Palindrome Rearrangement Queries

Problem Description

You are given a 0-indexed string s having an even length n. You are also given a 0-indexed 2D integer array, queries, where queries[i] = [a_i, b_i, c_i, d_i]. For each query i, you are allowed to perform operations on the substrings s[a_i:b_i] and s[c_i:d_i]. Your task is to determine whether it is possible to make s a palindrome by performing the operations specified by the queries. Return a 0-indexed array answer, where answer[i] == true if it is possible to make s a palindrome for the ith query, and false otherwise.

Key Insights

• Each query allows rearranging two disjoint substrings of s.
• To form a palindrome, the characters in the first half of the string must match the characters in the second half after rearrangement.
• Count the frequency of characters in both substrings and compare them to assess if they can form a palindrome.

Space and Time Complexity

Time Complexity: O(n + q * m), where n is the length of the string, q is the number of queries, and m is the average length of the substrings processed in each query. Space Complexity: O(1), as we only need a fixed amount of space for character counts.

Solution

We can approach this problem by:

1. Counting the frequency of characters in the two specified substrings for each query.
2. Checking if the total counts of characters from both substrings can be rearranged to form a palindrome.

A palindrome can be formed if each character has an even frequency or at most one character has an odd frequency (because it can be placed in the middle).

The algorithm can be outlined as follows:

1. For each query, extract the character counts for the specified substrings.
2. Combine the counts and check the frequency conditions for palindrome formation.

Code Solutions