## Algorithm

Problem Name: 1131. Maximum of Absolute Value Expression

Given two arrays of integers with equal lengths, return the maximum value of:

`|arr1[i] - arr1[j]| + |arr2[i] - arr2[j]| + |i - j|`

where the maximum is taken over all `0 <= i, j < arr1.length`.

Example 1:

```Input: arr1 = [1,2,3,4], arr2 = [-1,4,5,6]
Output: 13
```

Example 2:

```Input: arr1 = [1,-2,-5,0,10], arr2 = [0,-2,-1,-7,-4]
Output: 20
```

Constraints:

• `2 <= arr1.length == arr2.length <= 40000`
• `-10^6 <= arr1[i], arr2[i] <= 10^6`

## Code Examples

### #1 Code Example with Java Programming

```Code - Java Programming```

``````
class Solution {
public int maxAbsValExpr(int[] arr1, int[] arr2) {
int res = 0;
int n = arr1.length;
int[] dirs = {-1,1};
for (int dir1 : dirs) {
for (int dir2 : dirs) {
int closest = dir1 * arr1[0] + dir2 * arr2[0] + 0;
for (int i = 1; i  <  n; ++i) {
int cur = dir1 * arr1[i] + dir2 * arr2[i] + i;
res = Math.max(res, cur - closest);
closest = Math.min(closest, cur);
}
}
}
return res;
}
}
``````
Copy The Code &

Input

cmd
arr1 = [1,2,3,4], arr2 = [-1,4,5,6]

Output

cmd
13

### #2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def maxAbsValExpr(self, arr1: List[int], arr2: List[int]) -> int:
l1, l2 ,l3, l4 = [], [], [], []
for i in range(len(arr1)):
l1 += [arr1[i]+arr2[i]+i]
l2 += [arr1[i]-arr2[i]+i]
l3 += [-arr1[i]+arr2[i]+i]
l4 += [-arr1[i]-arr2[i]+i]
res = []
res += [max(l1)-min(l1)]
res += [max(l2) -min(l2)]
res += [max(l3)-min(l3)]
res += [max(l4)-min(l4)]
return max(res)
``````
Copy The Code &

Input

cmd
arr1 = [1,2,3,4], arr2 = [-1,4,5,6]

Output

cmd
13