[linear DP] longest common subsequence

subject

897. Longest common subsequence - AcWing Question bank  

AcWing 897. Longest common subsequence - AcWing

explain

• When a[i]==b[j] Update when
• f[i][j]=f[i-1][j-1]+1
• When a[i]!=b[j] When
• One of the letters must be discarded and not considered in the subsequence
• That is, the state transition is
• f(i,j)=max(f(i,j-1),f(i-1,j))

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>>m;
    cin>>a+1>>b+1;
    for(int i=1;i<=n;i++)
    for(int j=1;j<=m;j++)
    {
        if(a[i]==b[j])f[i][j]=f[i-1][j-1]+1;
        else
        {
            f[i][j]=max(f[i-1][j],f[i][j-1]);
        }
    }
    cout<<f[n][m]<<endl;
    
}