> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/greedy/assign-mice-to-holes.md).

# Assign Mice to Holes

There are `N` Mice and `N` holes are placed in a straight line.\
Each hole can accomodate only 1 mouse.\
A mouse can stay at his position, move one step right from `x` to `x + 1`, or move one step left from `x` to `x − 1`. Any of these moves consumes 1 minute.\
Assign mice to holes so that the time when the last mouse gets inside a hole is minimized.

**Example:**

```
positions of mice are:
4 -4 2
positions of holes are:
4 0 5

Assign mouse at position x=4 to hole at position x=4 : Time taken is 0 minutes 
Assign mouse at position x=-4 to hole at position x=0 : Time taken is 4 minutes 
Assign mouse at position x=2 to hole at position x=5 : Time taken is 3 minutes 
After 4 minutes all of the mice are in the holes.

Since, there is no combination possible where the last mouse's time is less than 4, 
answer = 4.
```

**Input:**

```
A :  list of positions of mice
B :  list of positions of holes
```

**Output:**

```
single integer value
```

> **NOTE:** The final answer will fit in a 32 bit signed integer.

```java
public class Solution {
    public int mice(int[] A, int[] B) {
        Arrays.sort(A);
        Arrays.sort(B);
        int ans = Integer.MIN_VALUE;
        for (int i = 0; i < A.length; i++)
            ans = Math.max(ans, Math.abs(A[i] - B[i]));
        return ans;
    }
}
```