1. 题目

给你两个长度相等的整数数组，返回下面表达式的最大值：

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

其中下标 i，j 满足 0 <= i, j < arr1.length。

示例 1：
输入：arr1 = [1,2,3,4], arr2 = [-1,4,5,6]
输出：13示例 2：
输入：arr1 = [1,-2,-5,0,10], arr2 = [0,-2,-1,-7,-4]
输出：20提示：
2 <= arr1.length == arr2.length <= 40000
-10^6 <= arr1[i], arr2[i] <= 10^6

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/maximum-of-absolute-value-expression
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

2. 解题

只有这8种可能
$$\begin{gathered} arr1[i]-arr1[j]+arr2[i]-arr2[j]+i-j; \\ -arr1[i]+arr1[j]-arr2[i]+arr2[j]-i+j; \\ -arr1[i]+arr1[j]+arr2[i]-arr2[j]+i-j; \\ arr1[i]-arr1[j]-arr2[i]+arr2[j]+i-j; \\ arr1[i]-arr1[j]+arr2[i]-arr2[j]-i+j; \\ -arr1[i]+arr1[j]-arr2[i]+arr2[j]+i-j; \\ arr1[i]-arr1[j]-arr2[i]+arr2[j]-i+j; \\ -arr1[i]+arr1[j]+arr2[i]-arr2[j]-i+j; \end{gathered}$$

把 j 拿走
$$\begin{gathered} arr1[i]+arr2[i]+i; \\ -arr1[i]-arr2[i]-i; \\ -arr1[i]+arr2[i]+i; \\ arr1[i]-arr2[i]+i; \\ arr1[i]+arr2[i]-i; \\ -arr1[i]-arr2[i]+i; \\ arr1[i]-arr2[i]-i; \\ -arr1[i]+arr2[i]-i; \end{gathered}$$
发现只有4种情况
$$\begin{gathered} arr1[i]+arr2[i]+iasA; \\ -arr1[i]-arr2[i]-ias-A; \\ -arr1[i]+arr2[i]+iasB; \\ arr1[i]-arr2[i]+iasC; \\ arr1[i]+arr2[i]-iasD; \\ -arr1[i]-arr2[i]+ias-D; \\ arr1[i]-arr2[i]-ias-B; \\ -arr1[i]+arr2[i]-ias-C; \end{gathered}$$
只需要取出ABCD，求其最大最小值，做差

class Solution {
public:int maxAbsValExpr(vector<int>& arr1, vector<int>& arr2) {int min1 = INT_MAX, min2 = INT_MAX, min3 = INT_MAX, min4 = INT_MAX;int max1 = INT_MIN, max2 = INT_MIN, max3 = INT_MIN, max4 = INT_MIN;for(int i = 0; i < arr1.size(); ++i){max1 = max(max1, arr1[i] + arr2[i] + i);max2 = max(max2,-arr1[i] + arr2[i] + i);max3 = max(max3, arr1[i] - arr2[i] + i);max4 = max(max4, arr1[i] + arr2[i] - i);min1 = min(min1, arr1[i] + arr2[i] + i);min2 = min(min2,-arr1[i] + arr2[i] + i);min3 = min(min3, arr1[i] - arr2[i] + i);min4 = min(min4, arr1[i] + arr2[i] - i);}return max(max(max1-min1, max2-min2),max(max3-min3, max4-min4));}
};

100 ms 23.2 MB

---

我的CSDN博客地址 https://michael.blog.csdn.net/

长按或扫码关注我的公众号（Michael阿明），一起加油、一起学习进步！