Median in a row-wise sorted Matrix.cpp

/*
Median in a row-wise sorted Matrix
====================================

Given a row wise sorted matrix of size RxC where R and C are always odd, find the median of the matrix.

Example 1:
Input:
R = 3, C = 3
M = [[1, 3, 5], 
     [2, 6, 9], 
     [3, 6, 9]]

Output: 5
Explanation:
Sorting matrix elements gives us 
{1,2,3,3,5,6,6,9,9}. Hence, 5 is median. 

Example 2:
Input:
R = 3, C = 1
M = [[1], [2], [3]]
Output: 2
Your Task:  
You don't need to read input or print anything. Your task is to complete the function median() which takes the integers R and C along with the 2D matrix as input parameters and returns the median of the matrix.

Expected Time Complexity: O(32 * R * log(C))
Expected Auxiliary Space: O(1)

Constraints:
1<= R,C <=150
1<= matrix[i][j] <=1000
*/

int median(vector<vector<int>> &m, int r, int c)
{
  int min = INT_MAX, max = INT_MIN;
  for (int i = 0; i < r; i++)
  {
    if (m[i][0] < min)
      min = m[i][0];
    if (m[i][c - 1] > max)
      max = m[i][c - 1];
  }

  int desired = (r * c + 1) / 2;
  while (min < max)
  {
    int mid = min + (max - min) / 2;
    int place = 0;

    for (int i = 0; i < r; ++i)
    {
      place += upper_bound(m[i].begin(), m[i].end(), mid) - m[i].begin();
    }
    if (place < desired)
      min = mid + 1;
    else
      max = mid;
  }
  return min;
}