Make Number of Distinct Characters Equal

Problem Description

You are given two 0-indexed strings word1 and word2. A move consists of choosing two indices i and j such that 0 <= i < word1.length and 0 <= j < word2.length and swapping word1[i] with word2[j]. Return true if it is possible to get the number of distinct characters in word1 and word2 to be equal with exactly one move. Return false otherwise.

Key Insights

• The distinct character count of both strings must be adjusted by exactly one swap.
• A swap can either increase or decrease the distinct character count in one of the strings.
• To equalize the distinct character counts, we need to analyze the current counts and the characters involved in the swap.

Space and Time Complexity

Time Complexity: O(n + m), where n is the length of word1 and m is the length of word2.
Space Complexity: O(1), since we only use a fixed amount of space for counting characters.

Solution

To solve the problem, we can follow these steps:

1. Count the distinct characters in word1 and word2.
2. Identify the characters that can be swapped between the two strings.
3. A swap can change the distinct character count in one string, so we need to check if a valid swap exists that results in equal distinct counts for both strings.
4. If the difference in distinct counts is exactly 1, we need to ensure that at least one character from word1 is in word2 and vice versa. If the distinct counts are equal, swapping any character will suffice.

Code Solutions