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72. Edit Distance

Hard

Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2.

You have the following three operations permitted on a word:

• Insert a character
• Delete a character
• Replace a character

Example 1:

Input: word1 = “horse”, word2 = “ros”

Output: 3

Explanation: horse -> rorse (replace ‘h’ with ‘r’) rorse -> rose (remove ‘r’) rose -> ros (remove ‘e’)

Example 2:

Input: word1 = “intention”, word2 = “execution”

Output: 5

Explanation: intention -> inention (remove ‘t’) inention -> enention (replace ‘i’ with ‘e’) enention -> exention (replace ‘n’ with ‘x’) exention -> exection (replace ‘n’ with ‘c’) exection -> execution (insert ‘u’)

Constraints:

• 0 <= word1.length, word2.length <= 500
• word1 and word2 consist of lowercase English letters.

Solution

# @param {String} word1
# @param {String} word2
# @return {Integer}
def min_distance(word1, word2)
  n1 = word1.length
  n2 = word2.length

  return min_distance(word2, word1) if n2 > n1

  dp = Array.new(n2 + 1) {|j| j}

  (1..n1).each do |i|
    pre = dp[0]
    dp[0] = i

    (1..n2).each do |j|
      tmp = dp[j]
      dp[j] = word1[i - 1] != word2[j - 1] ? 1 + [pre, dp[j], dp[j - 1]].min : pre
      pre = tmp
    end
  end

  dp[n2]
end

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