Levenshtein Distance
Levenshtein distance is the minimum number of single-character insertions, deletions and substitutions needed to transform one string into another.
Start with this mental model
Levenshtein distance is the minimum number of single-character insertions, deletions and substitutions needed to transform one string into another.
How it works, without unnecessary jargon
Dynamic programming defines dp[i][j] as the edit distance between prefixes of lengths i and j.
If current characters match, use the diagonal value; otherwise take 1 + min(insert, delete, replace).
Read the algorithm as a sequence of decisions
Clarify Unicode/case/normalization assumptions.
Define indexes or prefix state.
Reuse previously learned match information when the algorithm allows it.
Read a tiny input by hand and write down the state after every important operation. For Levenshtein Distance, the goal is to make the invariant visible rather than to memorize code.
O(mn)
Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.
Good fit
- Use specialized matching algorithms when repeated or large-string searching makes naive scanning too expensive.
What usually goes wrong
- Ignoring Unicode semantics.
- Confusing substring with subsequence.
- Off-by-one prefix/index bugs.
A professional answer shape
Define the DP state before recurrence. That makes the recurrence understandable rather than memorized.
What problem does Levenshtein Distance solve?
Levenshtein distance is the minimum number of single-character insertions, deletions and substitutions needed to transform one string into another.
What should I mention about complexity?
Its typical cost here is O(mn), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
What is the most common mistake?
Ignoring Unicode semantics.