Minimum Suffix Flips - Video Solutions

Problem Overview: You start with a binary string of all 0s and want to transform it into a target binary string. In one operation, you can flip every bit from an index i to the end of the string (a suffix flip). The task is to compute the minimum number of such flips needed to match the target.

Approach 1: Track Transitions in Target String (Greedy) (Time: O(n), Space: O(1))

The key observation is that a flip only matters when the desired bit changes relative to the current effective state. Start with the assumption that the string is all 0s. As you iterate through the target string, track whether the current state matches the desired character. Every time the desired bit differs from the current effective value, you must perform a suffix flip starting at that index. After a flip, the effective value toggles for the rest of the scan. This reduces the problem to counting transitions where the expected bit differs from the actual target bit. The algorithm performs a single pass through the string while applying a greedy decision at each position.

Approach 2: Pattern Matching from Index 0 (Simulation) (Time: O(n), Space: O(1))

Another way to think about the process is by simulating the flips logically without modifying the string. Maintain a variable representing the current flipped state (0 or 1). Iterate from index 0 to n-1. If the effective bit after considering previous flips differs from the target bit, perform a new flip and toggle the state variable. This effectively simulates applying the suffix flip while keeping the algorithm linear. Instead of physically flipping characters, you just track whether the sequence has been flipped an odd or even number of times so far.

Both approaches rely on the same core insight: the only moments that matter are when the required bit differs from the current effective value. Once a flip happens, the state of all remaining characters is inverted, so the algorithm simply keeps track of that inversion logically.

Recommended for interviews: The transition-count greedy approach is what most interviewers expect. It demonstrates that you recognized the flipping pattern and reduced the problem to counting state changes instead of simulating expensive operations. Explaining the reasoning behind why transitions correspond to flips shows strong understanding of greedy decision making on a string traversal.