A15459. Bestie
编程题
普及/提高-
知识点
题目描述
You are given an array $a$ consisting of $n$ integers $a_1, a_2, \ldots, a_n$ . Friends asked you to make the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of all numbers in the array equal to $1$ . In one operation, you can do the following:
- Select an arbitrary index in the array $1 \leq i \leq n$ ;
- Make $a_i = \gcd(a_i, i)$ , where $\gcd(x, y)$ denotes the GCD of integers $x$ and $y$ . The cost of such an operation is $n - i + 1$ .
You need to find the minimum total cost of operations we need to perform so that the GCD of the all array numbers becomes equal to $1$ .
- Select an arbitrary index in the array $1 \leq i \leq n$ ;
- Make $a_i = \gcd(a_i, i)$ , where $\gcd(x, y)$ denotes the GCD of integers $x$ and $y$ . The cost of such an operation is $n - i + 1$ .
You need to find the minimum total cost of operations we need to perform so that the GCD of the all array numbers becomes equal to $1$ .
输入格式
Each test consists of multiple test cases. The first line contains an integer $t$ ( $1 \leq t \leq 5\,000$ ) — the number of test cases. The description of test cases follows.
The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 20$ ) — the length of the array.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 10^9$ ) — the elements of the array.
The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 20$ ) — the length of the array.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 10^9$ ) — the elements of the array.
输出格式
For each test case, output a single integer — the minimum total cost of operations that will need to be performed so that the GCD of all numbers in the array becomes equal to $1$ .
We can show that it's always possible to do so.
We can show that it's always possible to do so.
输入输出样例
输入 #1
9 1 1 1 2 2 2 4 3 3 6 9 4 5 10 15 20 5 120 60 80 40 80 6 150 90 180 120 60 30 6 2 4 6 9 12 18 6 30 60 90 120 125 125
输出 #1
0 1 2 2 1 3 3 0 1
说明/提示
In the first test case, the GCD of the entire array is already equal to $1$ , so there is no need to perform operations.
In the second test case, select $i = 1$ . After this operation, $a_1 = \gcd(2, 1) = 1$ . The cost of this operation is $1$ .
In the third test case, you can select $i = 1$ , after that the array $a$ will be equal to $[1, 4]$ . The GCD of this array is $1$ , and the total cost is $2$ .
In the fourth test case, you can select $i = 2$ , after that the array $a$ will be equal to $[3, 2, 9]$ . The GCD of this array is $1$ , and the total cost is $2$ .
In the sixth test case, you can select $i = 4$ and $i = 5$ , after that the array $a$ will be equal to $[120, 60, 80, 4, 5]$ . The GCD of this array is $1$ , and the total cost is $3$ .
In the second test case, select $i = 1$ . After this operation, $a_1 = \gcd(2, 1) = 1$ . The cost of this operation is $1$ .
In the third test case, you can select $i = 1$ , after that the array $a$ will be equal to $[1, 4]$ . The GCD of this array is $1$ , and the total cost is $2$ .
In the fourth test case, you can select $i = 2$ , after that the array $a$ will be equal to $[3, 2, 9]$ . The GCD of this array is $1$ , and the total cost is $2$ .
In the sixth test case, you can select $i = 4$ and $i = 5$ , after that the array $a$ will be equal to $[120, 60, 80, 4, 5]$ . The GCD of this array is $1$ , and the total cost is $3$ .