i) {
            for (int j = 0; j < col; ++j) {
                s.push_back(matrix[i][j]);
            }
        }
        sort(s.begin(), s.end());
        return s[k-1];
    }
};

85 / 85 test cases passed.	Status:  Accepted
Runtime: 32 ms	Submitted: 1 hour, 59 minutes ago

Approach #2: Using Bianry Search in two-deminsional array.

class Solution {
public:
    int kthSmallest(vector<vector<int>>& matrix, int k) {
        int row = matrix.size();
        int col = matrix[0].size();
        int l = matrix[0][0];
        int r = matrix[row-1][col-1];
        while (l < r) {
            int m = l + (r - l) / 2;
            int num = 0;
            for (int i = 0; i < row; ++i) {
                int pos = upper_bound(matrix[i].begin(), matrix[i].end(), m) - matrix[i].begin();
                num += pos;
            }
            if (num < k) l = m + 1;
            else r = m;
        }
        return l;
    }
};

Runtime: 36 ms, faster than 44.09% of C++ online submissions for Kth Smallest Element in a Sorted Matrix.