> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Search a 2D Matrix Python Solution with Tests

> Tested Python solution for LeetCode 74 with 16 pytest cases. Generate a practice environment with lcpy.

LeetCode 74, Medium. Topics: Array, Binary Search, Matrix. [View on LeetCode](https://leetcode.com/problems/search-a-2d-matrix/description/).

Generate this problem as a practice environment: tested reference solution, 16 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 74   # by problem number
lcpy gen -s search_a_2d_matrix   # by problem name
```

## Problem

You are given an `m x n` integer matrix `matrix` with the following two properties:

* Each row is sorted in non-decreasing order.
* The first integer of each row is greater than the last integer of the previous row.

Given an integer `target`, return `true` *if* `target` *is in* `matrix` *or* `false` *otherwise*.

You must write a solution in `O(log(m * n))` time complexity.

### Examples

![Example 1](https://assets.leetcode.com/uploads/2020/10/05/mat.jpg)

```
Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 3
Output: true
```

![Example 2](https://assets.leetcode.com/uploads/2020/10/05/mat2.jpg)

```
Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13
Output: false
```

### Constraints

* m == matrix.length
* n == matrix\[i].length
* 1 \<= m, n \<= 100
* -10^4 \<= matrix\[i]\[j], target \<= 10^4

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/search_a_2d_matrix/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/search_a_2d_matrix/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(log(m * n))
    # Space: O(1)
    def search_matrix(self, matrix: list[list[int]], target: int) -> bool:
        rows, cols = len(matrix), len(matrix[0])
        lo, hi = 0, rows * cols - 1
        while lo <= hi:
            mid = (lo + hi) // 2
            value = matrix[mid // cols][mid % cols]
            if value == target:
                return True
            if value < target:
                lo = mid + 1
            else:
                hi = mid - 1
        return False
```

## Complexity

| Time           | Space |
| -------------- | ----- |
| O(log(m \* n)) | O(1)  |

## Tags

[Grind](/catalog/grind), [NeetCode 150](/catalog/neetcode-150), [NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode).