# Leetcode Search-A-2D-Matrix-II

2022-09-03 14:57

> ##### Algorithms:
> #algorithm #divide_and_conquer
> ##### Data structures:
> #DS #array 
> ##### Difficulty:
> #coding_problem #difficulty-medium
> ##### Additional tags:
> #leetcode 
> ##### Revisions:
> N/A

##### Links:
- [Link to problem](https://leetcode.com/problems/search-a-2d-matrix-ii/)
___
### Problem

Write an efficient algorithm that searches for a value `target` in an `m x n` integer matrix `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.

#### Examples

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/11/24/searchgrid2.jpg)

```
**Input:** 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]], target = 5
**Output:** true
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/11/24/searchgrid.jpg)

```
**Input:** 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]], target = 20
**Output:** false
```

#### Constraints

### Thoughts

> [!summary]
> This is a #divide_and_conquer problem.

It's divide and conquer, because every time we do a action, 
the problem is smaller.

Start from the top-right, (alternatively, bottom-left),
because walking left makes the number smaller, and down makes the number bigger.

### Solution