Edit Distance

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

此题编程之美有，其上使用的是递归。此处为dp!

 int minDistance(string word1, string word2)    {            if(word1.empty() && word2.empty())return 0;            if(word1.empty())return word2.size();            if(word2.empty())return word1.size();          vector< vector<int> > dp(word1.size()+1,vector<int>(word2.size()+1));             dp[0][0] = 0;              for(int i = 1;i <= word1.size();i++)       {           dp[i][0] = i;                  }               for(int i = 1;i <= word2.size();i++)        {            dp[0][i] = i;        }              for(int i = 1;i <= word1.size();i++)      {        for(int j = 1;j <= word2.size();j++)        {          if(word1[i-1] == word2[j-1])          {               dp[i][j] = dp[i-1][j-1] ;           }          else          {              int temp_min = min(dp[i-1][j-1],dp[i][j-1]);//3种可能的情况 替换，后面俩种添加与删除都有可能！              dp[i][j] = min(temp_min,dp[i-1][j]) + 1;          }        }      }        return dp[word1.size()][word2.size()];    }