LintCode (119) 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:

• Insert a character
• Delete a character
• Replace a character

Have you met this question in a real interview? 

Yes

Example

Given word1 = "mart" and word2 = "karma", return 3.

首先这是一道dp题目，两个串，干个啥，求最小。

然后要搞清楚三个操作：

插入和删除： f[i-1][j], f[i][j-1] +1

替换： f[i-1][j-1]+1

或者无操作 f[i-1][j-1]

这样就变成了之前的longest subsequence的题目了，

其实你想想就是这样的，longest subsequence不就是找找那些一样的么。。。那么这三种操作完全可以把longest subsequence变成全串儿。。。

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class Solution { public: /** * @param word1 & word2: Two string. * @return: The minimum number of steps. */ int minDistance(string word1, string word2) { // write your code here int m=word1.size(); int n=word2.size(); vector< vector<int> > f(m+1, vector<int>(n+1,0)); for (int i=1; i<=m; i++){ f[i][0]=i; } for (int j=1; j<=n; j++){ f[0][j]=j; } for (int i=1; i<=m; i++){ for (int j=1; j<=n; j++){ f[i][j]=min(f[i-1][j],f[i][j-1])+1; f[i][j]=min(f[i][j], word1[i-1]==word2[j-1]? f[i-1][j-1]: f[i-1][j-1]+1); } } return f[m][n]; } };