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:
4
Time Complexity: O(N)
Auxiliary Space: O(1)