Minimum Suffix Flips

Minimum Suffix Flips

What is this problem about?

The Minimum Suffix Flips problem gives you a target binary string. Starting from an all-zero string, in each operation you can flip all characters from any position to the end (a suffix flip). Find the minimum number of such flips to transform the all-zero string into the target. This Minimum Suffix Flips coding problem is an elegant greedy puzzle that rewards careful observation over complex algorithms.

Why is this asked in interviews?

J.P. Morgan, Microsoft, Morgan Stanley, Amazon, and IBM ask this to test the ability to identify greedy patterns from first principles. The key observation — that you only need to flip when adjacent characters in the target differ — is non-obvious without experimentation. The string and greedy interview pattern is cleanly represented.

Algorithmic pattern used

Greedy character scan. Notice that the all-zero string's current state changes only at flip boundaries. You need a flip every time the target character changes from its neighbor: specifically, whenever target[i] != target[i-1]. Additionally, if target[0] == '1', you need one flip at the start. Count the number of transitions plus the initial flip if needed.

Equivalently: count the number of positions where target[i] != target[i-1] for i ≥ 1, then add 1 if target[0] == '1'.

Example explanation

Target: "010111".

• target[0] = '1' → 1 flip at position 0.
• target[0] != target[1] (1 != 0) → 1 flip.
• target[1] != target[2] (0 != 1) → 1 flip.
• target[2] == target[3] → no flip.
• target[3] == target[4] → no flip.
• target[4] == target[5] → no flip. Total = 3 flips.

Common mistakes candidates make

• Simulating all flip operations explicitly — O(n) per flip, unnecessary.
• Off-by-one in counting transitions (comparing index 0 to a virtual "previous 0").
• Not handling the case where target[0] == '0' (no initial flip needed).
• Overcounting by including the last character as a possible flip point.

Interview preparation tip

Greedy insight problems often hide their elegance behind complex-seeming statements. When you see "minimum operations to reach a target string," try working backwards or simulating small examples (strings of length 2, 3, 4) to find the pattern. Here, the answer is simply the number of "change points" in the target. Developing the habit of empirical observation before algorithm selection is a differentiating skill for medium greedy problems.