# Find nth term of the Dragon Curve Sequence

Dragon Curve Sequence is an infinite binary sequence of 0s and 1s. The first term of the sequence is 1.
From the next term, we alternately insert 1 and 0 between each element of the previous term.
To understand better refer the following explanations:

The first few terms are:

• 1 (starts with 1)
• “1” 1 “0”
1 and 0 are inserted alternately to the left and right of the previous term. Here the number in the double quotes represents the newly added elements.

So the second term becomes
1 1 0

• “1” 1 “0” 1 “1” 0 “0”
So the third term becomes
1 1 0 1 1 0 0
• “1” 1 “0” 1 “1” 0 “0” 1 “1” 1 “0” 0 “1” 0 “0”
The fourth term becomes
1 1 0 1 1 0 0 1 1 1 0 0 1 0 0

This is also popularly known as the regular paperfolding sequence. Given a natural number n. The task is to find the nth string formed by Dragon Curve sequence of length .

Examples:

```Input: n = 4
Output: 110110011100100
Explanation:
We get 1 as the first term,
"110" as the second term,
"1101100" as the third term ,
And hence our fourth term will be
"110110011100100"

Input: n = 3
Output: 1101100
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Start with the first term 1. Then add 1 and 0 alternately after each element of the preceding term. The new term obtained becomes the current term. Repeat the process in a loop from 1 to n to generate each term and finally the nth term.

Below is the implementation of above idea:

## C++

 `// CPP code to find nth term ` `// of the Dragon Curve Sequence ` `#include ` `using` `namespace` `std; ` ` `  `// function to generate the nth term ` `string Dragon_Curve_Sequence(``int` `n)  ` `{ ` `    ``// first term ` `    ``string s = ``"1"``;  ` ` `  `    ``// generating each term of the sequence ` `    ``for` `(``int` `i = 2; i <= n; i++)  ` `    ``{ ` `        ``string temp = ``"1"``; ` `        ``char` `prev = ``'1'``, zero = ``'0'``, one = ``'1'``; ` ` `  `        ``// loop to generate the ith term ` `        ``for` `(``int` `j = 0; j < s.length(); j++)  ` `        ``{ ` `            ``// add character from the  ` `            ``// original string ` `            ``temp += s[j]; ` ` `  `            ``// add alternate 0 and 1 in between ` `            ``if` `(prev == ``'0'``)  ` `            ``{ ` `                ``// if previous added term ` `                ``// was '0' then add '1' ` `                ``temp += one; ` ` `  `                ``// now current term becomes ` `                ``// previous term ` `                ``prev = one; ` `            ``} ` `            ``else`  `            ``{ ` `                ``// if previous added term ` `                ``// was '1', then add '0' ` `                ``temp += zero; ` ` `  `                ``// now current term becomes ` `                ``// previous term ` `                ``prev = zero; ` `            ``} ` `        ``} ` `         `  `        ``// s becomes the ith term of the sequence ` `        ``s = temp; ` `    ``} ` `    ``return` `s; ` `} ` ` `  `// Driver program ` `int` `main() ` `{ ` `    ``// Taking inputs ` `    ``int` `n = 4; ` ` `  `    ``// generate nth term of dragon curve sequence ` `    ``string s = Dragon_Curve_Sequence(n); ` `     `  `    ``// Printing output ` `    ``cout << s << ``"\n"``; ` `} `

## Java

 `// Java code to find nth term ` `// of the Dragon Curve Sequence ` `import` `java.util.*; ` ` `  `class` `solution ` `{ ` ` `  `// function to generate the nth term ` `static` `String Dragon_Curve_Sequence(``int` `n)  ` `{ ` `    ``// first term ` `    ``String s = ``"1"``;  ` ` `  `    ``// generating each term of the sequence ` `    ``for` `(``int` `i = ``2``; i <= n; i++)  ` `    ``{ ` `        ``String temp = ``"1"``; ` `        ``char` `prev = ``'1'``, zero = ``'0'``, one = ``'1'``; ` ` `  `        ``// loop to generate the ith term ` `        ``for` `(``int` `j = ``0``; j < s.length(); j++)  ` `        ``{ ` `            ``// add character from the  ` `            ``// original string ` `            ``temp += s.charAt(j); ` ` `  `            ``// add alternate 0 and 1 in between ` `            ``if` `(prev == ``'0'``)  ` `            ``{ ` `                ``// if previous added term ` `                ``// was '0' then add '1' ` `                ``temp += one; ` ` `  `                ``// now current term becomes ` `                ``// previous term ` `                ``prev = one; ` `            ``} ` `            ``else`  `            ``{ ` `                ``// if previous added term ` `                ``// was '1', then add '0' ` `                ``temp += zero; ` ` `  `                ``// now current term becomes ` `                ``// previous term ` `                ``prev = zero; ` `            ``} ` `        ``} ` `         `  `        ``// s becomes the ith term of the sequence ` `        ``s = temp; ` `    ``} ` `    ``return` `s; ` `} ` ` `  `// Driver program ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``// Taking inputs ` `    ``int` `n = ``4``; ` ` `  `    ``// generate nth term of dragon curve sequence ` `    ``String s = Dragon_Curve_Sequence(n); ` `     `  `    ``// Printing output ` `    ``System.out.println(s); ` `} ` ` `  `} ` ` `  `//This code is contributed by  ` `//Surendra_Gangwar `

## Python

 `# Python code to find nth term ` `# of the Dragon Curve Sequence ` ` `  `# function to generate  ` `# the nth term ` `def` `Dragon_Curve_Sequence(n): ` `     `  `    ``# first term ` `    ``s ``=` `"1"` ` `  `    ``# generating each term ` `    ``# of the sequence ` `    ``for` `i ``in` `range``(``2``, n ``+` `1``): ` `        ``temp ``=` `"1"` `        ``prev ``=` `'1'` `        ``zero ``=` `'0'` `        ``one ``=` `'1'` ` `  `        ``# loop to generate the ith term ` `        ``for` `j ``in` `range``(``len``(s)): ` `             `  `            ``# add character from the ` `            ``# original string ` `            ``temp ``+``=` `s[j] ` ` `  `            ``# add alternate 0 and  ` `            ``# 1 in between ` `            ``if` `(prev ``=``=` `'0'``): ` `                 `  `                ``# if previous added term ` `                ``# was '0' then add '1' ` `                ``temp ``+``=` `one ` ` `  `                ``# now current term becomes ` `                ``# previous term ` `                ``prev ``=` `one ` ` `  `            ``else``: ` `                 `  `                ``# if previous added term ` `                ``# was '1', then add '0' ` `                ``temp ``+``=` `zero ` ` `  `                ``# now current term becomes ` `                ``# previous term ` `                ``prev ``=` `zero ` ` `  `        ``# s becomes the ith term ` `        ``# of the sequence ` `        ``s ``=` `temp ` ` `  `    ``return` `s ` ` `  `# Driver Code ` `n ``=` `4` ` `  `# generate nth term of  ` `# dragon curve sequence ` `s ``=` `Dragon_Curve_Sequence(n) ` ` `  `# Printing output ` `print``(s) ` ` `  `# This code is contributed by ` `# Sanjit_Prasad `

## C#

 `// C# code to find nth term  ` `// of the Dragon Curve Sequence  ` `using` `System; ` ` `  `class` `GFG ` `{  ` ` `  `// function to generate the nth term  ` `static` `String Dragon_Curve_Sequence(``int` `n)  ` `{  ` `    ``// first term  ` `    ``String s = ``"1"``;  ` ` `  `    ``// generating each term of the sequence  ` `    ``for` `(``int` `i = 2; i <= n; i++)  ` `    ``{  ` `        ``String temp = ``"1"``;  ` `        ``char` `prev = ``'1'``, zero = ``'0'``, one = ``'1'``;  ` ` `  `        ``// loop to generate the ith term  ` `        ``for` `(``int` `j = 0; j < s.Length; j++)  ` `        ``{  ` `            ``// add character from the  ` `            ``// original string  ` `            ``temp += s[j];  ` ` `  `            ``// add alternate 0 and 1 in between  ` `            ``if` `(prev == ``'0'``)  ` `            ``{  ` `                ``// if previous added term  ` `                ``// was '0' then add '1'  ` `                ``temp += one;  ` ` `  `                ``// now current term becomes  ` `                ``// previous term  ` `                ``prev = one;  ` `            ``}  ` `            ``else` `            ``{  ` `                ``// if previous added term  ` `                ``// was '1', then add '0'  ` `                ``temp += zero;  ` ` `  `                ``// now current term becomes  ` `                ``// previous term  ` `                ``prev = zero;  ` `            ``}  ` `        ``}  ` ` `  `        ``// s becomes the ith term of the sequence  ` `        ``s = temp;  ` `    ``}  ` `    ``return` `s;  ` `}  ` ` `  `// Driver Code ` `public` `static` `void` `Main()  ` `{  ` `    ``// Taking inputs  ` `    ``int` `n = 4;  ` ` `  `    ``// generate nth term of dragon ` `    ``// curve sequence  ` `    ``String s = Dragon_Curve_Sequence(n);  ` ` `  `    ``// Printing output  ` `    ``Console.WriteLine(s);  ` `}  ` `}  ` ` `  `// This code is contributed by Rajput-Ji `

## PHP

 ` `

Output:

```110110011100100
```

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