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
最小编辑距离
设dp[i][j]为w1前i个字符转换成w2前j个字符所需要的最小步骤，那么有
dp[i][j] = min{ 增加一个字符 dp[i-1][j] + 1, 删除一个字符 dp[i][j-1] + 1, 替换一个字符 dp[i-1][j-1] + 1 }
1 class Solution { 2 public: 3 int minDistance(string word1, string word2) { 4 const int len1 = word1.length(); 5 const int len2 = word2.length(); 6 int dp[len1+1][len2+1]; 7 dp[0][0] = 0; //初试化 8 for(int j=1; j<=len2; ++j) dp[0][j] = j; //不断增加字符 9 for(int i=1; i<=len1; ++i) dp[i][0] = i; //不断删除字符 10 for(int i=1; i<=len1; ++i) 11 for(int j=1; j<=len2; ++j) 12 dp[i][j] = min( dp[i-1][j-1] + (word1[i-1] == word2[j-1] ? 0 : 1), min(dp[i-1][j]+1, dp[i][j-1]+1) ); 13 return dp[len1][len2]; 14 } 15 };
原文：http://www.cnblogs.com/bugfly/p/3959818.html