{ "slug": "edit-distance", "title": "DP — Edit Distance", "category": "Recursion & DP", "difficulty": "hard", "complexity": { "time": "O(m × n)", "space": "O(m × n)" }, "idea": "Cell (i, j) holds the edit distance between the first i letters of one word and the first j of the other. If the letters match, nothing to do — carry the diagonal. Otherwise take the cheapest of insert, delete or replace and add one.", "code": [ "dp[i][0] = i ; dp[0][j] = j", "if a[i-1] == b[j-1]: dp[i][j] = dp[i-1][j-1]", "else: dp[i][j] = 1 + min(dp[i-1][j], # delete", " dp[i][j-1], # insert", " dp[i-1][j-1]) # replace" ], "example": { "array": [] }, "invariant": "Each step is the real data structure at that step — the picture is a pure function of it.", "stepCount": 19, "steps": [ { "i": 0, "op": "grid", "caption": "Turn \"flaw\" into \"lawn\" with as few edits as possible. 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