A15029. Optimal Partition
编程题
普及/提高-
知识点
题目描述
You are given an array $a$ consisting of $n$ integers. You should divide $a$ into continuous non-empty subarrays (there are $2^{n-1}$ ways to do that).
Let $s=a_l+a_{l+1}+\ldots+a_r$ . The value of a subarray $a_l, a_{l+1}, \ldots, a_r$ is:
- $(r-l+1)$ if $s>0$ ,
- $0$ if $s=0$ ,
- $-(r-l+1)$ if $s<0$ .
What is the maximum sum of values you can get with a partition?
Let $s=a_l+a_{l+1}+\ldots+a_r$ . The value of a subarray $a_l, a_{l+1}, \ldots, a_r$ is:
- $(r-l+1)$ if $s>0$ ,
- $0$ if $s=0$ ,
- $-(r-l+1)$ if $s<0$ .
What is the maximum sum of values you can get with a partition?
输入格式
The input consists of multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 5 \cdot 10^5$ ) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $n$ ( $1 \le n \le 5 \cdot 10^5$ ).
The second line of each test case contains $n$ integers $a_1$ , $a_2$ , ..., $a_n$ ( $-10^9 \le a_i \le 10^9$ ).
It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^5$ .
The first line of each test case contains a single integer $n$ ( $1 \le n \le 5 \cdot 10^5$ ).
The second line of each test case contains $n$ integers $a_1$ , $a_2$ , ..., $a_n$ ( $-10^9 \le a_i \le 10^9$ ).
It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^5$ .
输出格式
For each test case print a single integer — the maximum sum of values you can get with an optimal parition.
输入输出样例
输入 #1
5 3 1 2 -3 4 0 -2 3 -4 5 -1 -2 3 -1 -1 6 -1 2 -3 4 -5 6 7 1 -1 -1 1 -1 -1 1
输出 #1
1 2 1 6 -1
说明/提示
Test case $1$ : one optimal partition is $[1, 2]$ , $[-3]$ . $1+2>0$ so the value of $[1, 2]$ is $2$ . $-3<0$ , so the value of $[-3]$ is $-1$ . $2+(-1)=1$ .
Test case $2$ : the optimal partition is $[0, -2, 3]$ , $[-4]$ , and the sum of values is $3+(-1)=2$ .
Test case $2$ : the optimal partition is $[0, -2, 3]$ , $[-4]$ , and the sum of values is $3+(-1)=2$ .