> For the complete documentation index, see [llms.txt](https://blog.bernardw.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://blog.bernardw.com/problems/search-a-2d-matrix.md).

# Search a 2D Matrix

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 from left to right.
* The first integer of each row is greater than the last integer of the previous row.

For example, Consider the following matrix:

> ```
> [ [1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 50] ]
> ```

```
Given 
> target = 3

return 
> true
```

{% tabs %}
{% tab title="Scala" %}

```scala
def searchMatrix(matrix: Array[Array[Int]], target: Int): Boolean = {
  if (matrix.isEmpty) false
  else {
    val (m, n) = (matrix.length, matrix(0).length)
    val length = m * n
    def find(start: Int, end: Int): Boolean = {
      if (end < start) false
      else {
        val mid = (start + end) / 2
        matrix(mid / n)(mid % n) match {
          case num if num == target => true
          case num if num < target => find(mid + 1, end)
          case num if num > target => find(start, mid - 1)
        }
      }
    }
    find(0, length - 1)
  }
}

val mat = Array(
  Array(1, 3, 5, 7),
  Array(10, 11, 16, 20),
  Array(23, 30, 34, 50)
)

searchMatrix(mat, 11)
searchMatrix(mat, 99)
```

{% endtab %}

{% tab title="Second Tab" %}

{% endtab %}
{% endtabs %}