The recording path LCS +

https://blog.csdn.net/someone_and_anyone/article/details/81044153

When the position i and the string 1 and string 2 position j of the matching is successful,

dp [i] [j] = dp [i-1] [j-1] +1, that is to say in this state by the state dp [i-1] [j-1] from the transfer, with an array of records,

When the match is not successful, dp [i-1] [j] and dp [i] [j-1] to a maximum, referred to as an array 2 and 3 respectively.

Looking path based on an array of records:

When the recording of the array 1, i and j at times want to wait instructions, and this state is a i-1 and j-1 from the transfer, so that i = i-1, j = j-1

When the array is recorded. 2, this time number corresponding to i and j ranging symbol, and this state is transferred from the j-1, J, so directly;

When the array is recorded. 2, this time number corresponding to i and j ranging symbol, and this state is transferred from the i-1, so the direct i--;

example:

#include<bits/stdc++.h>
using namespace std;
const int N=1000+7;
int dp[N][N];
int mark[N][N];
char s1[N],s2[N];
int main()
{
    cin>>s1+1>>s2+1;
    int n=strlen(s1+1);
    int m=strlen(s2+1);
    for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++){
            if(s1[i]==s2[j]){
                dp[i][j]=dp[i-1][j-1]+1;
                mark[i][j]=1;
            }
            else if(dp[i][j-1]>dp[i-1][j]){
                dp[i][j]=dp[i][j-1];
                mark[i][j]=2;    
            }
            else {
                dp[i][j]=dp[i-1][j];
                mark[i][j]=3;
            }
         }
    string ans="";
    int i=m,j=n;
    while(i>0&&j>0){
        if(mark[i][j]==1) {
            ans+=s1[i];
            i--;j--;
        }
        else if(mark[i][j]==2) {
            j--;
        }
        else i--;
    }
    reverse(ans.begin(),ans.end());
    cout<<ans<<endl;
    
    return 0;
}