Minimum Time to Revert Word to Initial State II

Minimum Time to Revert Word to Initial State II

What is this problem about?

The Minimum Time to Revert Word to Initial State II is the harder variant of the reversion problem with the same mechanics but significantly longer strings, requiring more efficient string matching. The naive Z-function approach from Part I still applies but must handle very large inputs efficiently. This Minimum Time to Revert Word to Initial State II coding problem specifically tests rolling hash or optimized Z-function implementations for large-scale string matching.

Why is this asked in interviews?

Sprinklr uses this hard variant to test whether candidates can scale their string matching solutions to large inputs using rolling hash — a probabilistic but extremely fast string matching technique. The string matching, hash function, rolling hash, and string interview pattern at scale is the core focus, distinguishing candidates with deep string algorithm knowledge.

Algorithmic pattern used

Rolling hash for O(n) string matching. Precompute rolling hash values for all prefixes of word. For each candidate suffix word[t*k:], compute its hash using precomputed suffix hashes and compare with the hash of the corresponding prefix of word. If hashes match (and length condition holds), return t. Use double hashing (two different bases/mods) to minimize collision probability.

Example explanation

word = "aabaabaab", k = 3.

• t=1: word[3:] = "aabaab". Rolling hash of "aabaab" vs hash of "aabaa..." prefix of length 6. Match? Check. If yes, t=1.
• If not, t=2: word[6:] = "aab". Hash of "aab" vs prefix of length 3. Match? Yes → t = 2.

Common mistakes candidates make

• Using naive string comparison O(n²) instead of rolling hash O(n).
• Single hashing with high collision risk (use double hash for safety).
• Incorrect rolling hash computation when slicing substrings.
• Not handling the edge case when t*k >= n (whole word replaced, always a valid reversion).

Interview preparation tip

Rolling hash is an essential technique for advanced string problems. The key formula: hash(s[i:j]) = (hash(s[0:j]) - hash(s[0:i]) * base^(j-i)) % mod. Precompute prefix hashes and powers of the base, then compute any substring hash in O(1). Always use two independent hash functions (different base, mod pairs) to reduce collision probability to near zero. Practice rolling hash on problems like "find all occurrences of pattern in text" — it's faster than KMP in practice and more broadly applicable.