Leetcode | | 72. Edit Distance

Problem:

Given 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

Hide TagsDynamic Programming StringTest instructions: Word1 the minimum number of steps required to convert a string to Word2, including inserting, replacing, and deleting one character

Thinking:

(1) Seeking global optimal solution, locking DP Method

(2) DP State transfer formula is not easy to find, there are a few are DP method Common, can be a little inspiration: 1, DP mostly with the use of the array to implement the recursive operation 2, the time complexity of DP method: one-dimensional O (N), two-dimensional: O (m*n)

(3)

If we use I to represent the subscript of the current string A, J represents the subscript of the current string B. If we use D[i, J] to represent the minimum number of edit operations between a[1, ..., i] b[1, ..., j]. Then we will have the following findings:
1. d[0, j] = J;
2. d[i, 0] = i;
3. D[i, J] = D[i-1, j-1] if a[i] = = B[j]
4. D[i, J] = min (d[i-1, j-1], D[i, j-1], D[i-1, J]) + 1 if a[i]! = B[j]//represent replace, INSERT, delete, respectively

Code

Class Solution {public:    int mindistance (string word1, String word2) {        vector<vector<int> > F ( Word1.size () +1, vector<int> (Word2.size () +1));                F[0][0] = 0;        for (int i = 1; I <= word2.size (); i++)            f[0][i] = i;                for (int i = 1; I <= word1.size (); i++)            f[i][0] = i;                    for (int i = 1; I <= word1.size (), i++) for            (int j = 1; J <= Word2.size (); j + +)            {                F[i][j] = int_max;
   
    if (word1[i-1] = = word2[j-1])                     f[i][j] = f[i-1][j-1];                                F[i][j] = min (F[i][j], f[i-1][j-1] + 1); Replace                f[i][j] = min (f[i][j], min (F[i-1][j], f[i][j-1]) + 1);//delete or insert                           }                    return f[word1.size ()][word2.size ()];}    ;
   

Leetcode | | 72. Edit Distance