#1737

Medium

LeetCode Problem Workspace

Change Minimum Characters to Satisfy One of Three Conditions

This problem asks for the minimum operations to change two strings so that one of three conditions is met.

Problem Statement

You are given two strings, a and b, consisting of lowercase letters. You can change any character in a or b to any lowercase letter in one operation.

Your task is to determine the minimum number of operations required to make one of the following conditions true: (1) all characters in a are less than all characters in b, (2) all characters in b are less than all characters in a, or (3) all characters in both strings are the same.

Examples

Example 1

Input: a = "aba", b = "caa"

Output: 2

Consider the best way to make each condition true:

Change b to "ccc" in 2 operations, then every letter in a is less than every letter in b.
Change a to "bbb" and b to "aaa" in 3 operations, then every letter in b is less than every letter in a.
Change a to "aaa" and b to "aaa" in 2 operations, then a and b consist of one distinct letter. The best way was done in 2 operations (either condition 1 or condition 3).

Example 2

Input: a = "dabadd", b = "cda"

Output: 3

The best way is to make condition 1 true by changing b to "eee".

Constraints

1 <= a.length, b.length <= 105
a and b consist only of lowercase letters.

Solution Approach

Iterate over each letter of the alphabet

For each letter in the alphabet, compute how many operations it would take to make both strings satisfy one of the three conditions. This can be done by transforming characters to a common letter and counting the changes needed.

Use a hash table for frequency counting

Use a hash table to track the frequency of each letter in both strings. This will help efficiently calculate the operations needed to achieve each condition by counting how many letters need to be changed.

Determine the optimal condition

For each possible condition, calculate the number of operations required to meet it, and return the minimum value. The goal is to minimize the number of operations while ensuring that one of the three conditions is satisfied.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time and space complexity depend on the approach used for counting and iterating over the alphabet. If iterating through all possible letters, the complexity is proportional to the length of the strings and the size of the alphabet, which is constant at 26 characters. In total, the time complexity is O(n + 26), where n is the length of the longest string. Space complexity is O(26) due to the frequency table.

What Interviewers Usually Probe

Look for candidates who can efficiently use hash tables for counting operations.
Evaluate how well the candidate handles the three conditions with a minimal number of iterations.
Check if the candidate can optimize the solution by focusing on constant-time operations for each condition.

Common Pitfalls or Variants

Common pitfalls

Failing to use hash tables efficiently can result in unnecessary recalculations.
Incorrectly handling edge cases such as when strings are already equal or when one string is empty.
Not minimizing the operations correctly and selecting suboptimal conditions.

Follow-up variants

Modify the problem by limiting the alphabet to only vowels or consonants.
Allow a different character set (e.g., uppercase or digits) and test the solution’s scalability.
Add constraints that require the solution to handle much larger input sizes while maintaining optimal performance.

FAQ

What are the key strategies for solving 'Change Minimum Characters to Satisfy One of Three Conditions'?

Focus on using hash tables to track letter frequencies and iterating over the alphabet to find the optimal solution.

How do hash tables help in solving this problem?

Hash tables allow you to efficiently count the occurrences of each letter in the strings, which helps minimize operations needed to satisfy the conditions.

What is the best approach to minimize operations?

Iterate over the alphabet, calculate the number of changes for each condition, and select the one with the fewest operations.

Can you explain the three conditions in this problem?

The three conditions are: (1) all characters in a must be less than those in b, (2) all characters in b must be less than those in a, or (3) both strings must consist of the same characters.

What are some common mistakes in solving this problem?

Common mistakes include inefficiently using hash tables, failing to handle edge cases, and not optimizing the number of operations correctly.

terminal

Solution

Solution 1: Counting + Enumeration

First, we count the number of occurrences of each letter in strings $a$ and $b$, denoted as $cnt_1$ and $cnt_2$.

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class Solution:
    def minCharacters(self, a: str, b: str) -> int:
        def f(cnt1, cnt2):
            for i in range(1, 26):
                t = sum(cnt1[i:]) + sum(cnt2[:i])
                nonlocal ans
                ans = min(ans, t)

        m, n = len(a), len(b)
        cnt1 = [0] * 26
        cnt2 = [0] * 26
        for c in a:
            cnt1[ord(c) - ord('a')] += 1
        for c in b:
            cnt2[ord(c) - ord('a')] += 1
        ans = m + n
        for c1, c2 in zip(cnt1, cnt2):
            ans = min(ans, m + n - c1 - c2)
        f(cnt1, cnt2)
        f(cnt2, cnt1)
        return ans

Continue Practicing

#1781 sum of beauty of all substrings #1684 count the number of consistent strings #1790 check if one string swap can make strings equal