# 240. Search a 2D Matrix II (Medium)

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`.

## Solutions

``````class Solution {

// It is not recommended to adopt naive binary search since the time complexity will be n*log(n) whether you search
// horizontally or vertically.

// If we stand on the top-right corner of the matrix and look diagonally, it's kind of like a
// BST, we can go through this matrix to find the target like how we traverse the BST. The computation time
// scale will be decreased to O(n + m)

public boolean searchMatrix(int[][] matrix, int target) {
if (matrix == null || matrix.length == 0 || matrix[0].length == 0)
return false;

int n = matrix.length, m = matrix[0].length;
int i = 0, j = m - 1;

while (i < n && j >= 0) {
if (matrix[i][j] == target) {
return true;
}

if (matrix[i][j] > target) {
j--;
} else {
i++;
}
}

return false;
}
}
``````