Given an array of N elements, the task is to find the longest subarray which is Fibonacci-like.
A Fibonacci-like sub-array is defined as an array in which:
A[i]=A[i-1]+A[i-2] where i>2 and, A[1] and A[2] can be anything.
Examples:
Input : N = 5, arr[] = {2, 4, 6, 10, 2}
Output : 4
The sub-array 2, 4, 6, 10 is Fibonacci like.
Input : N = 3, arr[] = {0, 0, 0}
Output : 3
The entire array is Fibonacci-like.
Approach:
The idea is to observe that any array of length of less than or equal to 2 is Fibonacci-like. Now, for arrays of length greater than 2:
- Maintain a variable len initialized to 2 and a variable mx to store the maximum length so far.
- Start traversing the array from 3rd index.
- If the fibonacci like array can be extended for this index, i.e. if a[i] = a[i-1] + a[i-2]
- Then increment the value of variable len by 1.
- Otherwise reinitialize the variable len to 2.
- Store the maximum of mx and len in the variable mx for current iteration.
Below is the implementation of the above approach:
C++
// C++ program to find length of longest// Fibonacci-like subarray#include <bits/stdc++.h>using namespace std;// Function to find the length of the // longest Fibonacci-like subarrayint longestFibonacciSubarray(int n, int a[]){ // Any 2 terms are Fibonacci-like if (n <= 2) return n; int len = 2; int mx = INT_MIN; for (int i = 2; i < n; i++) { // If previous subarray can be extended if (a[i] == a[i - 1] + a[i - 2]) len++; // Any 2 terms are Fibonacci-like else len = 2; // Find the maximum length mx = max(mx, len); } return mx;}// Driver Codeint main(){ int n = 5; int a[] = {2, 4, 6, 10, 2}; cout << longestFibonacciSubarray(n, a); return 0;} |
Java
// Java program to find length of longest // Fibonacci-like subarray class GFG { // Function to find the length of the // longest Fibonacci-like subarray static int longestFibonacciSubarray(int n, int a[]) { // Any 2 terms are Fibonacci-like if (n <= 2) return n; int len = 2; int mx = Integer.MIN_VALUE; for (int i = 2; i < n; i++) { // If previous subarray can be extended if (a[i] == a[i - 1] + a[i - 2]) len++; // Any 2 terms are Fibonacci-like else len = 2; // Find the maximum length mx = Math.max(mx, len); } return mx; } // Driver Code public static void main (String[] args) { int n = 5; int a[] = {2, 4, 6, 10, 2}; System.out.println(longestFibonacciSubarray(n, a)); } }// This code is contributed by Ryuga |
Python3
# Python3 program to find Length of # longest Fibonacci-like subarray# Function to find the Length of the # longest Fibonacci-like subarraydef longestFibonacciSubarray(n, a): # Any 2 terms are Fibonacci-like if (n <= 2): return n Len = 2 mx = -10**9 for i in range(2, n): # If previous subarray can be extended if (a[i] == a[i - 1] + a[i - 2]): Len += 1 # Any 2 terms are Fibonacci-like else: Len = 2 # Find the maximum Length mx = max(mx, Len) return mx# Driver Coden = 5a = [2, 4, 6, 10, 2]print(longestFibonacciSubarray(n, a))# This code is contributed by Mohit Kumar |
C#
// C# program to find length of longest // Fibonacci-like subarray using System;class GFG { // Function to find the length of the // longest Fibonacci-like subarray static int longestFibonacciSubarray(int n, int[] a) { // Any 2 terms are Fibonacci-like if (n <= 2) return n; int len = 2; int mx = int.MinValue; for (int i = 2; i < n; i++) { // If previous subarray can be extended if (a[i] == a[i - 1] + a[i - 2]) len++; // Any 2 terms are Fibonacci-like else len = 2; // Find the maximum length mx = Math.Max(mx, len); } return mx; } // Driver Code public static void Main () { int n = 5; int[] a = {2, 4, 6, 10, 2}; Console.WriteLine(longestFibonacciSubarray(n, a)); } }// This code is contributed by Code_Mech. |
PHP
<?php// PHP program to find length of longest// Fibonacci-like subarray// Function to find the length of the // longest Fibonacci-like subarrayfunction longestFibonacciSubarray($n, $a){ // Any 2 terms are Fibonacci-like if ($n <= 2) return $n; $len = 2; $mx = PHP_INT_MIN; for ($i = 2; $i < $n; $i++) { // If previous subarray can be extended if ($a[$i] == $a[$i - 1] + $a[$i - 2]) $len++; // Any 2 terms are Fibonacci-like else $len = 2; // Find the maximum length $mx = max($mx, $len); } return $mx;}// Driver Code$n = 5;$a = array(2, 4, 6, 10, 2); echo longestFibonacciSubarray($n, $a);// This code is contributed // by Akanksha Rai ?> |
Javascript
<script>// javascript program to find length of longest// Fibonacci-like subarray // Function to find the length of the // longest Fibonacci-like subarray function longestFibonacciSubarray( n, a) { // Any 2 terms are Fibonacci-like if (n <= 2) return n; var len = 2; var mx = Number.MIN_VALUE; for (var i = 2; i < n; i++) { // If previous subarray can be extended if (a[i] == a[i - 1] + a[i - 2]) len++; // Any 2 terms are Fibonacci-like else len = 2; // Find the maximum length mx = Math.max(mx, len); } return mx; } // Driver Code var n = 5; var a = [2, 4, 6, 10, 2]; document.write(longestFibonacciSubarray(n, a)); // This code is contributed by bunnyram19.</script> |
Output:
4
Time Complexity: O(N)
Auxiliary Space: O(1)
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