A15116. Everything Everywhere All But One
编程题
普及/提高-
知识点
题目描述
You are given an array of $n$ integers $a_1, a_2, \ldots, a_n$ . After you watched the amazing film "Everything Everywhere All At Once", you came up with the following operation.
In one operation, you choose $n-1$ elements of the array and replace each of them with their arithmetic mean (which doesn't have to be an integer). For example, from the array $[1, 2, 3, 1]$ we can get the array $[2, 2, 2, 1]$ , if we choose the first three elements, or we can get the array $[\frac{4}{3}, \frac{4}{3}, 3, \frac{4}{3}]$ , if we choose all elements except the third.
Is it possible to make all elements of the array equal by performing a finite number of such operations?
In one operation, you choose $n-1$ elements of the array and replace each of them with their arithmetic mean (which doesn't have to be an integer). For example, from the array $[1, 2, 3, 1]$ we can get the array $[2, 2, 2, 1]$ , if we choose the first three elements, or we can get the array $[\frac{4}{3}, \frac{4}{3}, 3, \frac{4}{3}]$ , if we choose all elements except the third.
Is it possible to make all elements of the array equal by performing a finite number of such operations?
输入格式
The first line of the input contains a single integer $t$ ( $1 \le t \le 200$ ) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $n$ ( $3 \le n \le 50$ ) — the number of integers.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \le a_i \le 100$ ).
The first line of each test case contains a single integer $n$ ( $3 \le n \le 50$ ) — the number of integers.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \le a_i \le 100$ ).
输出格式
For each test case, if it is possible to make all elements equal after some number of operations, output $\texttt{YES}$ . Otherwise, output $\texttt{NO}$ .
You can output $\texttt{YES}$ and $\texttt{NO}$ in any case (for example, strings $\texttt{yEs}$ , $\texttt{yes}$ , $\texttt{Yes}$ will be recognized as a positive response).
You can output $\texttt{YES}$ and $\texttt{NO}$ in any case (for example, strings $\texttt{yEs}$ , $\texttt{yes}$ , $\texttt{Yes}$ will be recognized as a positive response).
输入输出样例
输入 #1
4 3 42 42 42 5 1 2 3 4 5 4 4 3 2 1 3 24 2 22
输出 #1
YES YES NO NO
说明/提示
In the first test case, all elements are already equal.
In the second test case, you can choose all elements except the third, their average is $\frac{1 + 2 + 4 + 5}{4} = 3$ , so the array will become $[3, 3, 3, 3, 3]$ .
It's possible to show that it's impossible to make all elements equal in the third and fourth test cases.
In the second test case, you can choose all elements except the third, their average is $\frac{1 + 2 + 4 + 5}{4} = 3$ , so the array will become $[3, 3, 3, 3, 3]$ .
It's possible to show that it's impossible to make all elements equal in the third and fourth test cases.