查找龙曲线序列的第n个项

龙曲线序列是一个0和1的无限二进制序列。序列的第一项是1。
从下一项开始，我们在上一项的每个元素之间交替插入1和0。
为了更好地理解，请参考以下说明：

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

这也被称为常规折纸顺序。给定自然数n 。任务是找到由龙形曲线形成的第n个字符串，其长度为$2^n - 1$ 。

例子：

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

方法：从第一个术语1开始。然后在前一个术语的每个元素之后交替添加1和0。获得的新术语将成为当前术语。从1到n的循环中重复此过程，以生成每个项，最后生成第n个项。

下面是上述想法的实现：

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

输出：

110110011100100