TheAlgorithms-C-Plus-Plus/Dynamic Programming/Longest Common Subsequence.cpp

//Longest common subsequence - Dynamic Programming
#include <iostream>
using namespace std;

void Print(int trace[20][20], int m, int n, string a)
{
	if (m==0 || n==0)
	{
		return;
	}
	if (trace[m][n]==1)
	{
		Print(trace, m-1, n-1, a);
		cout<<a[m-1];
	}
	else if(trace[m][n]==2)
	{
		Print(trace, m-1,n, a);
	}
	else if (trace[m][n]==3)
	{
		Print(trace, m,n-1, a);
	}
}



int lcs(string a, string b){
	int m = a.length(), n = b.length();
	int res[m+1][n+1];
	int trace[20][20];
	for (int i = 0; i < m+1; ++i)
	{
		for (int j = 0; j < n+1; ++j)
		{
			if(i==0||j==0)
				{
					res[i][j] = 0;	
					trace[i][j]=0;
				}
				
			else if(a[i-1]==b[j-1])
			{
				res[i][j] = 1 + res[i-1][j-1];
				trace[i][j]=1;			// 1 means trace the matrix in upper left diagonal direction.
			}
			else
			{
				if (res[i-1][j]>res[i][j-1])
				{
					res[i][j]=res[i-1][j];
					trace[i][j]=2;		// 2 means trace the matrix in upwards direction.
				}
				else
				{
					res[i][j]=res[i][j-1];
					trace[i][j]=3;		//  means trace the matrix in left direction.
				}	
			}
		}
	}
	Print(trace, m, n, a);
	return res[m][n];
}




int main()
{
	string a,b;
	cin>>a>>b;
	cout<<lcs(a,b);
	return 0;
}