Find the longest Fibonacci-like subarray of the given array

Last Updated : 13 May, 2021

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 subarray
int 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 Code
int 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 subarray
def 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 Code
n = 5
a = [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 subarray
function 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:

Time Complexity: O(N)
Auxiliary Space: O(1)

Find length of longest Fibonacci like subsequence

Abdullah Aslam

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Find the longest Fibonacci-like subarray of the given array

C++

Java

Python3

C#

PHP

Javascript

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