## Longest Common Subsequence

QUESTION

Given two strings, find the longest common subsequence shared by the two.\n\nInput Format\n\nYou will be given two strings on two lines.\n\nOutput Format\n\nA single string which contains the longest common subsequence of characters in the two input strings.

``````#include <bits/stdc++.h>
using namespace std;
#define N 100

int L[N][N];

set<string> findLCS(string X, string Y, int m, int n)
{
set<string> s;
if (m == 0 || n == 0)
{
s.insert("");
return s;
}
if (X[m - 1] == Y[n - 1])
{
set<string> tmp = findLCS(X, Y, m - 1, n - 1);

for (string str : tmp)
s.insert(str + X[m - 1]);
}

else
{
if (L[m - 1][n] >= L[m][n - 1])
s = findLCS(X, Y, m - 1, n);

if (L[m][n - 1] >= L[m - 1][n])
{
set<string> tmp = findLCS(X, Y, m, n - 1);

s.insert(tmp.begin(), tmp.end());
}
}
return s;
}

int LCS(string X, string Y, int m, int n)
{
for (int i = 0; i <= m; i++)
{
for (int j = 0; j <= n; j++)
{
if (i == 0 || j == 0)
L[i][j] = 0;
else if (X[i - 1] == Y[j - 1])
L[i][j] = L[i - 1][j - 1] + 1;
else
L[i][j] = max(L[i - 1][j], L[i][j - 1]);
}
}
return L[m][n];
}
int main()
{
string X;
string Y;
cin >> X;
cin >> Y;
int m = X.length();
int n = Y.length();
LCS(X, Y, m, n);
set<string> s = findLCS(X, Y, m, n);
cout << "The Longest Common Subsequence is ";
for (string str : s){
cout << str << endl;
break;
}
return 0;
}``````