LeetCode 240. Search a 2D Matrix II

Description

https://leetcode.com/problems/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.

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.

Explanation

do binary searches on each row

Python Solution

class Solution:
    def searchMatrix(self, matrix, target):
        """
        :type matrix: List[List[int]]
        :type target: int
        :rtype: bool
        """
        if matrix == None or len(matrix) == 0 or len(matrix[0]) == 0:
            return False
        
        start = 0
        end = len(matrix[0])
        
        for i in range(0, len(matrix)):
            start = 0
            end = len(matrix[0]) - 1
            while start + 1 < end:
                mid = start + (end - start) // 2

                if matrix[i][mid] == target:
                    return True
                elif matrix[i][mid] > target:
                    end = mid
                else:
                    start = mid
            
            if matrix[i][start] == target or matrix[i][end] == target:
                return True
        
                
        return False
  • Time complexity: ~ Mlog(N)
  • Space complexity: ~1

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