A16344. Brukhovich and Exams
编程题
普及/提高-
知识点
题目描述
The boy Smilo is learning algorithms with a teacher named Brukhovich.
Over the course of the year, Brukhovich will administer $n$ exams. For each exam, its difficulty $a_i$ is known, which is a non-negative integer.
Smilo doesn't like when the greatest common divisor of the difficulties of two consecutive exams is equal to $1$ . Therefore, he considers the sadness of the academic year to be the number of such pairs of exams. More formally, the sadness is the number of indices $i$ ( $1 \leq i \leq n - 1$ ) such that $gcd(a_i, a_{i+1}) = 1$ , where $gcd(x, y)$ is the greatest common divisor of integers $x$ and $y$ .
Brukhovich wants to minimize the sadness of the year of Smilo. To do this, he can set the difficulty of any exam to $0$ . However, Brukhovich doesn't want to make his students' lives too easy. Therefore, he will perform this action no more than $k$ times.
Help Smilo determine the minimum sadness that Brukhovich can achieve if he performs no more than $k$ operations.
As a reminder, the greatest common divisor (GCD) of two non-negative integers $x$ and $y$ is the maximum integer that is a divisor of both $x$ and $y$ and is denoted as $gcd(x, y)$ . In particular, $gcd(x, 0) = gcd(0, x) = x$ for any non-negative integer $x$ .
Over the course of the year, Brukhovich will administer $n$ exams. For each exam, its difficulty $a_i$ is known, which is a non-negative integer.
Smilo doesn't like when the greatest common divisor of the difficulties of two consecutive exams is equal to $1$ . Therefore, he considers the sadness of the academic year to be the number of such pairs of exams. More formally, the sadness is the number of indices $i$ ( $1 \leq i \leq n - 1$ ) such that $gcd(a_i, a_{i+1}) = 1$ , where $gcd(x, y)$ is the greatest common divisor of integers $x$ and $y$ .
Brukhovich wants to minimize the sadness of the year of Smilo. To do this, he can set the difficulty of any exam to $0$ . However, Brukhovich doesn't want to make his students' lives too easy. Therefore, he will perform this action no more than $k$ times.
Help Smilo determine the minimum sadness that Brukhovich can achieve if he performs no more than $k$ operations.
As a reminder, the greatest common divisor (GCD) of two non-negative integers $x$ and $y$ is the maximum integer that is a divisor of both $x$ and $y$ and is denoted as $gcd(x, y)$ . In particular, $gcd(x, 0) = gcd(0, x) = x$ for any non-negative integer $x$ .
输入格式
The first line contains a single integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. The descriptions of the test cases follow.
The first line of each test case contains two integers $n$ and $k$ ( $1 \leq k \leq n \leq 10^5$ ) — the total number of exams and the maximum number of exams that can be simplified, respectively.
The second line of each test case contains $n$ integers $a_1, a_2, a_3, \ldots, a_n$ — the elements of array $a$ , which are the difficulties of the exams ( $0 \leq a_i \leq 10^9$ ).
It is guaranteed that the sum of $n$ across all test cases does not exceed $10^5$ .
The first line of each test case contains two integers $n$ and $k$ ( $1 \leq k \leq n \leq 10^5$ ) — the total number of exams and the maximum number of exams that can be simplified, respectively.
The second line of each test case contains $n$ integers $a_1, a_2, a_3, \ldots, a_n$ — the elements of array $a$ , which are the difficulties of the exams ( $0 \leq a_i \leq 10^9$ ).
It is guaranteed that the sum of $n$ across all test cases does not exceed $10^5$ .
输出格式
For each test case, output the minimum possible sadness that can be achieved by performing no more than $k$ operations.
输入输出样例
输入 #1
9 5 2 1 3 5 7 9 5 2 3 5 7 9 11 8 2 17 15 10 1 1 5 14 8 5 3 1 1 1 1 1 5 5 1 1 1 1 1 19 7 1 1 2 3 4 5 5 6 6 7 8 9 10 1 1 1 2 3 1 15 6 2 1 1 1 1 2 1 1 2 1 1 1 2 1 2 5 2 1 1 1 1 2 5 2 1 0 1 0 1
输出 #1
1 0 2 2 0 5 5 2 1
说明/提示
In the first test case, a sadness of $1$ can be achieved. To this, you can simplify the second and fourth exams. After this, there will be only one pair of adjacent exams with a greatest common divisor (GCD) equal to one, which is the first and second exams.
In the second test case, a sadness of $0$ can be achieved by simplifying the second and fourth exams.
In the second test case, a sadness of $0$ can be achieved by simplifying the second and fourth exams.