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  • 72. Edit Distance

    Problem statement:

    Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)

    You have the following 3 operations permitted on a word:

    a) Insert a character
    b) Delete a character
    c) Replace a character

    Solution:

    This is also a DP problem, which is a little complicated than 583. Delete Operation for Two Strings. We can do two more operations: insert and replace.

    The dp formular is complicated when word1[i] != word2[j].

    But the initialization and return value is the same.

    class Solution {
    public:
        int minDistance(string word1, string word2) {
            int m = word1.size();
            int n = word2.size();
            vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
            
            // initialize
            for(int i = 0; i <= m; i++){
                dp[i][0] = i;
            }
            for(int j = 0; j <= n; j++){
                dp[0][j] = j;
            }
            // dynamic programming
            for(int i = 1; i <= m; i++){
                for(int j = 1; j <= n; j++){
                    // two character is equal
                    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 - 1][j], dp[i][j - 1])) + 1;
                    }
                }
            }
            return dp[m][n];
        }
    };
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  • 原文地址:https://www.cnblogs.com/wdw828/p/6854765.html
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