Write an efficient algorithm that searches for a target value in an m x n integer matrix. The 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 1:**

**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:**

**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:**

m == matrix.length

n == matrix[i].length

1 <= n, m <= 300

-109 <= matix[i][j] <= 109

All the integers in each row are

**sorted**in ascending order.All the integers in each column are

**sorted**in ascending order.-109 <= target <= 109

**Solution:**

**Iterative:**

```
class Solution {
public boolean searchMatrix(int[][] matrix, int target) {
int i=matrix.length-1,j=0;
while(i>=0 && j<=matrix[0].length-1)
{
if(matrix[i][j]==target) return true;
else
{
if(matrix[i][j]>target) i--;
else
j++;
}
}
return false;
}
}
```

**Recursive:**

```
class Solution {
public boolean searchMatrix(int[][] matrix, int target) {
return helper(matrix,target,matrix.length-1,0);
}
public boolean helper(int[][] matrix,int target,int i,int j)
{
if(i<0 || j<0 || i>matrix.length-1 || j>matrix[0].length-1) return false;
if(matrix[i][j]==target) return true;
return (matrix[i][j]>target)? helper(matrix,target,i-1,j):helper(matrix,target,i,j+1);
}
}
```

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