Minimum Changes To Make Alternating Binary String

Updated on 11 June, 2025
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Problem Statement

In this problem, you have a binary string s that consists solely of the characters '0' and '1'. To solve this task, you can perform operations where you switch any '0' into a '1' or any '1' into a '0'. The goal is to transform the string into an "alternating" sequence. An alternating binary string is defined as one in which no two consecutive characters are the same. Your job is to determine the minimum number of such switches (operations) required to convert the given string into an alternating one. This is crucial in optimizing binary sequences for various algorithmic applications where such patterns might impact performance or outcomes.

Examples

Example 1

Input:

s = "0100"

Output:

1

Explanation:

If you change the last character to '1', s will be "0101", which is alternating.

Example 2

Input:

s = "10"

Output:

0

Explanation:

s is already alternating.

Example 3

Input:

s = "1111"

Output:

2

Explanation:

You need two operations to reach "0101" or "1010".

Constraints

  • 1 <= s.length <= 104
  • s[i] is either '0' or '1'.

Approach and Intuition

To tackle this problem of transforming a binary string into an alternating sequence with minimum operations, we can use the following strategy:

  1. Identify the Target Patterns:

    • An alternating string of length n can either start with '0' or '1'. There are exactly two possible alternating patterns for a given length:
      • Starting with '0': Alternates like "010101..." up to the length of the string.
      • Starting with '1': Alternates like "101010..." similarly up to the length of the string.
  2. Calculate Mismatches for Both Patterns:

    • For the first pattern (starting with '0'), iterate through the string s and count how many characters do not match the pattern. This gives the number of required changes to make the string alternate starting with '0'.
    • Similarly, compute the required changes for the string to alternate starting with '1'.
  3. Choosing the Minimum:

    • The final step is simply to choose the lesser count of changes required from the two patterns. This count represents the minimum number of operations needed to make the string alternating.

This approach is efficient with a time complexity of O(n), where n is the length of the string, since it involves just a couple of linear scans to compute the changes needed for each pattern. The simplicity and efficiency of this method make it suitable for even the upper limits of the constraints given, where the string length can go up to 10^4.

Solutions

  • C++
  • Java
  • Python
cpp
class Solution {
public:
    int minOps(string s) {
        int op0 = 0;
        
        for (int idx = 0; idx < s.length(); idx++) {
            if (idx % 2 == 0) {
                op0 += s[idx] != '0';
            } else {
                op0 += s[idx] != '1';
            }
        }
        
        return min(op0, (int) s.length() - op0);
    }
};

The objective of the C++ solution provided is to find the minimum number of changes required to convert a given binary string into an alternating binary string (where no two adjacent characters are the same). This approach is implemented in the minOps function. Here's a streamline of its operation:

  • Introduce an integer variable op0 to count the number of operations required to pattern the string starting with '0'.

  • Loop through the string using an index idx. If the index is even, check if the current character is '0'; if not, increment op0. If the index is odd, check if the current character is '1'; if not, also increment op0.

  • Calculate the minimum number of operations needed by comparing op0 with the number of changes required to pattern the string starting with '1'. To find this, subtract op0 from the string length.

  • Return the minimum of the two calculated values, which represents the fewer number of changes required to make the string alternate perfectly starting with either '0' or '1'.

Apply this function to determine how efficiently a given binary string can be modified to satisfy the alternating condition.

java
class Solution {
    public int minimumSwaps(String str) {
        int count0 = 0;

        for (int idx = 0; idx < str.length(); idx++) {
            if (idx % 2 == 0) {
                if (str.charAt(idx) != '0') {
                    count0++;
                }
            } else {
                if (str.charAt(idx) != '1') {
                    count0++;
                }
            }
        }

        return Math.min(count0, str.length() - count0);
    }
}

The provided solution in Java addresses the problem of transforming a given binary string into an alternating binary string with the minimum number of swaps. An alternating binary string is one where no two adjacent characters are the same. The solution involves these key steps:

  • Initialize a counter (count0) to keep track of the total swaps needed for the pattern "010101...".
  • Traverse each character of the input string using a loop. Check the index:
    • If the index is even and the character at that index isn’t '0', increment the count0.
    • If the index is odd and the character at that index isn’t '1', increment the count0.
  • Calculate the minimum number of swaps needed by considering the lesser of count0 and the total length of the string minus count0. This comparison accounts for the two possible alternating patterns ("0101..." or "1010...").

Finally, the method returns the minimum number of swaps needed to convert a given binary string into an alternating binary string pattern. This solution effectively evaluates both possible patterns and selects the one requiring fewer changes, ensuring efficiency.

python
class Solution:
    def minimumOperations(self, input_string: str) -> int:
        count0 = 0
        
        for index in range(len(input_string)):
            if index % 2 == 0:
                if input_string[index] == "1":
                    count0 += 1
            else:
                if input_string[index] == "0":
                    count0 += 1
        
        return min(count0, len(input_string) - count0)

The Python function minimumOperations calculates the minimal number of changes required to convert a given binary string into an alternating binary string, where no two adjacent characters are the same. Here's the approach:

  • Initialize a counter (count0) to track the number of changes needed assuming the first character in the alternating pattern is '0'.
  • Loop through each character in the string using its index to check its adherence to the alternating pattern:
    • If the character's index is even and the character is '1', it violates the pattern assuming a start with '0'. Increment count0.
    • If the character's index is odd and the character is '0', it also violates the pattern. Increment count0.
  • Calculate count1, the number of changes needed if the first character in the alternating pattern is '1', as the total length of the string minus count0.
  • Return the smaller value between count0 and count1 as the result, representing the minimum changes required.

This function effectively and efficiently determines the fewest switches needed to ensure the string alternates properly.

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