ELEMENTS OF LCS

I have recently learnt how to find the length of the longest common subsequence of two strings, but cannot understand how can I print the elements of the LCS. For example, if the strings are “AASDGX” and “AAWD”, then the output will be “AAD” Please help!

#include
#include
#include
using namespace std;

/* Returns length of LCS for X[0..m-1], Y[0..n-1] */
void lcs( char *X, char *Y, int m, int n )
{
	   int L[m+1][n+1];
 
   	/* Following steps build L[m+1][n+1] in bottom up fashion. Note
      	that L[i][j] contains length of LCS of X[0..i-1] and Y[0..j-1] */
   	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]);
     	}
   	}
 
   	// Following code is used to print LCS
   	int index = L[m][n];
 
   	// Create a character array to store the lcs string
   	char lcs[index+1];
   	lcs[index] = '\0'; // Set the terminating character
 
   	// Start from the right-most-bottom-most corner and
   	// one by one store characters in lcs[]
   	int i = m, j = n;
   	while (i > 0 && j > 0)
   	{
      	// If current character in X[] and Y are same, then
      	// current character is part of LCS
      	if (X[i-1] == Y[j-1])
      	{
          	lcs[index-1] = X[i-1]; // Put current character in result
          	i--; j--; index--;     // reduce values of i, j and index
      	}
 
      	// If not same, then find the larger of two and
      	// go in the direction of larger value
      	else if (L[i-1][j] > L[i][j-1])
         	i--;
      	else
         	j--;
   	}
 
   	// Print the lcs
   	cout << "LCS of " << X << " and " << Y << " is " << lcs;
}
 
int main()
{
  	char X[] = "AASDGX";
  	char Y[] = "AAWD";
  	
  	int m = strlen(X);
  	int n = strlen(Y);
  	
  	lcs(X, Y, m, n);
  	
  	return 0;
}

Link to this code.

Thanks a lot!! It was exactly what I required

@anupam_datta welcome :slight_smile:

https://uva.onlinejudge.org/index.php?option=onlinejudge&page=show_problem&problem=1346

3 Likes
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