72. Edit Distance

https://leetcode.com/problems/edit-distance/description/

DP

class Solution {
public:
    int minDistance(string word1, string word2) {
        int m = word1.length(), n = word2.length();
        vector<vector<int>> dp(m+1, vector<int>(n+1, INT_MAX));
        for (int i = 0; i <= m; i++)
            dp[i][0] = i;
        for (int j = 0; j <= n; j++)
            dp[0][j] = j;
        for (int i = 1; i <= m; i++)
            for (int j = 1; j <= n; j++) {
                if (word1[i-1] == word2[j-1])
                    dp[i][j] = dp[i-1][j-1];
                else
                    dp[i][j] = min(dp[i-1][j-1], min(dp[i][j-1], dp[i-1][j])) + 1;
            }
        return dp[m][n];
    }
};

递归 (bad performance, should change cache key to index [i,j] in the two words)

class Solution {
public:
    map<pair<string,string>, int> cache;
    int minDistance(string word1, string word2) {
        auto key = make_pair(word1, word2);
        if (cache.count(key))   return cache[key];
            
        if (word1 == word2) return 0;
        int idx = 0;
        while (word1[idx] == word2[idx])    idx++;
        if (idx == word1.length())  return word2.length() - idx;
        if (idx == word2.length())  return word1.length() - idx;
        int res = 1 + min(
            minDistance(word1.substr(idx+1),word2.substr(idx+1)),    // replace current
            min(
                minDistance(word1.substr(idx+1),word2.substr(idx)),  // delete one from first
                minDistance(word1.substr(idx),word2.substr(idx+1))   // delete one from second
            ));
        cache[key] = res;
        return res;
    }
};