P17444 Range Spread Array Operations / Range Minimization

The **range spread** of an array is defined as the difference between its maximum element and its minimum element. Given an integer array $a$ of length $n$, you may perform the following operation any number of times (including zero times): - Choose two different indices $i, j$ ($1 \le i, j \le n$ and $i \ne j$), then update: $$ a_i \leftarrow a_i + 3,\qquad a_j \leftarrow a_j - 1. $$ Compute the minimum possible range spread of array $a$ after performing some operations.

This problem contains multiple testcases. The first line contains an integer $T$ ($1 \le T \le 10^4$), the number of testcases. For each testcase: - The first line contains an integer $n$ ($1 \le n \le 2 \times 10^5$), the length of array $a$. - The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($-10^9 \le a_i \le 10^9$), the elements of array $a$. It is guaranteed that the sum of $n$ over all testcases does not exceed $2 \times 10^5$.

For each testcase, output one integer per line, the minimum range spread that can be achieved after any finite number of operations.

In the first testcase, there is only one element, so the range spread is always $0$. Translated by ChatGPT 5