[05 Feb 2020] Printing Longest Common Subsequence


Printing Longest Common Subsequence


Given two sequences, print the longest subsequence present in both of them.
Examples:
LCS for input Sequences “ABCDGH” and “AEDFHR” is “ADH” of length 3.
LCS for input Sequences “AGGTAB” and “GXTXAYB” is “GTAB” of length 4.
/* Dynamic Programming implementation of LCS problem */
#include<iostream>
#include<cstring>
#include<cstdlib>
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;
}
  
/* Driver program to test above function */
int main()
{
  char X[] = "AGGTAB";
  char Y[] = "GXTXAYB";
  int m = strlen(X);
  int n = strlen(Y);
  lcs(X, Y, m, n);
  return 0;
}
# Dynamic programming implementation of LCS problem
  
# Returns length of LCS for X[0..m-1], Y[0..n-1] 
def lcs(X, Y, m, n):
    L = [[0 for x in xrange(n+1)] for x in xrange(m+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 i in xrange(m+1):
        for j in xrange(n+1):
            if i == 0 or j == 0:
                L[i][j] = 0
            elif 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
    index = L[m][n]
  
    # Create a character array to store the lcs string
    lcs = [""] * (index+1)
    lcs[index] = ""
  
    # Start from the right-most-bottom-most corner and
    # one by one store characters in lcs[]
    i = m
    j = n
    while i > 0 and 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]
            i-=1
            j-=1
            index-=1
  
        # If not same, then find the larger of two and
        # go in the direction of larger value
        elif L[i-1][j] > L[i][j-1]:
            i-=1
        else:
            j-=1
  
    print "LCS of " + X + " and " + Y + " is " + "".join(lcs) 
  
# Driver program
X = "AGGTAB"
Y = "GXTXAYB"
m = len(X)
n = len(Y)
lcs(X, Y, m, n)
  
# This code is contributed by BHAVYA JAIN

Output:
LCS of AGGTAB and GXTXAYB is GTAB


















































































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