Kth Smallest Number In Sorted Matrix(Binary Search)

Given a matrix of size N x M. For each row the elements are sorted in ascending order, and for each column the elements are also sorted in ascending order. Find the Kth smallest number in it.

Assumptions:

the matrix is not null, N > 0 and M > 0
K > 0 and K <= N * M

Examples:

{ {1, 3, 5, 7},

{2, 4, 8, 9},

{3, 5, 11, 15},

{6, 8, 13, 18} }

the 5th smallest number is 4
the 8th smallest number is 6

class Solution(object):
  def kthSmallest(self, matrix, k):
    n = len(matrix)
    m = len(matrix[0])
    min = matrix[0][0]
    max = matrix[n-1][m-1]
    mid = 0
    count = 0
    while min < max:
      mid = (min + max)/2
      for i in xrange(0,n):
        for j in xrange(0,m):
          if matrix[i][j] <= mid:
            count += 1
      if k <= count:
        max = mid
      else:
        min = mid + 1
      count = 0
    return min