CF1579G.Minimal Coverage

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

You are given $n$ lengths of segments that need to be placed on an infinite axis with coordinates.

The first segment is placed on the axis so that one of its endpoints lies at the point with coordinate $0$ . Let's call this endpoint the "start" of the first segment and let's call its "end" as that endpoint that is not the start.

The "start" of each following segment must coincide with the "end" of the previous one. Thus, if the length of the next segment is $d$ and the "end" of the previous one has the coordinate $x$ , the segment can be placed either on the coordinates $[x-d, x]$ , and then the coordinate of its "end" is $x - d$ , or on the coordinates $[x, x+d]$ , in which case its "end" coordinate is $x + d$ .

The total coverage of the axis by these segments is defined as their overall union which is basically the set of points covered by at least one of the segments. It's easy to show that the coverage will also be a segment on the axis. Determine the minimal possible length of the coverage that can be obtained by placing all the segments on the axis without changing their order.

输入格式

The first line contains an integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases.

The next $2t$ lines contain descriptions of the test cases.

The first line of each test case description contains an integer $n$ ( $1 \le n \le 10^4$ ) — the number of segments. The second line of the description contains $n$ space-separated integers $a_i$ ( $1 \le a_i \le 1000$ ) — lengths of the segments in the same order they should be placed on the axis.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^4$ .

输出格式

Print $t$ lines, each line containing the answer to the corresponding test case. The answer to a test case should be a single integer — the minimal possible length of the axis coverage.

输入输出样例

输入#1

6
2
1 3
3
1 2 3
4
6 2 3 9
4
6 8 4 5
7
1 2 4 6 7 7 3
8
8 6 5 1 2 2 3 6

输出#1

说明/提示

In the third sample test case the segments should be arranged as follows: $[0, 6] \rightarrow [4, 6] \rightarrow [4, 7] \rightarrow [-2, 7]$ . As you can see, the last segment $[-2, 7]$ covers all the previous ones, and the total length of coverage is $9$ .

In the fourth sample test case the segments should be arranged as $[0, 6] \rightarrow [-2, 6] \rightarrow [-2, 2] \rightarrow [2, 7]$ . The union of these segments also occupies the area $[-2, 7]$ and has the length of $9$ .

首页