Edit Distance(dp)

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

一道dp题

Use f[i][j] to represent the shortest edit distance between word1[0,i) and word2[0, j). Then compare the last character of word1[0,i) and word2[0,j), which are c and d respectively (c == word1[i-1], d == word2[j-1]):

if c == d, then : f[i][j] = f[i-1][j-1]

Otherwise we can use three operations to convert word1 to word2:

(a) if we replaced c with d: f[i][j] = f[i-1][j-1] + 1;

(b) if we added d after c: f[i][j] = f[i][j-1] + 1;

(c) if we deleted c: f[i][j] = f[i-1][j] + 1;

class Solution {public:    int minDistance(string word1, string word2) {        int m=word1.size();        int n=word2.size();        int dp[m+1][n+1];        dp[0][0]=0;        for (int i = 1; i <= m; i++)            dp[i][0] = i;        for (int j = 1; j <= n; j++)            dp[0][j] = j;         for(int i=1;i<=m;i++)        for(int j=1;j<=n;j++){        int c=word1[i-1];        int d=word2[j-1];        if(d==c)dp[i][j]=dp[i-1][j-1];        else         {            dp[i][j]=min(min(dp[i-1][j],dp[i][j-1]),dp[i-1][j-1])+1;        }        }        return dp[m][n];    }};