#include<bits/stdc++.h>
using namespace std;
string a,b;int len_a,len_b;
int dp[2010][2010];
int dfs(int i_a,int i_b){
    if(i_a==len_a and i_b==len_b)
        return 0;
    if(i_a==len_a or i_b==len_b)
        return 2000;
    if(dp[i_a][i_b])return dp[i_a][i_b];
    int ans=dfs(i_a,i_b+1)+1;
    ans=min(ans,dfs(i_a+1,i_b)+1);
    ans=min(ans,dfs(i_a+1,i_b+1)+(a[i_a]==b[i_b]?0:1));
    return dp[i_a][i_b]=ans;
}
signed main(){
    cin>>a>>b;
    len_a=a.length(),len_b=b.length();
    cout<<dfs(0,0);
}

#8答案是1212，我的运行结果是1213，是逻辑哪里错了吗？