IBM Coding Question: Min Insertions to Form 'abc' Problem
Question Description
You are given a lowercase string s and you may only insert characters (no deletions or replacements) to transform it into a string that is one or more repetitions of the pattern "abc" (i.e., ("abc")^k for some k >= 0). The goal is to compute the minimum number of insertions required.
Key idea: think of the target as a repeating pattern "abc". You can scan s left-to-right while maintaining which character in the pattern you currently expect (a, then b, then c). When s[i] matches the expected pattern character, advance both the input index and the pattern state. When it doesn't match, you must insert the expected pattern character (count++), advance the pattern state, but keep the same input index so you still try to match s[i] against the next expected character. Continue until you exhaust s, then add any remaining insertions to finish the last partial "abc" block.
Interview flow: you'll likely start by explaining this greedy, state-machine approach, then write a two-pointer/one-pass implementation and prove correctness. Discuss time O(n) and O(1) extra space. Expect follow-ups on correctness, handling edge cases (empty string, repeated letters), and variations like allowing deletions or different patterns.
Skills demonstrated: string manipulation, greedy algorithms, two-pointers/state machine reasoning, edge-case handling, and time/space complexity analysis. Practicing this type of question helps in technical screens for backend/SWE roles where concise, linear-time string transforms are common.
Common Follow-up Questions
- •If deletions are allowed in addition to insertions, how would you compute the minimum edits to form ("abc")^k?
- •How would you modify the algorithm to return the resulting string (not just the count) and prove it is minimal?
- •Generalize the solution to an arbitrary pattern p (length m): how does complexity change and what edge cases appear?
- •Can you prove the greedy strategy is optimal — why is it never beneficial to postpone an insertion?
- •How would you adapt the algorithm to a streaming input (you can't rewind the string)?
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