240. Search a 2D Matrix II

https://leetcode.com/problems/search-a-2d-matrix-ii/#/description

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.

 

 

Sol :

 

class Solution(object):
    def searchMatrix(self, matrix, target):
        """
        :type matrix: List[List[int]]
        :type target: int
        :rtype: bool
        """
        
        # exclusive method
        # Time O(M+N) Space O(1)
        
        
        # Compare the target with the top right corner element of the martix. If target < right corner, search target on area with smaller values, i.e. go leftwards; if target > right corner, search target on area with bigger values, i.e. go downwards.
        
        if len(matrix) == 0 or len(matrix[0]) == 0:
            return False
        
        # start from the top right corner, and compare matrix[i][j] with target
        i = 0
        j = len(matrix[0]) - 1
        while i< len(matrix) and j >= 0:
            x = matrix[i][j]
            if target == x:
                return True
            elif x < target:
                # search target on the lower side
                i += 1
            else:
                # search target on the left side
                j -= 1
                
        return False