[linear DP] shortest editing distance

subject

explain

• 

• 

Code segment

#include<iostream>
using namespace std;
int n,m;
const int N=1010;
char a[N],b[N];
int f[N][N];
int main()
{
    cin>>n>>a+1;
    cin>>m>>b+1;
    for(int i=1;i<=n;i++)f[i][0]=i;
    for(int i=1;i<=m;i++)f[0][i]=i;
    for(int i=1;i<=n;i++)
    for(int j=1;j<=m;j++)
    {
        f[i][j]=min(f[i-1][j]+1,f[i][j-1]+1);
        if(a[i]==b[j])f[i][j]=min(f[i-1][j-1],f[i][j]);
        f[i][j]=min(f[i-1][j-1]+1,f[i][j]);
    }
    cout<<f[n][m]<<endl;
}