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To make the binary string beautiful, we need to ensure that each pair of adjacent characters forms a part of a longer sequence of identical numbers. For instance, if there is '10' or '01', we can choose to change one of the characters to make the pair '11' or '00'. We will count how many changes are needed to make all pairs in the desired format.
Since the string length is even, we can consider every odd index with its preceding even index in the string. We will check how many such pairs would need to be changed either to '00' or '11'. The sum of these changes will be our answer.
Time Complexity: O(n), where n is the length of the string. We make a single pass through the string, examining pairs of characters.
Space Complexity: O(1), only a few variables are used for counting.
1using System;
2
3class Program {
4 static int MinChangesToBeautiful(string s) {
5 int changes = 0;
6 for (int i = 0; i < s.Length; i += 2) {
7 if (s[i] != s[i + 1]) {
8 changes++;
9 }
10 }
11 return changes;
12 }
13
14 static void Main() {
15 string s = "1001";
16 Console.WriteLine(MinChangesToBeautiful(s));
17 }
18}This C# solution utilizes a method to calculate necessary changes by examining each adjacent pair to see if a conversion is essential.
This approach utilizes a sliding window that calculates the cumulative changes required to transform each segment of the string into either '00' or '11'. While iterating over pairs of characters, we check the discrepancy from '00' alternations and '11' alternations. To achieve this, two patterns are monitored: one representing making all pairs '00' and the other '11'. The minimum between these two paths will give the total minimum steps needed.
Time Complexity: O(n), where n is the length of the string, involving one linear iteration over the data.
Space Complexity: O(1), requiring no additional space except variables.
1function minChangesToBeautiful(s) {
2 let changesPattern1 = 0, changesPattern2 = 0;
3 for (let i = 0; i < s.length;
This JavaScript solution iteratively relies on maintaining two counters to decide which starting pattern produces the lesser changes, continuously aligning binary characters correctly by pattern.