Minimum Number of Changes to Make Binary String Beautiful
Nov 08, 2024 am 09:53 AM2914. Minimum Number of Changes to Make Binary String Beautiful
Difficulty: Medium
Topics: String
You are given a 0-indexed binary string s having an even length.
A string is beautiful if it's possible to partition it into one or more substrings such that:
- Each substring has an even length.
- Each substring contains only 1's or only 0's.
You can change any character in s to 0 or 1.
Return the minimum number of changes required to make the string s beautiful.
Example 1:
- Input: s = "1001"
- Output: 2
-
Explanation: We change s[1] to 1 and s[3] to 0 to get string "1100".
- It can be seen that the string "1100" is beautiful because we can partition it into "11|00".
- It can be proven that 2 is the minimum number of changes needed to make the string beautiful.
Example 2:
- Input: s = "10"
- Output: 1
-
Explanation: We change s[1] to 1 to get string "11".
- It can be seen that the string "11" is beautiful because we can partition it into "11".
- It can be proven that 1 is the minimum number of changes needed to make the string beautiful.
Example 3:
- Input: s = "0000"
- Output: 0
- Explanation: We don't need to make any changes as the string "0000" is beautiful already.
Constraints:
- 2 <= s.length <= 105
- s has an even length.
- s[i] is either '0' or '1'.
Hint:
- For any valid partition, since each part consists of an even number of the same characters, we can further partition each part into lengths of exactly 2.
- After noticing the first hint, we can decompose the whole string into disjoint blocks of size 2 and find the minimum number of changes required to make those blocks beautiful.
Solution:
We need to ensure that every pair of characters in the binary string s is either "00" or "11". If a pair is not in one of these two patterns, we will need to change one of the characters to make it match.
Here's the step-by-step solution approach:
Divide the String into Blocks: Since a beautiful string can be formed from blocks of length 2, we can iterate through the string in steps of 2.
Count Changes: For each block of 2 characters, we need to determine the majority character (either 0 or 1). We will change the minority character in the block to match the majority character.
Calculate Minimum Changes: For each block, if both characters are different, we will need 1 change; if they are the same, no changes are required.
Let's implement this solution in PHP: 2914. Minimum Number of Changes to Make Binary String Beautiful
Explanation:
Function Definition: We define a function minChanges that takes a binary string s.
Initialization: We initialize a variable $changes to keep track of the number of changes required.
Iterate Over the String: We loop through the string, incrementing by 2 each time to check each block of two characters:
- $first is the character at the current position.
- $second is the character at the next position.
Check for Changes: If the characters in the current block are different, we increment the $changes counter by 1.
Return Result: Finally, we return the total number of changes required.
Complexity:
- Time Complexity: O(n), where n is the length of the string, as we are iterating over the string once.
- Space Complexity: O(1), since we are using a constant amount of extra space.
This solution operates in O(n) time complexity, where n is the length of the string, making it efficient for the given constraints.
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