19.2.13 [LeetCode 72] Edit Distance

Given two words word1 and word2, find the minimum number of operations required to convert word1 to word2.

You have the following 3 operations permitted on a word:

1. Insert a character
2. Delete a character
3. 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')

题意

求最小编辑距离

有3个操作：删除，插入和替换

题解

一开始想了个dp，不够快

class Solution {
public:
    int minDistance(string word1, string word2) {
        int l1 = word1.length(), l2 = word2.length();
        vector<vector<int>>dp(l1+1, vector<int>(l2+1, INT_MAX));
        for (int i = 0; i <= l1; i++)dp[i][0] = i;
        for (int i = 0; i <= l2; i++)dp[0][i] = i;
        for (int i = 1; i <= l1; i++) {
            int minnum = INT_MAX;
            for (int j = 1; j <= l2; j++) {
                if (word1[i-1] == word2[j-1])
                    dp[i][j] =  dp[i - 1][j - 1];
                else {
                    int dp1 = dp[i - 1][j] + 1;
                    int dp2 = dp[i - 1][j - 1] + 1;
                    dp[i][j] = min(dp1, dp2);
                    if (minnum != INT_MAX)
                        dp[i][j] = min(minnum + j, dp[i][j]);
                }
                minnum = min(dp[i][j] - j, minnum);
            }
        }
        return dp[l1][l2];
    }
};

其实是有个地方我没注意到： dp[i][j] 与 dp[i][j-1] 的关系实际上是映射着插入操作的

class Solution {
public:
    int minDistance(string word1, string word2) {
        int l1 = word1.length(), l2 = word2.length();
        vector<vector<int>>dp(l1+1, vector<int>(l2+1, INT_MAX));
        for (int i = 0; i <= l1; i++)dp[i][0] = i;
        for (int i = 0; i <= l2; i++)dp[0][i] = i;
        for (int i = 1; i <= l1; i++) {
            for (int j = 1; j <= l2; 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], min(dp[i - 1][j - 1], dp[i][j - 1])) + 1;
                }
            }
        }
        return dp[l1][l2];
    }
};

貌似换成数组会更快，我还是第一次知道可以不动态申请内存这样写数组……

class Solution {
public:
    int minDistance(string word1, string word2) {
        int l1 = word1.length(), l2 = word2.length();
        int dp[l1+1][l2+1];
        for (int i = 0; i <= l1; i++)dp[i][0] = i;
        for (int i = 0; i <= l2; i++)dp[0][i] = i;
        for (int i = 1; i <= l1; i++) {
            for (int j = 1; j <= l2; 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], min(dp[i - 1][j - 1], dp[i][j - 1])) + 1;
                }
            }
        }
        return dp[l1][l2];
    }
};