Find the longest Fibonacci-like subarray of the given array
Last Updated :
13 May, 2021
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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++ 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 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 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# 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 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
?>
<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)
