# 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:
return False

start = 0
end = len(matrix)

for i in range(0, len(matrix)):
start = 0
end = len(matrix) - 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