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++ 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;
} |
/*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 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# 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 |
<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>
|
4
Time Complexity: O(N)
Auxiliary Space: O(1)