# Largest and smallest Fibonacci numbers in an Array

• Last Updated : 10 Jan, 2023

Given an array arr[] of N positive integers, the task is to find the minimum (smallest) and maximum (largest) Fibonacci elements in the given array.
Examples:

Input: arr[] = 1, 2, 3, 4, 5, 6, 7
Output: 1, 5
Explanation :
The array contains 4 fibonacci values 1, 2, 3 and 5.
Hence, the maximum is 5 and the minimum is 1.
Input: arr[] = 13, 3, 15, 6, 8, 11
Output:3, 13
Explanation:
The array contains 3 fibonacci values 13, 3 and 8.
Hence, the maximum is 13 and the minimum is 3.

Approach: This approach is similar to finding the minimum and maximum element in an array. Traverse the array one by one, and check if it is a Fibonacci number or not. If it is, then find the maximum and minimum among such numbers.
Inorder to check if the number is a Fibonacci number or not optimally O(1), generate all Fibonacci numbers up to the maximum element of the array using dynamic programming and store them in a hash table.
Below is the implementation of above approach:

## C++

 `// C++ program to find minimum and maximum``// fibonacci number in given array``#include ``using` `namespace` `std;` `// Function to create hash table``// to check Fibonacci numbers``void` `createHash(set<``int``>& hash,``                ``int` `maxElement)``{``    ``// Insert initial two numbers``    ``// in the hash table``    ``int` `prev = 0, curr = 1;``    ``hash.insert(prev);``    ``hash.insert(curr);` `    ``while` `(curr <= maxElement) {` `        ``// Sum of previous two numbers``        ``int` `temp = curr + prev;` `        ``hash.insert(temp);` `        ``// Update the variable each time``        ``prev = curr;``        ``curr = temp;``    ``}``}` `// Function to find minimum and maximum``// fibonacci number in given array``void` `fibonacci(``int` `arr[], ``int` `n)``{` `    ``// Find maximum value in the array``    ``int` `max_val``        ``= *max_element(``            ``arr, arr + n);` `    ``// Creating a set containing``    ``// all Fibonacci numbers up to``    ``// maximum value in the array``    ``set<``int``> hash;``    ``createHash(hash, max_val);` `    ``// For storing the Minimum``    ``// and Maximum Fibonacci number``    ``int` `minimum = INT_MAX;``    ``int` `maximum = INT_MIN;` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// Check if current element``        ``// is a fibonacci number``        ``if` `(hash.find(arr[i]) != hash.end()) {` `            ``// Update the maximum and``            ``// minimum accordingly``            ``minimum = min(minimum, arr[i]);``            ``maximum = max(maximum, arr[i]);``        ``}``    ``}` `    ``cout << minimum << ``", "``         ``<< maximum << endl;``}` `// Driver code``int` `main()``{` `    ``int` `arr[] = { 1, 2, 3, 4, 5, 6, 7 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``fibonacci(arr, n);` `    ``return` `0;``}`

## Java

 `// Java program to find minimum and maximum``// fibonacci number in given array``import` `java.util.*;` `class` `GFG{`` ` `// Function to create hash table``// to check Fibonacci numbers``static` `void` `createHash(HashSet hash,``                ``int` `maxElement)``{``    ``// Insert initial two numbers``    ``// in the hash table``    ``int` `prev = ``0``, curr = ``1``;``    ``hash.add(prev);``    ``hash.add(curr);`` ` `    ``while` `(curr <= maxElement) {`` ` `        ``// Sum of previous two numbers``        ``int` `temp = curr + prev;`` ` `        ``hash.add(temp);`` ` `        ``// Update the variable each time``        ``prev = curr;``        ``curr = temp;``    ``}``}`` ` `// Function to find minimum and maximum``// fibonacci number in given array``static` `void` `fibonacci(``int` `arr[], ``int` `n)``{`` ` `    ``// Find maximum value in the array``    ``int` `max_val= Arrays.stream(arr).max().getAsInt();`` ` `    ``// Creating a set containing``    ``// all Fibonacci numbers up to``    ``// maximum value in the array``    ``HashSet hash = ``new` `HashSet();``    ``createHash(hash, max_val);`` ` `    ``// For storing the Minimum``    ``// and Maximum Fibonacci number``    ``int` `minimum = Integer.MAX_VALUE;``    ``int` `maximum = Integer.MIN_VALUE;`` ` `    ``for` `(``int` `i = ``0``; i < n; i++) {`` ` `        ``// Check if current element``        ``// is a fibonacci number``        ``if` `(hash.contains(arr[i])) {`` ` `            ``// Update the maximum and``            ``// minimum accordingly``            ``minimum = Math.min(minimum, arr[i]);``            ``maximum = Math.max(maximum, arr[i]);``        ``}``    ``}`` ` `    ``System.out.print(minimum+ ``", "``         ``+ maximum +``"\n"``);``}`` ` `// Driver code``public` `static` `void` `main(String[] args)``{`` ` `    ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7` `};``    ``int` `n = arr.length;`` ` `    ``fibonacci(arr, n);`` ` `}``}` `// This code is contributed by sapnasingh4991`

## Python3

 `# Python 3 program to find minimum and maximum``# fibonacci number in given array` `import` `sys` `# Function to create hash table``# to check Fibonacci numbers``def` `createHash(``hash``, maxElement):``    ``# Insert initial two numbers``    ``# in the hash table``    ``prev ``=` `0``    ``curr ``=` `1``    ``hash``.add(prev)``    ``hash``.add(curr)` `    ``while` `(curr <``=` `maxElement):``        ``# Sum of previous two numbers``        ``temp ``=` `curr ``+` `prev` `        ``hash``.add(temp)``        ``# Update the variable each time``        ``prev ``=` `curr``        ``curr ``=` `temp` `# Function to find minimum and maximum``# fibonacci number in given array``def` `fibonacci(arr, n):` `    ``# Find maximum value in the array``    ``max_val ``=` `max``(arr)` `    ``# Creating a set containing``    ``# all Fibonacci numbers up to``    ``# maximum value in the array``    ``hash` `=` `set``()``    ``createHash(``hash``, max_val)` `    ``# For storing the Minimum``    ``# and Maximum Fibonacci number``    ``minimum ``=` `sys.maxsize``    ``maximum ``=` `-``sys.maxsize``-``1` `    ``for` `i ``in` `range``(n):` `        ``# Check if current element``        ``# is a fibonacci number``        ``if` `(arr[i] ``in` `hash``):` `            ``# Update the maximum and``            ``# minimum accordingly``            ``minimum ``=` `min``(minimum, arr[i])``            ``maximum ``=` `max``(maximum, arr[i])` `    ``print``(minimum,end ``=` `", "``)``    ``print``(maximum)` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``arr ``=` `[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``]``    ``n ``=` `len``(arr)` `    ``fibonacci(arr, n)` `# This code is contributed by Surendra_Gangwar`

## C#

 `// C# program to find minimum and maximum``// fibonacci number in given array``using` `System;``using` `System.Linq;``using` `System.Collections.Generic;` `class` `GFG{` `// Function to create hash table``// to check Fibonacci numbers``static` `void` `createHash(HashSet<``int``> hash,``                ``int` `maxElement)``{``    ``// Insert initial two numbers``    ``// in the hash table``    ``int` `prev = 0, curr = 1;``    ``hash.Add(prev);``    ``hash.Add(curr);` `    ``while` `(curr <= maxElement) {` `        ``// Sum of previous two numbers``        ``int` `temp = curr + prev;` `        ``hash.Add(temp);` `        ``// Update the variable each time``        ``prev = curr;``        ``curr = temp;``    ``}``}` `// Function to find minimum and maximum``// fibonacci number in given array``static` `void` `fibonacci(``int` `[]arr, ``int` `n)``{` `    ``// Find maximum value in the array``    ``int` `max_val= arr.Max();` `    ``// Creating a set containing``    ``// all Fibonacci numbers up to``    ``// maximum value in the array``    ``HashSet<``int``> hash = ``new` `HashSet<``int``>();``    ``createHash(hash, max_val);` `    ``// For storing the Minimum``    ``// and Maximum Fibonacci number``    ``int` `minimum = ``int``.MaxValue;``    ``int` `maximum = ``int``.MinValue;` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// Check if current element``        ``// is a fibonacci number``        ``if` `(hash.Contains(arr[i])) {` `            ``// Update the maximum and``            ``// minimum accordingly``            ``minimum = Math.Min(minimum, arr[i]);``            ``maximum = Math.Max(maximum, arr[i]);``        ``}``    ``}` `    ``Console.Write(minimum+ ``", "``        ``+ maximum +``"\n"``);``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 1, 2, 3, 4, 5, 6, 7 };``    ``int` `n = arr.Length;` `    ``fibonacci(arr, n);``}``}` `// This code is contributed by Princi Singh`

## Javascript

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Output:

`1, 5`

Time Complexity: O(n + log(m)), where n is the size of the given array and m is the maximum element in the array.
Auxiliary Space: O(n)

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