Like Fibonacci numbers, a Fibonacci word. is a specific sequence of binary digits (or symbols from any two-letter alphabet). The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci numbers are formed by repeated addition. But unlike the fibonacci number, Fibonacci word has its first two terms different from each other.
In Fibonacci word, S(0) = 0, S(1) = 01, S(2) = 010, S(3) = 01001 ..... where S(n) = S(n-1) + S(n-2) and + represents the concatenation of strings.
The task is to find nth Fibonacci word for a given number n.
Examples:
Input : n = 4 Output : S(4) = 01001010 Input : n = 2 Output : S(2) = 010
Just like in program of Fibonacci number, we use the iterative concept of finding nth Fibonacci number here for finding nth Fibonacci word we can use the iterative concept. So for finding n-th Fibonacci word we will take two string Sn and Sn_1 which represent S(n) and S(n-1) respectively and on each iteration we will update tmp = Sn, Sn = Sn + Sn_1 and Sn_1 = tmp in this way we can find nth fibonacci word.
Implementation:
// program for nth Fibonacci word #include<bits/stdc++.h> using namespace std;
// Returns n-th Fibonacci word string fibWord( int n)
{ string Sn_1 = "0" ;
string Sn = "01" ;
string tmp;
for ( int i=2; i<=n; i++)
{
tmp = Sn;
Sn += Sn_1;
Sn_1 = tmp;
}
return Sn;
} // driver program int main()
{ int n = 6;
cout << fibWord(n);
return 0;
} |
// Java program for nth Fibonacci word import java.util.*;
class Eulerian
{ // Returns n-th Fibonacci word
public static String fibWord( int n)
{
String Sn_1 = "0" ;
String Sn = "01" ;
String tmp;
for ( int i= 2 ; i<=n; i++)
{
tmp = Sn;
Sn += Sn_1;
Sn_1 = tmp;
}
return Sn;
}
// driver code
public static void main(String[] args)
{
int n = 6 ;
System.out.print(fibWord(n));
}
} // This code is contributed by rishabh_jain |
# Python3 program for nth Fibonacci word # Returns n-th Fibonacci word def fibWord(n):
Sn_1 = "0"
Sn = "01"
tmp = ""
for i in range ( 2 , n + 1 ):
tmp = Sn
Sn + = Sn_1
Sn_1 = tmp
return Sn
# driver program n = 6
print (fibWord(n))
# This code is contributed by Sachin Bisht |
// C# program for nth Fibonacci word using System;
class GFG
{ // Returns n-th Fibonacci word
public static String fibWord( int n)
{
String Sn_1 = "0" ;
String Sn = "01" ;
String tmp;
for ( int i = 2; i <= n; i++)
{
tmp = Sn;
Sn += Sn_1;
Sn_1 = tmp;
}
return Sn;
}
// Driver code
public static void Main()
{
int n = 6;
Console.WriteLine(fibWord(n));
}
} // This code is contributed by vt_m |
<script> // program for nth Fibonacci word // Returns n-th Fibonacci word function fibWord(n)
{ var Sn_1 = "0" ;
var Sn = "01" ;
var tmp;
for ( var i = 2; i <= n; i++)
{
tmp = Sn;
Sn += Sn_1;
Sn_1 = tmp;
}
return Sn;
} // driver program var n = 6;
document.write( fibWord(n)); // This code is contributed by noob2000. </script> |
010010100100101001010