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
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However, this approach is obsolete for large numbers as it takes too much time.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 [2K – 1, 2K – 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 = 2K - 1 right_index = 2K - 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; } |
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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 |
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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 = 4printLevel(K) # This code is contributed by shivanisinghss2110 |
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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 |
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Output:
13 21 34 55 89 144 233 377
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