Maximum of Absolute Value Expression
<p>Given two arrays of integers with equal lengths, return the maximum value of:</p>

<p><code>|arr1[i] - arr1[j]| + |arr2[i] - arr2[j]| + |i - j|</code></p>

<p>where the maximum is taken over all <code>0 &lt;= i, j &lt; arr1.length</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,2,3,4], arr2 = [-1,4,5,6]
<strong>Output:</strong> 13
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,-2,-5,0,10], arr2 = [0,-2,-1,-7,-4]
<strong>Output:</strong> 20
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= arr1.length == arr2.length &lt;= 40000</code></li>
	<li><code>-10^6 &lt;= arr1[i], arr2[i] &lt;= 10^6</code></li>
</ul>
Array; Math
class Solution {
    public int maxAbsValExpr(int[] arr1, int[] arr2) {
        int[] dirs = {1, -1, -1, 1, 1};
        final int inf = 1 << 30;
        int ans = -inf;
        int n = arr1.length;
        for (int k = 0; k < 4; ++k) {
            int a = dirs[k], b = dirs[k + 1];
            int mx = -inf, mi = inf;
            for (int i = 0; i < n; ++i) {
                mx = Math.max(mx, a * arr1[i] + b * arr2[i] + i);
                mi = Math.min(mi, a * arr1[i] + b * arr2[i] + i);
                ans = Math.max(ans, mx - mi);
            }
        }
        return ans;
    }
}