Find the numbers present at Kth level of a Fibonacci Binary Tree

Given a number K, the task is to print the fibonacci numbers present at Kth level of a Fibonacci Binary Tree.

Examples:

Input: K = 3
Output: 2, 3, 5, 8
Explanation:
Fibonacci Binary Tree for 3 levels:
        0
       / \
      1   1
     /\  / \
    2  3 5  8
Numbers present at level 3: 2, 3, 5, 8

Input: K = 2
Output: 1, 1
Explanation:
Fibonacci Binary Tree for 2 levels:
        0
       / \
      1   1
Numbers present at level 2: 1, 1

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

Naive Approach: The naive approach is to build a Fibonacci Binary Tree (binary tree of Fibonacci numbers) and then get elements at a particular level K.
However, this approach is obsolete for large numbers as it takes too much time.

Efficient approach: Since the elements which would be present at some arbitrary level K of the tree can be found by finding the elements in the range [2^{K – 1}, 2^K – 1]. Therefore:

Find the Fibonacci numbers up to 10⁶ using Dynamic Programming and store them in an array.
Calculate the left_index and right_index of the level as:
```
left_index = 2^{K - 1} 
right_index = 2^K - 1
```
Print the fibonacci numbers from left_index to right_index of fibonacci array.

Below is the implementation of the above approach:

C++

// C++ program to print the Fibonacci numbers 
// present at K-th level of a Binary Tree 
  
#include <bits/stdc++.h> 
using namespace std; 
  
// Initializing the max value 
#define MAX_SIZE 100005 
  
// Array to store all the 
// fibonacci numbers 
int fib[MAX_SIZE + 1]; 
  
// Function to generate fibonacci numbers 
// using Dynamic Programming 
void fibonacci() 
{ 
    int i; 
  
    // 0th and 1st number of the series 
    // are 0 and 1 
    fib[0] = 0; 
    fib[1] = 1; 
  
    for (i = 2; i <= MAX_SIZE; i++) { 
  
        // Add the previous two numbers in the 
        // series and store it 
        fib[i] = fib[i - 1] + fib[i - 2]; 
    } 
} 
  
// Function to print the Fibonacci numbers 
// present at Kth level of a Binary Tree 
void printLevel(int level) 
{ 
    // Finding the left and right index 
    int left_index = pow(2, level - 1); 
    int right_index = pow(2, level) - 1; 
  
    // Iterating and printing the numbers 
    for (int i = left_index; 
         i <= right_index; i++) { 
  
        cout << fib[i - 1] << " "; 
    } 
    cout << endl; 
} 
  
// Driver code 
int main() 
{ 
    // Precomputing Fibonacci numbers 
    fibonacci(); 
  
    int K = 4; 
    printLevel(K); 
  
    return 0; 
} 

Java

// Java program to print the Fibonacci numbers 
// present at K-th level of a Binary Tree 
import java.util.*; 
  
class GFG{ 
   
// Initializing the max value 
static final int MAX_SIZE = 100005; 
   
// Array to store all the 
// fibonacci numbers 
static int []fib = new int[MAX_SIZE + 1]; 
   
// Function to generate fibonacci numbers 
// using Dynamic Programming 
static void fibonacci() 
{ 
    int i; 
   
    // 0th and 1st number of the series 
    // are 0 and 1 
    fib[0] = 0; 
    fib[1] = 1; 
   
    for (i = 2; i <= MAX_SIZE; i++) { 
   
        // Add the previous two numbers in the 
        // series and store it 
        fib[i] = fib[i - 1] + fib[i - 2]; 
    } 
} 
   
// Function to print the Fibonacci numbers 
// present at Kth level of a Binary Tree 
static void printLevel(int level) 
{ 
    // Finding the left and right index 
    int left_index = (int) Math.pow(2, level - 1); 
    int right_index = (int) (Math.pow(2, level) - 1); 
   
    // Iterating and printing the numbers 
    for (int i = left_index; 
         i <= right_index; i++) { 
   
        System.out.print(fib[i - 1]+ " "); 
    } 
    System.out.println(); 
} 
   
// Driver code 
public static void main(String[] args) 
{ 
    // Precomputing Fibonacci numbers 
    fibonacci(); 
   
    int K = 4; 
    printLevel(K); 
} 
} 
  
// This code is contributed by Rajput-Ji 

Python3

# Python program to print the Fibonacci numbers 
# present at K-th level of a Binary Tree 
  
# Initializing the max value 
MAX_SIZE = 100005
  
# Array to store all the 
# fibonacci numbers 
fib =[0]*(MAX_SIZE + 1) 
  
# Function to generate fibonacci numbers 
# using Dynamic Programming 
def fibonacci(): 
      
    # 0th and 1st number of the series 
    # are 0 and 1 
    fib[0] = 0
    fib[1] = 1
      
    for i in range(2, MAX_SIZE + 1): 
          
        # Add the previous two numbers in the 
        # series and store it 
        fib[i] = fib[i - 1] + fib[i - 2] 
          
# Function to print the Fibonacci numbers 
# present at Kth level of a Binary Tree 
def printLevel(level): 
      
    # Finding the left and right index 
    left_index = pow(2, level - 1) 
    right_index = pow(2, level) - 1
      
    # Iterating and printing the numbers 
    for i in range(left_index, right_index+1): 
        print(fib[i - 1],end=" ") 
          
    print() 
  
# Driver code 
  
# Precomputing Fibonacci numbers 
fibonacci() 
  
K = 4
printLevel(K) 
  
# This code is contributed by shivanisinghss2110 

C#

// C# program to print the Fibonacci numbers  
// present at K-th level of a Binary Tree  
using System; 
  
class GFG{  
      
    // Initializing the max value  
    static int MAX_SIZE = 100005;  
      
    // Array to store all the  
    // fibonacci numbers  
    static int []fib = new int[MAX_SIZE + 1];  
      
    // Function to generate fibonacci numbers  
    // using Dynamic Programming  
    static void fibonacci()  
    {  
        int i;  
      
        // 0th and 1st number of the series  
        // are 0 and 1  
        fib[0] = 0;  
        fib[1] = 1;  
      
        for (i = 2; i <= MAX_SIZE; i++) {  
      
            // Add the previous two numbers in the  
            // series and store it  
            fib[i] = fib[i - 1] + fib[i - 2];  
        }  
    }  
      
    // Function to print the Fibonacci numbers  
    // present at Kth level of a Binary Tree  
    static void printLevel(int level)  
    {  
        // Finding the left and right index  
        int left_index = (int) Math.Pow(2, level - 1);  
        int right_index = (int) (Math.Pow(2, level) - 1);  
      
        // Iterating and printing the numbers  
        for (int i = left_index;  
            i <= right_index; i++) {  
      
            Console.Write(fib[i - 1]+ " ");  
        }  
            Console.WriteLine();  
    }  
      
    // Driver code  
    public static void Main(string[] args)  
    {  
        // Precomputing Fibonacci numbers  
        fibonacci();  
      
        int K = 4;  
        printLevel(K);  
    }  
}  
  
// This code is contributed by Yash_R 

Output:

13 21 34 55 89 144 233 377

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My Personal Notes

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

C++

Java

Python3

C#

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