Change Minimum Characters to Satisfy One of Three Conditions

Change Minimum Characters to Satisfy One of Three Conditions

What is this problem about?

The "Change Minimum Characters to Satisfy One of Three Conditions interview question" is a string optimization problem. You are given two strings, a and b, consisting of lowercase English letters. You want to change the minimum number of characters in both strings so that they satisfy one of three conditions:

1. Every character in a is strictly less than every character in b.
2. Every character in b is strictly less than every character in a.
3. Both a and b consist of only one unique character (and it's the same character for both).

Why is this asked in interviews?

Amazon and Google use the "Change Minimum Characters coding problem" to test a candidate's ability to simplify complex constraints. It evaluates "Hash Table interview pattern" skills (frequency counting) and the ability to use "Prefix Sum" techniques to avoid nested loops. It also checks if you can identify the three distinct sub-problems and find the global minimum across them.

Algorithmic pattern used

This problem relies on Frequency Counting and Prefix Sums.

1. Count Frequencies: Count the occurrences of each letter (a-z) in both strings.
2. Condition 3 (Same Character): The cost is $(length(a) + length(b) - freqA[char] - freqB[char])$. Iterate through all 26 characters to find the minimum.
3. Conditions 1 & 2 (Strictly Less): To make all a < b, pick a pivot character i (from 'b' to 'z'). Change all characters in a that are $\geq i$ and all characters in b that are $< i$. Use prefix sums of the frequency counts to calculate these costs in $O(1)$ for each pivot.

Example explanation

String a = "aba", b = "caa"

• Condition 3: Try making everything 'a'. Cost = (count of non-'a' in $a$) + (count of non-'a' in $b$) = $1 + 1 = 2$.
• Condition 1 (a < b): Try pivot 'c'. All chars in $a$ must be $< 'c'$. $a$ has 'a', 'b', 'a'. All are already $< 'c'$. All chars in $b$ must be $\geq 'c'$. $b$ has 'c', 'a', 'a'. We must change the two 'a's. Cost = 2. Result: Minimum changes = 2.

Common mistakes candidates make

• Nested Loops: Trying to compare every character of $a$ with every character of $b$, resulting in $O(N imes M)$ complexity. The frequency-based approach is $O(N + M + 26)$.
• Pivot Boundaries: Forgetting that for a < b, the pivot character for $b$ cannot be 'a' (because nothing is strictly less than 'a').
• Missing Condition 3: Only focusing on the "less than" conditions and forgetting the "all same character" case.

Interview preparation tip

Whenever a problem involves lowercase English letters, think about using a frequency array of size 26. This often transforms a string problem into a fixed-size mathematical problem, which is much faster.