leetcode

Given two words word1 and word2, find the minimum number of steps required to convertword1 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

int minDistance(string word1, string word2) {
int t=word1.size();
int s=word2.size();
if(t==0)
return s;
if(s==0)
return t;
int A[t+1][s+1];
for(int i=0;i<=t;i++)
A[i][0]=i;
for(int j=0;j<=s;j++)
A[0][j]=j;
for(int i=1;i<=t;i++)
{
for(int j=1;j<=s;j++)
{
if(word1[i-1]==word2[j-1])
A[i][j]=A[i-1][j-1];
else
A[i][j]=min(A[i][j-1],min(A[i-1][j-1],A[i-1][j]))+1;
}
}
return A[t][s];
}

说明：DP[x][y]记录的是字符串1，字符串2前i,j的最小公共值，一般的我们假定知道了D[i][j-1],D[i-1][j],D[]i-1[j-1],当S1[i]=S2[j]时，需要求助D[i][j]，当不等时，由于后来加的字符不等，所以一定有一个字符的距离，所以去最小的情况加1.