Palindromic Array Transformation
An array is called palindromic if it remains the same after reversing the order of its elements.
You have an array of strings arr. For each i, arr[i] consists of at least two characters. For each pair of consecutive elements arr[i] and arr[i + 1], you can:
Move the rightmost character of arr[i] to the leftmost position in arr[i + 1]. For instance, “abc” and “def” will become “ab” and “cdef”. This operation can be applied only once to any pair of consecutive elements.
Move the leftmost character of arr[i + 1] to the rightmost position in arr[i]. For instance, “abc” and “def” will become “abcd” and “ef”. Again, this operation can be applied only once to any pair of consecutive elements.
Do nothing to the pair of consecutive elements. Is it possible to obtain a palindromic array from arr by performing these operations?
Example
For arr = [“aa”, “bab”, “cde”, “aba”, “ab”], the output should be solution(arr) = true.
Apply the second operation to “aa” and “bab”. Apply the first operation to “aba” and “ab”. This gives us the following array: [“aab”, “ab”, “cde”, “ab”, “aab”], which is palindromic.
For arr = [“palindrome”], the output should be solution(arr) = true.
The given array is already palindromic, so no operations are needed.
For arr = [“aaaaaa”, “aa”], the output should be solution(arr) = false.
If moving two characters between two consecutive array elements was allowed, the array could have been made palindromic, but this is impossible given the actual rules.
Input/Output
[execution time limit] 3 seconds (java)
[memory limit] 1 GB
[input] array.string arr
An array of strings.
Guaranteed constraints: 1 ≤ arr.length ≤ 105, 2 ≤ arr[i].length ≤ 10.
[output] boolean
Return true if the given array can be turned into a palindromic array, otherwise return false.
Solution
Basic Thought Process:
 Character Counts: Identify the frequency of each character in the entire array.
 Odd Count: Count the number of characters with an odd frequency.
 Palindromic Check: If more than one character has an odd frequency, the array cannot be made palindromic.
 Element Boundary Checks: Verify that moving a single character between pairs doesn’t invalidate the palindrome property.
Code:


Here’s the Java code:


Insights:
 The frequency of each character across the entire array informs us whether making a palindrome is even possible.
 If more than one character has an odd frequency, it is not possible to create a palindrome.
 Due to the constraint that operations can be applied only once to any pair, more complex edge cases related to boundary characters are inherently handled.