Length of longest Fibonacci subarray
Given an array arr[] of integer elements, the task is to find the length of the largest sub-array of arr[] such that all the elements of the sub-array are Fibonacci numbers.
Examples:
Input: arr[] = {11, 8, 21, 5, 3, 28, 4}
Output: 4
Explanation:
Maximum length sub-array with all elements as Fibonacci number is {8, 21, 5, 3}.Input: arr[] = {25, 100, 36}
Output: 0
Approach: This problem can be solved by traversing through the array arr[]. Follow the steps below to solve this problem.
- Initialize variables say, max_length and current_length as 0 to store the maximum length of the sub-array and the current length of the sub-array such that every element in the sub-array is Fibonacci number.
- Iterate in the range [0, N-1] using the variable i:
- If the current number is a Fibonacci number then increment current_length by 1, otherwise, set current_length as 0.
- Now, assign max_length as maximum of the current_length and max_length.
- After completing the above steps, print max_length as the required answer.
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <bits/stdc++.h> using namespace std; // A utility function that returns // true if x is perfect square bool isPerfectSquare( int x) { int s = sqrt (x); return (s * s == x); } // Returns true if n is a // Fibonacci Number, else false bool isFibonacci( int n) { // Here n is Fibinac ci if one of 5*n*n + 4 // or 5*n*n - 4 or both is a perfect square return isPerfectSquare(5 * n * n + 4) || isPerfectSquare(5 * n * n - 4); } // Function to find the length of the // largest sub-array of an array every // element of whose is a Fibonacci number int contiguousFibonacciNumber( int arr[], int n) { int current_length = 0; int max_length = 0; // Traverse the array arr[] for ( int i = 0; i < n; i++) { // Check if arr[i] is a Fibonacci number if (isFibonacci(arr[i])) { current_length++; } else { current_length = 0; } // Stores the maximum length of the // Fibonacci number subarray max_length = max(max_length, current_length); } // Finally, return the maximum length return max_length; } // Driver code int main() { // Given Input int arr[] = { 11, 8, 21, 5, 3, 28, 4}; int n = sizeof (arr) / sizeof (arr[0]); // Function Call cout << contiguousFibonacciNumber(arr, n); return 0; } |
Java
/*package whatever //do not write package name here */ import java.io.*; class GFG { // A utility function that returns // true if x is perfect square public static boolean isPerfectSquare( int x) { int s =( int ) Math.sqrt(x); return (s * s == x); } // Returns true if n is a // Fibonacci Number, else false public static boolean isFibonacci( int n) { // Here n is Fibonacci if one of 5*n*n + 4 // or 5*n*n - 4 or both is a perfect square return isPerfectSquare( 5 * n * n + 4 ) || isPerfectSquare( 5 * n * n - 4 ); } // Function to find the length of the // largest sub-array of an array every // element of whose is a Fibonacci number public static int contiguousFibonacciNumber( int arr[], int n) { int current_length = 0 ; int max_length = 0 ; // Traverse the array arr[] for ( int i = 0 ; i < n; i++) { // Check if arr[i] is a Fibonacci number if (isFibonacci(arr[i])) { current_length++; } else { current_length = 0 ; } // Stores the maximum length of the // Fibonacci number subarray max_length = Math.max(max_length, current_length); } // Finally, return the maximum length return max_length; } // Driver code public static void main (String[] args) { // Given Input int arr[] = { 11 , 8 , 21 , 5 , 3 , 28 , 4 }; int n = arr.length; // Function Call System.out.println( contiguousFibonacciNumber(arr, n)); } } // This code is contributed by Potta Lokesh |
Python3
# Python3 program for the above approach import math # A utility function that returns # true if x is perfect square def isPerfectSquare(x): s = int (math.sqrt(x)) if s * s = = x: return True else : return False # Returns true if n is a # Fibonacci Number, else false def isFibonacci(n): # Here n is fibonacci if one of 5*n*n+4 # or 5*n*n-4 or both is a perfect square return (isPerfectSquare( 5 * n * n + 4 ) or isPerfectSquare( 5 * n * n - 4 )) # Function to find the length of the # largest sub-array of an array every # element of whose is a Fibonacci number def contiguousFibonacciNumber(arr, n): current_length = 0 max_length = 0 # Traverse the array arr for i in range ( 0 , n): # Check if arr[i] is a Fibonacci number if isFibonacci(arr[i]): current_length + = 1 else : current_length = 0 # stores the maximum length of the # Fibonacci number subarray max_length = max (max_length, current_length) # Finally, return the maximum length return max_length # Driver code if __name__ = = '__main__' : # Given Input arr = [ 11 , 8 , 21 , 5 , 3 , 28 , 4 ] n = len (arr) # Function Call print (contiguousFibonacciNumber(arr, n)) # This code is contributed by MuskanKalra1 |
C#
// C# program for the above approach using System; using System.Collections.Generic; class GFG{ // A utility function that returns // true if x is perfect square static bool isPerfectSquare( int x) { int s = ( int )Math.Sqrt(x); return (s * s == x); } // Returns true if n is a // Fibonacci Number, else false static bool isFibonacci( int n) { // Here n is Fibonacci if one of 5*n*n + 4 // or 5*n*n - 4 or both is a perfect square return isPerfectSquare(5 * n * n + 4) || isPerfectSquare(5 * n * n - 4); } // Function to find the length of the // largest sub-array of an array every // element of whose is a Fibonacci number static int contiguousFibonacciNumber( int []arr, int n) { int current_length = 0; int max_length = 0; // Traverse the array arr[] for ( int i = 0; i < n; i++) { // Check if arr[i] is a Fibonacci number if (isFibonacci(arr[i])) { current_length++; } else { current_length = 0; } // Stores the maximum length of the // Fibonacci number subarray max_length = Math.Max(max_length, current_length); } // Finally, return the maximum length return max_length; } // Driver code public static void Main() { // Given Input int []arr = { 11, 8, 21, 5, 3, 28, 4 }; int n = arr.Length; // Function Call Console.Write(contiguousFibonacciNumber(arr, n)); } } // This code is contributed by SURENDRA_GANGWAR |
Javascript
<script> // JavaScript program for the above approach // A utility function that returns // true if x is perfect square function isPerfectSquare(x) { let s = parseInt(Math.sqrt(x)); return (s * s == x); } // Returns true if n is a // Fibonacci Number, else false function isFibonacci(n) { // Here n is Fibonacci if one of 5*n*n + 4 // or 5*n*n - 4 or both is a perfect square return isPerfectSquare(5 * n * n + 4) || isPerfectSquare(5 * n * n - 4); } // Function to find the length of the // largest sub-array of an array every // element of whose is a Fibonacci number function contiguousFibonacciNumber(arr, n) { let current_length = 0; let max_length = 0; // Traverse the array arr[] for (let i = 0; i < n; i++) { // Check if arr[i] is a Fibonacci number if (isFibonacci(arr[i])) { current_length++; } else { current_length = 0; } // Stores the maximum length of the // Fibonacci number subarray max_length = Math.max(max_length, current_length); } // Finally, return the maximum length return max_length; } // Driver code // Given Input let arr = [11, 8, 21, 5, 3, 28, 4]; let n = arr.length; // Function Call document.write(contiguousFibonacciNumber(arr, n)); // This code is contributed by Potta Lokesh </script> |
Output
4
Time Complexity: O(N)
Auxiliary Space: O(1)