A16015. Tenzing and Necklace
编程题
普及/提高-
知识点
题目描述
bright, sunny and innocent......
Tenzing has a beautiful necklace. The necklace consists of $n$ pearls numbered from $1$ to $n$ with a string connecting pearls $i$ and $(i \text{ mod } n)+1$ for all $1 \leq i \leq n$ .
One day Tenzing wants to cut the necklace into several parts by cutting some strings. But for each connected part of the necklace, there should not be more than $k$ pearls. The time needed to cut each string may not be the same. Tenzing needs to spend $a_i$ minutes cutting the string between pearls $i$ and $(i \text{ mod } n)+1$ .
Tenzing wants to know the minimum time in minutes to cut the necklace such that each connected part will not have more than $k$ pearls.
Tenzing has a beautiful necklace. The necklace consists of $n$ pearls numbered from $1$ to $n$ with a string connecting pearls $i$ and $(i \text{ mod } n)+1$ for all $1 \leq i \leq n$ .
One day Tenzing wants to cut the necklace into several parts by cutting some strings. But for each connected part of the necklace, there should not be more than $k$ pearls. The time needed to cut each string may not be the same. Tenzing needs to spend $a_i$ minutes cutting the string between pearls $i$ and $(i \text{ mod } n)+1$ .
Tenzing wants to know the minimum time in minutes to cut the necklace such that each connected part will not have more than $k$ pearls.
输入格式
Each test contains multiple test cases. The first line of input contains a single integer $t$ ( $1 \le t \le 10^5$ ) — the number of test cases. The description of test cases follows.
The first line of each test case contains two integers $n$ and $k$ ( $2\leq n\leq 5\cdot 10^5$ , $1\leq k <n$ ).
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $1\leq a_i\leq 10^9$ ).
It is guaranteed that the sum of $n$ of all test cases does not exceed $5 \cdot 10^5$ .
The first line of each test case contains two integers $n$ and $k$ ( $2\leq n\leq 5\cdot 10^5$ , $1\leq k <n$ ).
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $1\leq a_i\leq 10^9$ ).
It is guaranteed that the sum of $n$ of all test cases does not exceed $5 \cdot 10^5$ .
输出格式
For each test case, output the minimum total time in minutes required.
输入输出样例
输入 #1
4 5 2 1 1 1 1 1 5 2 1 2 3 4 5 6 3 4 2 5 1 3 3 10 3 2 5 6 5 2 1 7 9 7 2
输出 #1
3 7 5 15
说明/提示
In the first test case, the necklace will be cut into $3$ parts: $[1,2][3,4][5]$ , so the total time is $3$ .
In the second test case, the necklace will be cut into $3$ parts: $[5,1][2][3,4]$ , Tenzing will cut the strings connecting $(1,2), (2,3)$ and $(4,5)$ , so the total time is $a_1+a_2+a_4=7$ .
In the second test case, the necklace will be cut into $3$ parts: $[5,1][2][3,4]$ , Tenzing will cut the strings connecting $(1,2), (2,3)$ and $(4,5)$ , so the total time is $a_1+a_2+a_4=7$ .