Question

15.4-1 -- Determine an LCS of (1, 0, 0, 1, 0, 1, 0, 1) and (0, 1, 0, 1, 1,0, 1, 1, 0)

4. -- Implement algorithm for finding LCS of any two binary strings x and y. Use it to find the LCS of two strings in 15.4-1

Answer 1

Code:

#include<iostream>
#include<algorithm>
using namespace std;
int main(){
string s1,s2;
cout<<"Enter first binary string\n";
cin>>s1;
cout<<"Enter second binary string\n";
cin>>s2;
//creating lcs array for dp
int lcs_array[s1.length()+1][s2.length()+1];
for(int i=0;i<=s1.length();i++){
for(int j=0;j<=s2.length();j++){
if(i==0 || j==0){
lcs_array[i][j]=0;
}
else if(s1[i-1]==s2[j-1]){
lcs_array[i][j]=lcs_array[i-1][j-1]+1;
}
else{
lcs_array[i][j]=max(lcs_array[i-1][j],lcs_array[i][j-1]);
}
}
}

string result="";
int i=s1.length(),j=s2.length();
while(i>0 && j>0){
if(s1[i-1]==s2[j-1]){
result+=s1[i-1];
i-=1;
j-=1;
}
else if(lcs_array[i-1][j]>lcs_array[i][j-1]){
i--;
}
else{
j--;
}

}
// as the answer we get from bottom up dp would be in reverse order
//thus by reversing we get the correct answer
reverse(result.begin(), result.end());
cout<<"The longest common subsequence is : "<<result<<endl;
}

Output:

Feel free to reach out to me in the comment in case of any doubt or clarification. I will be more than happy to reply.

Java Code:

import java.util.*;
public class lcs{
public static int max(int a,int b)
{
if(a>b)
return a;
else
return b;
}

public static void main(String []args){
String s1,s2;
Scanner sc=new Scanner(System.in);
System.out.println("Enter first binary string");
s1=sc.nextLine();
System.out.println("Enter second binary string");
s2=sc.nextLine();
//creating lcs array for dp
int lcs_array [][] = new int[s1.length()+1][s2.length()+1];
for(int i=0;i<=s1.length();i++){
for(int j=0;j<=s2.length();j++){
if(i==0 || j==0){
lcs_array[i][j]=0;
}
else if(s1.charAt(i-1)==s2.charAt(j-1)){
lcs_array[i][j]=lcs_array[i-1][j-1]+1;
}
else{
lcs_array[i][j]=max(lcs_array[i-1][j],lcs_array[i][j-1]);
}
}
}

String result="";
int i=s1.length(),j=s2.length();
while(i>0 && j>0){
if(s1.charAt(i-1)==s2.charAt(j-1)){
result+=s1.charAt(i-1);
i-=1;
j-=1;
}
else if(lcs_array[i-1][j]>lcs_array[i][j-1]){
i--;
}
else{
j--;
}
}
// as the answer we get from bottom up dp would be in reverse order
//thus by reversing we get the correct answer
StringBuilder b=new StringBuilder(result);
System.out.println("The longest common subsequence is : "+b.reverse().toString());
}
}

Output:

Select C:\Users\virus\Desktop\LCS.exe Enter first binary string 10010101 Enter second binary string 010110110 The longest common subsequence is : 010101 Process returned @ (exe) execution time : 14.099 s Press any key to continue.

Select C:\Users\virus\Desktop\LCS.exe Enter first binary string 10010101 Enter second binary string 010110110 The longest common subsequence is : 010101 Process returned @ (exe) execution time : 14.099 s Press any key to continue.

1. Result $javac lcs.java Sjava -Xmx128M -Xms 16M lcs Enter first binary string 10010101 Enter second binary string 010110110 The longest common subsequence is : 010101