[Solution] Yet Another Palindrome Problem CodeChef Solution

Problem

Chef has an array $A$ of size $N$. He can perform the following operation on $A$:

• Select an $i$ $(1 \le i \le N)$ and for all $1 \le j \le i$, set $A_j := A_j + 1$ (i.e. add $1$ to every element in the prefix of length $i$).

Chef wants to convert $A$ to a palindrome by using the above operation minimum number of times. Can you help Chef?
If it is not possible to convert $A$ to a palindrome, output $-1$.

Note: An array is called palindrome if it reads the same backwards and forwards, for e.g. $[1, 4, 1]$ and $[7, 3, 3, 7]$ are palindromic arrays.

Input Format

• The first line contains a single integer $T$ — the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer $N$ — the size of the array $A$.
• The second line of each test case contains $N$ space-separated integers $A_1, A_2, \dots, A_N$ denoting the array $A$.

Output Format

For each test case, output the minimum number of operations required to convert $A$ to a palindromic array.

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If it is not possible to do so, output $-1$.

Explanation:

Test case $1$: The given array is already a palindrome.

Test case $2$: It can be proven that it is not possible to convert $A$ to a palindromic array using the given operation.

Test case $3$: We can perform the following operations:

• Select $i = 1$, $[1, 2, 3, 4] \rightarrow [2, 2, 3, 4]$
• Select $i = 2$, $[2, 2, 3, 4] \rightarrow [3, 3, 3, 4]$
• Select $i = 1$, $[3, 3, 3, 4] \rightarrow [4, 3, 3, 4]$