[Leetcode] Binary search, Divide and conquer--240. Search a 2D Matrix II

Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:

• Integers in each row are sorted in ascending from left to right.
• Integers in each column are sorted in ascending from top to bottom.

For example,

Consider the following matrix:

[
  [1,   4,  7, 11, 15],
  [2,   5,  8, 12, 19],
  [3,   6,  9, 16, 22],
  [10, 13, 14, 17, 24],
  [18, 21, 23, 26, 30]
]

Given target = 5, return true.

Given target = 20, return false.

Solution:

  1. 1st idea use one binary search

   iterate every rows , binary search from row i to find the insertion position p (bisect_right)

   m = len(matrix), n = len(matrix[0]) time complexity O(m*logn)

 if len(matrix) == 0 or len(matrix[0]) == 0:
            return False
        i = 0
        while (i < len(matrix)):
            pos = bisect_right(matrix[i], target)            #use binary search
            #print(" aaas: ",i, pos-1)
            if matrix[i][pos-1] == target:
                return True
            i += 1
        return False

2. 2nd utilize the ordered row and column,  start from bottom left value v, if v is bigger than target, then go the upper column, else go the right row. time complexity o(m+n)

 

if len(matrix) == 0 or len(matrix[0]) == 0:
            return False
        m = len(matrix)
        n = len(matrix[0])
        i = m-1             #row
        j = 0           #column
        while ( i >= 0 and j <= n-1):
            if matrix[i][j] == target:
                return True
            elif matrix[i][j] > target:
                i -= 1
            else:
                j += 1
        return False

3. we can also use divide and conquer:

   reference:

 http://www.geeksforgeeks.org/divide-conquer-set-6-search-row-wise-column-wise-sorted-2d-array/