Minimum Number of Flips to Reverse Binary String - Solution & Explanation

Problem Overview: You are given a binary string. The goal is to determine the minimum number of bit flips required so the string becomes equal to its reverse. A flip changes a character from 0 to 1 or from 1 to 0. The task reduces to fixing mismatched mirrored positions in the string.

Approach 1: Reverse String + Compare (Simulation) (O(n) time, O(n) space)

Create the reversed version of the string and compare it with the original character by character. For every index i, check whether s[i] matches rev[i]. If the characters differ, a flip is required to make them equal. Count the number of mismatches and divide by two because each mismatch pair corresponds to a mirrored conflict between two positions. This approach is straightforward and mirrors how you would reason about the problem manually, but it allocates an extra string.

Approach 2: Two Pointers (Simulation) (O(n) time, O(1) space)

Instead of explicitly reversing the string, compare mirrored characters directly using the two pointers technique. Start one pointer at the beginning (left) and another at the end (right). Move both toward the center while checking whether s[left] equals s[right]. If they differ, one flip is enough to make the pair match, so increment the flip counter. Continue until the pointers meet. This works because each pair must contain identical bits for the string to match its reverse. The algorithm performs a single pass through the string and uses constant extra memory.

This method is essentially a direct simulation of the constraints imposed by the reversed string. Since each step compares symmetric indices, it naturally aligns with problems involving string processing and simple bit manipulation. The key insight is that every mirrored pair can be corrected with at most one flip.

Recommended for interviews: The two‑pointer approach is what interviewers typically expect. It shows you recognize the symmetry in the string and avoid unnecessary memory allocation. Mentioning the reverse‑and‑compare simulation first demonstrates baseline reasoning, while the two‑pointer solution shows you can optimize both space and implementation clarity.