LeetCode-in-All

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 {number}
 */
var minDistance = function(w1, w2) {
    const n1 = w1.length
    const n2 = w2.length

    if (n2 > n1) {
        return minDistance(w2, w1)
    }

    const dp = new Array(n2 + 1).fill(0)
    for (let j = 0; j <= n2; j++) {
        dp[j] = j
    }

    for (let i = 1; i <= n1; i++) {
        let pre = dp[0]
        dp[0] = i
        for (let j = 1; j <= n2; j++) {
            const tmp = dp[j]
            dp[j] =
                w1[i - 1] !== w2[j - 1]
                    ? 1 + Math.min(pre, Math.min(dp[j], dp[j - 1]))
                    : pre
            pre = tmp
        }
    }

    return dp[n2]
};

export { minDistance }

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