Levenshtein Distance
Levenshtein distance is the minimum number of single-character insertions, deletions and substitutions needed to transform one string into another.
先从这个心智模型开始
Levenshtein distance is the minimum number of single-character insertions, deletions and substitutions needed to transform one string into another.
它如何工作，不堆砌不必要的术语
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).
把算法读成一连串决策
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Do not quote this complexity mechanically.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.
适用场景
- Use specialized matching algorithms when repeated or large-string searching makes naive scanning too expensive.
通常哪里会出错
- Ignoring Unicode semantics.
- Confusing substring with subsequence.
- Off-by-one prefix/index bugs.
专业回答结构
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.
关于复杂度应该提到什么？
Its typical cost here is O(mn), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
最常见的错误是什么？
Ignoring Unicode semantics.