Maximum Cake Tastiness

题意翻译

给定一个长度为 $n$ 的数组 $a$，定义其权值为 $\max\limits_{1\leqslant i<n}{(a_i+a_{i+1})}$。 你可以选择数组中的任意一个子段并将其翻转，换句话说，你可以选择两个下标 $l,r(1\leqslant l\leqslant r\leqslant n)$，然后将数组变为 $a_1,a_2,\cdots,a_{l-1},\underline{a_r,a_{r-1},\cdots,a_l},a_{r+1},a_{r+2},\cdots,a_n$。 求在执行上述操作至多一次的情况下，数组 $a$ 的权值的最大值。 数据范围： - $t$ 组数据，$1\leqslant t\leqslant 50$。 - $2\leqslant n\leqslant 1000$。 - $1\leqslant a_i\leqslant 10^9$。 Translated by Eason_AC

题目描述

There are $ n $ pieces of cake on a line. The $ i $ -th piece of cake has weight $ a_i $ ( $ 1 \leq i \leq n $ ). The tastiness of the cake is the maximum total weight of two adjacent pieces of cake (i. e., $ \max(a_1+a_2,\, a_2+a_3,\, \ldots,\, a_{n-1} + a_{n}) $ ). You want to maximize the tastiness of the cake. You are allowed to do the following operation at most once (doing more operations would ruin the cake): - Choose a contiguous subsegment $ a[l, r] $ of pieces of cake ( $ 1 \leq l \leq r \leq n $ ), and reverse it. The subsegment $ a[l, r] $ of the array $ a $ is the sequence $ a_l, a_{l+1}, \dots, a_r $ . If you reverse it, the array will become $ a_1, a_2, \dots, a_{l-2}, a_{l-1}, \underline{a_r}, \underline{a_{r-1}}, \underline{\dots}, \underline{a_{l+1}}, \underline{a_l}, a_{r+1}, a_{r+2}, \dots, a_{n-1}, a_n $ . For example, if the weights are initially $ [5, 2, 1, 4, 7, 3] $ , you can reverse the subsegment $ a[2, 5] $ , getting $ [5, \underline{7}, \underline{4}, \underline{1}, \underline{2}, 3] $ . The tastiness of the cake is now $ 5 + 7 = 12 $ (while before the operation the tastiness was $ 4+7=11 $ ). Find the maximum tastiness of the cake after doing the operation at most once.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 50 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 2 \le n \le 1000 $ ) — the number of pieces of cake. The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 10^9 $ ) — $ a_i $ is the weight of the $ i $ -th piece of cake.

输出格式

For each test case, print a single integer: the maximum tastiness of the cake after doing the operation at most once.

输入输出样例

输入样例 #1

5
6
5 2 1 4 7 3
3
32 78 78
3
69 54 91
8
999021 999021 999021 999021 999652 999021 999021 999021
2
1000000000 1000000000

输出样例 #1

12
156
160
1998673
2000000000

说明

In the first test case, after reversing the subsegment $ a[2, 5] $ , you get a cake with weights $ [5, \underline{7}, \underline{4}, \underline{1}, \underline{2}, 3] $ . The tastiness of the cake is now $ \max(5+7, 7+4, 4+1, 1+2, 2+3) = 12 $ . This is the maximum possible tastiness of the cake one can obtain by performing the operation at most once. In the second test case, it's optimal not to do any operation. The tastiness is $ 78+78 = 156 $ . In the third test case, after reversing the subsegment $ a[1, 2] $ , you get a cake with weights $ [\underline{54}, \underline{69}, 91] $ . The tastiness of the cake is now $ \max(54+69, 69+91) = 160 $ . There is no way to make the tastiness of the cake greater than $ 160 $ by performing at most one operation.