# Find the longest Fibonacci-like subarray of the given array

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.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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:

1. Maintain a variable len initialized to 2 and a variable mx to store the maximum length so far.
2. Start traversing the array from 3rd index.
3. 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 ` `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; ` `} `

## 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 [tabbyending]

Output:

```4
```

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

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