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
D(i,j)=min { D(i-1, j) +1, D(i, j-1) +1 , D(i-1, j-1) + s1[i]==s2[j] ? 0 : 1}
class Solution {
public:
int minDistance(string word1, string word2) {
int m=word1.size();
int n=word2.size();
vector<vector<int>> dis(m+1);
for(int i=0;i<=m;i++)dis[i].assign(n+1,INT_MAX);
dis[0][0]=0;
for(int i=0;i<=m;i++)
for(int j=0;j<=n;j++){
if(i>0) dis[i][j] = min(dis[i][j],dis[i-1][j]+1); //delete
if(j>0) dis[i][j] = min(dis[i][j],dis[i][j-1]+1);//insert
//substitute
if(i>0&&j>0)
{
if(word1[i-1]!=word2[j-1])
dis[i][j] = min(dis[i][j],dis[i-1][j-1]+1);
else
dis[i][j] = min(dis[i][j],dis[i-1][j-1]);
}
}
return dis[m][n];
}
};