Like Fibonacci word, a Tribonacci word. is a specific sequence of digits. The Tribonacci word is formed by repeated concatenation in the same way that the Fibonacci word is formed by repeated addition. But unlike the fibonacci word, Tribonacci word is formed by repeated addition of last three terms and it has its first three terms different from each other.
In Tribonacci word,
S(0) = 1,
S(1) = 12,
S(2) = 1213,
S(3) = 1213121
.....
where S(n) = S(n-1) + S(n-2) + S(n-3) and +
represents the concatenation of
strings.
The task is to find nth Tribonacci word for a given number n.
Examples:
Input : n = 4
Output : S(4) = 1213121121312
Input : n = 3
Output : S(3) = 1213121
Just like in program of Fibonacci word, we use the iterative concept of finding nth Fibonacci word here for finding nth Tribonacci word we can use the iterative concept. So for finding nth Tribonacci word we will take three string Sn_1, Sn_2 and Sn_3 which represent S(n-1), S(n-2) and S(n-3) respectively and on each iteration we will update tmp = Sn_3, Sn_3 = Sn_3 + Sn_2 + Sn_1, Sn_1 = Sn_2 and Sn_2 = tmp in this way we can find nth tribonacci word.
Implementation:
C++
#include <bits/stdc++.h>
using namespace std;
string tribWord( int n) {
string Sn_1 = "1" ;
string Sn_2 = "12" ;
string Sn_3 = "1213" ;
string tmp;
for ( int i = 3; i <= n; i++) {
tmp = Sn_3;
Sn_3 += (Sn_2 + Sn_1);
Sn_1 = Sn_2;
Sn_2 = tmp;
}
return Sn_3;
}
int main() {
int n = 6;
cout << tribWord(n);
return 0;
}
|
Java
class GFG {
static String tribWord( int n) {
String Sn_1 = "1" ;
String Sn_2 = "12" ;
String Sn_3 = "1213" ;
String tmp;
for ( int i = 3 ; i <= n; i++) {
tmp = Sn_3;
Sn_3 += (Sn_2 + Sn_1);
Sn_1 = Sn_2;
Sn_2 = tmp;
}
return Sn_3;
}
public static void main(String[] args) {
int n = 6 ;
System.out.print(tribWord(n));
}
}
|
Python3
def tribWord(n):
Sn_1 = "1"
Sn_2 = "12"
Sn_3 = "1213"
for i in range ( 3 , n + 1 ):
tmp = Sn_3
Sn_3 + = (Sn_2 + Sn_1)
Sn_1 = Sn_2
Sn_2 = tmp
return Sn_3
n = 6
print (tribWord(n))
|
C#
using System;
class GFG {
static string tribWord( int n)
{
string Sn_1 = "1" ;
string Sn_2 = "12" ;
string Sn_3 = "1213" ;
string tmp;
for ( int i = 3; i <= n; i++) {
tmp = Sn_3;
Sn_3 += (Sn_2 + Sn_1);
Sn_1 = Sn_2;
Sn_2 = tmp;
}
return Sn_3;
}
public static void Main() {
int n = 6;
Console.WriteLine(tribWord(n));
}
}
|
PHP
<?php
function tribWord( $n )
{
$Sn_1 = "1" ;
$Sn_2 = "12" ;
$Sn_3 = "1213" ;
$tmp ;
for ( $i = 3; $i <= $n ; $i ++)
{
$tmp = $Sn_3 ;
$Sn_3 .= ( $Sn_2 . $Sn_1 );
$Sn_1 = $Sn_2 ;
$Sn_2 = $tmp ;
}
return $Sn_3 ;
}
$n = 6;
echo tribWord( $n );
?>
|
Javascript
<script>
function tribWord(n) {
var Sn_1 = "1" ;
var Sn_2 = "12" ;
var Sn_3 = "1213" ;
var tmp;
for ( var i = 3; i <= n; i++) {
tmp = Sn_3;
Sn_3 += (Sn_2 + Sn_1);
Sn_1 = Sn_2;
Sn_2 = tmp;
}
return Sn_3;
}
var n = 6;
document.write( tribWord(n));
</script>
|
Output
12131211213121213121121312131211213121213121
Time Complexity: O(n), where n is the given input.
Auxiliary Space: O(n), where n is the given input.
Last Updated :
21 Nov, 2022
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