Leetcode 72. Edit Distance

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

[Solution]

Use Table[i][j] to represent the minimum steps required to change from word1[i] to word2[j].

1) Match: If WORD1[I]=WORD2[J], then simply turn word1[0...i-1] into word2[0...j-1]. ==> Table[i][j] = table[i-1][j-1].

2) Replace: Replace the word1[i] with Word2[j] is the smallest change from word1 to Word2, then the word1[0...i-1] is changed to the minimum cost word2[0...j-1], and then replaced. ==> Table[i][j] = table[i-1][j-1] + 1.

3) Insert: If in word1[i] insert a character is word1 to word2[minimum change, then word1[0...i] to the minimum cost to word2[0...j-1], on this basis add word2[j], ==> table[i][j] = TABLE[I][J-1] + 1.

4) Delete: If delete word1[i] is word1 to word2 minimum change, then word1[0...i-1] to the minimum cost to WORD2[0...J], and then delete word1[j], table[i][j] = Table[i-1][j] + 1.

1 intMindistance (stringWord1,stringWord2)2     {3         intI, J, Ndelete, Ninsert, Nreplace, Min_step;4         intm = Word1.size (), n =word2.size ();5         if(M = =0|| n = =0) 6             return(M = =0) ?n:m;7             8         int**table =New int* [M +1];//table[i][j] means change word1[i] to word2[j];9          for(i =0; I <= m; i++)TenTable[i] =New int[n +1]; One          A          for(i =0; I <= m; i++) -table[i][0] =i; -          for(j =0; J <= N; J + +) thetable[0][J] =J; -                  -          for(i =1; I <= m; i++) -         {     +              for(j =1; J <= N; J + +) -             { +Ndelete = Table[i-1][J] +1; ANinsert = Table[i][j-1] +1; at                 if(Word1[i-1] = = Word2[j-1]) -Nreplace = Table[i-1][j-1]; -                 Else -Nreplace = Table[i-1][j-1] +1; -TABLE[I][J] =min (nreplace, min (ndelete, Ninsert)); -             } in         } -Min_step =Table[m][n]; to          +          for(i =0; I <= m; i++) - delete[] table[i]; the delete[] table; *          $         returnMin_step;Panax Notoginseng}

Leetcode 72. Edit Distance