# Largest and smallest Fibonacci numbers in an Array

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.

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

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); ` ` `  `    ``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 `

Output:

```1, 5
```

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