Determine if Two Strings Are Close

Problem Description

Given two strings, word1 and word2, determine if they are considered "close". Two strings are considered close if you can attain one from the other using the following operations:

1. Swap any two existing characters.
2. Transform every occurrence of one existing character into another existing character, and do the same with the other character.

Return true if word1 and word2 are close, and false otherwise.

Key Insights

• The characters in both strings must be the same (though not necessarily in the same order).
• The frequency of each character must be able to match through swaps.
• If one string has a character that the other does not, they cannot be close.
• The count of occurrences of each character needs to match between the two strings after sorting.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the frequency counts. Space Complexity: O(1) - since we are using a fixed size array for character counts.

Solution

To determine if two strings are close:

1. First, check if both strings have the same length. If not, return false.
2. Use a frequency count for each string to count the occurrences of each character.
3. Compare the character sets of both strings; they must contain the same characters.
4. Sort the frequency counts of each string and compare them; if they match, the strings are close.

This approach utilizes hash tables (or arrays) to count character frequencies and sorting to compare the counts.

Code Solutions