[Leetcode 93] 72 Edit Distance
Problem:
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
Analysis:
This is the classic dynamic programming problem. With the following inductive formula, it's easy to solve this problem:
D(i, j) = min{D(i-1, j)+1, D(i, j-1)+1, D(i-1, j-1)+replace_cost}, replace_cost = 1 if word[i] != word[j] else euqals 0. Remember here the 1 can be changed to any other proper value.
What the formula is saying is that: a new state can be obtained by 1). delete a character from string A; 2). insert a character into string B; 3). replace a character in string A to string B.
Code:
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
1 class Solution { 2 public: 3 int minDistance(string word1, string word2) { 4 // Start typing your C/C++ solution below 5 // DO NOT write int main() function 6 int len1 = word1.length()+1, len2 = word2.length()+1; 7 int way[len1][len2]; 8 9 for (int i=0; i<len1; i++) 10 way[i][0] = i; 11 12 for (int j=0; j<len2; j++) 13 way[0][j] = j; 14 15 int rep; 16 for (int i=1; i<len1; i++) 17 for (int j=1; j<len2; j++) { 18 way[i][j] = min(way[i-1][j]+1, way[i][j-1]+1); 19 rep = (word1[i-1] == word2[j-1]) ? 0 : 1; 20 way[i][j] = min(way[i][j], way[i-1][j-1]+rep); 21 } 22 23 24 return way[len1-1][len2-1]; 25 } 26 };