Largest and smallest Fibonacci numbers in an Array
Last Updated :
18 Dec, 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 1:
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 <bits/stdc++.h>
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 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<Integer> 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<Integer> hash = new HashSet<Integer>();
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
# 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# 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
<script>
// Javascript program to find minimum and maximum
// fibonacci number in given array
// Function to create hash table
// to check Fibonacci numbers
function createHash(hash, maxElement)
{
// Insert initial two numbers
// in the hash table
let prev = 0, curr = 1;
hash.add(prev);
hash.add(curr);
while (curr <= maxElement) {
// Sum of previous two numbers
let 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
function fibonacci(arr, n)
{
// Find maximum value in the array
let max_val= Math.max(...arr);
// Creating a set containing
// all Fibonacci numbers up to
// maximum value in the array
let hash = new Set();
createHash(hash, max_val);
// For storing the Minimum
// and Maximum Fibonacci number
let minimum = Number.MAX_VALUE;
let maximum = Number.MIN_VALUE;
for (let i = 0; i < n; i++) {
// Check if current element
// is a fibonacci number
if (hash.has(arr[i])) {
// Update the maximum and
// minimum accordingly
minimum = Math.min(minimum, arr[i]);
maximum = Math.max(maximum, arr[i]);
}
}
document.write(minimum+ ", "
+ maximum +"<br/>");
}
// Driver code
let arr = [ 1, 2, 3, 4, 5, 6, 7 ];
let n = arr.length;
fibonacci(arr, n);
// This code is contributed by sanjoy_62.
</script>
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)
Approach 2:
This approach use the below formula to check if the current number is Fibonacci number or not:
A number is Fibonacci if and only if one or both of (5*n2 + 4) or (5*n2 – 4) is a perfect square (Source: Wiki).
Steps:
To find the largest and smallest Fibonacci numbers in an array, we do the following steps:
- First initialize max and min Fibonacci number as INT_MIN and INT_MAX respectively.
- Then we iterate array and for each element check if the element is Fibonacci number or not.
- In each iteration:
- If the element is Fibonacci number then compare it with max and min Fibonacci numbers and as per its value change max or min.
- And at the end print the max and min Fibonacci number.
Below is the implementation of the above approach:
C++
// C++ program to find minimum and maximum
// fibonacci number in given array
#include <bits/stdc++.h>
using namespace std;
// A utility function that returns true if x is perfect
// square
bool isPerfectSquare(int x)
{
int s = sqrt(x);
return (s * s == x);
}
// Returns true if n is a Fibonacci Number, else false
bool isFibonacci(int n)
{
// n is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or
// both is a perfect square
return isPerfectSquare(5 * n * n + 4)
|| isPerfectSquare(5 * n * n - 4);
}
// Function to find minimum and maximum
// fibonacci number in given array
void fibonacci(int arr[], int n)
{
// 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 (isFibonacci(arr[i])) {
// 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;
}
// This code is contributed by Susobhan Akhuli
import java.util.*;
public class FibonacciMinMax {
// A utility function that returns true if x is a perfect square
static boolean isPerfectSquare(int x) {
int s = (int) Math.sqrt(x);
return (s * s == x);
}
// Returns true if n is a Fibonacci Number, else false
static boolean isFibonacci(int n) {
// n is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or both is a perfect square
return isPerfectSquare(5 * n * n + 4) || isPerfectSquare(5 * n * n - 4);
}
// Function to find minimum and maximum Fibonacci numbers in the given array
static void fibonacci(int[] arr) {
int minimum = Integer.MAX_VALUE;
int maximum = Integer.MIN_VALUE;
for (int i = 0; i < arr.length; i++) {
// Check if the current element is a Fibonacci number
if (isFibonacci(arr[i])) {
// Update the maximum and minimum accordingly
minimum = Math.min(minimum, arr[i]);
maximum = Math.max(maximum, arr[i]);
}
}
System.out.println(minimum + ", " + maximum);
}
// Driver code
public static void main(String[] args) {
int[] arr = { 1, 2, 3, 4, 5, 6, 7 };
fibonacci(arr);
}
}
import math
# A utility function that returns true if x is a perfect square
def isPerfectSquare(x):
s = int(math.sqrt(x))
return s * s == x
# Returns true if n is a Fibonacci Number, else false
def isFibonacci(n):
# n is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or both is a perfect square
return isPerfectSquare(5 * n * n + 4) or isPerfectSquare(5 * n * n - 4)
# Function to find minimum and maximum Fibonacci number in the given array
def fibonacci(arr):
# For storing the Minimum and Maximum Fibonacci number
minimum = float('inf')
maximum = float('-inf')
for num in arr:
# Check if the current element is a Fibonacci number
if isFibonacci(num):
# Update the maximum and minimum accordingly
minimum = min(minimum, num)
maximum = max(maximum, num)
print(f" {minimum}, {maximum}")
# Driver code
if __name__ == "__main__":
arr = [1, 2, 3, 4, 5, 6, 7]
n = len(arr)
fibonacci(arr)
using System;
class Program
{
// A utility function that returns true if x is a perfect square
static bool IsPerfectSquare(int x)
{
int s = (int)Math.Sqrt(x);
return (s * s == x);
}
// Returns true if n is a Fibonacci Number, else false
static bool IsFibonacci(int n)
{
// n is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or both is a perfect square
return IsPerfectSquare(5 * n * n + 4) || IsPerfectSquare(5 * n * n - 4);
}
// Function to find the minimum and maximum Fibonacci numbers in a given array
static void Fibonacci(int[] arr)
{
int minimum = int.MaxValue;
int maximum = int.MinValue;
foreach (int num in arr)
{
if (IsFibonacci(num))
{
minimum = Math.Min(minimum, num);
maximum = Math.Max(maximum, num);
}
}
Console.WriteLine(minimum + ", " + maximum);
}
// Driver code
static void Main(string[] args)
{
int[] arr = { 1, 2, 3, 4, 5, 6, 7 };
Fibonacci(arr);
}
}
// JavaScript function to check if a number is a perfect square
function isPerfectSquare(x) {
const s = Math.sqrt(x);
return s * s === x;
}
// JavaScript function to check if a number is a Fibonacci number
function isFibonacci(n) {
// n is Fibonacci if 5*n*n + 4 or 5*n*n - 4 is a perfect square
return isPerfectSquare(5 * n * n + 4) || isPerfectSquare(5 * n * n - 4);
}
// Function to find the minimum and maximum Fibonacci number in a given array
function fibonacci(arr) {
// Initialize variables to store the minimum and maximum Fibonacci numbers
let minimum = Infinity;
let maximum = -Infinity;
for (let i = 0; i < arr.length; i++) {
// Check if the current element is a Fibonacci number
if (isFibonacci(arr[i])) {
// Update the minimum and maximum accordingly
minimum = Math.min(minimum, arr[i]);
maximum = Math.max(maximum, arr[i]);
}
}
console.log(`${minimum}, ${maximum}`);
}
// Driver code
function main() {
const arr = [1, 2, 3, 4, 5, 6, 7];
fibonacci(arr);
}
// Call the main function to execute the code
main();
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(1)
Approach 3:
This approach is one of the optimal approach to find the largest and smallest Fibonacci numbers in an array.
Steps:
To find the largest and smallest Fibonacci numbers in an array, we do the following steps:
- First initialize max and min Fibonacci number as INT_MIN and INT_MAX respectively.
- Then we iterate array and for each element check if the element is Fibonacci number or not.
- To check if the element is Fibonacci number or not we:
- First check if the number is 0 or 1, then return true.
- Then till the number comes do while loop.
- In each iteration:
- First calculate fibonacci of that iteration.
- Then check if it matches with given number or not.
- If matches, return true.
- If the value goes beyond, given number then return false.
- Otherwise continue.
- In each iteration:
- If the element is Fibonacci number then compare it with max and min Fibonacci numbers and as per its value change max or min.
- And at the end print the max and min Fibonacci number.
Below
C++
// C++ program to find minimum and maximum
// fibonacci number in given array
#include <bits/stdc++.h>
using namespace std;
// Function to check Fibonacci number
bool isFibonacci(int N)
{
if (N == 0 || N == 1)
return true;
int a = 0, b = 1, c;
while (true) {
c = a + b;
a = b;
b = c;
if (c == N)
return true;
else if (c >= N) {
return false;
}
}
}
// Function to find minimum and maximum
// fibonacci number in given array
void fibonacci(int arr[], int n)
{
// 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 (isFibonacci(arr[i])) {
// 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;
}
// This code is contributed by Susobhan Akhuli
import java.util.Arrays;
public class FibonacciMinMax {
// Function to check if a number is a Fibonacci number
public static boolean isFibonacci(int N) {
if (N == 0 || N == 1) {
return true;
}
int a = 0, b = 1, c;
while (true) {
c = a + b;
a = b;
b = c;
if (c == N) {
return true;
} else if (c >= N) {
return false;
}
}
}
// Function to find the minimum and maximum Fibonacci number in the given array
public static void fibonacci(int[] arr) {
int minimum = Integer.MAX_VALUE;
int maximum = Integer.MIN_VALUE;
for (int i = 0; i < arr.length; i++) {
if (isFibonacci(arr[i])) {
minimum = Math.min(minimum, arr[i]);
maximum = Math.max(maximum, arr[i]);
}
}
System.out.println("Minimum: " + minimum + ", Maximum: " + maximum);
}
public static void main(String[] args) {
int[] arr = {1, 2, 3, 4, 5, 6, 7};
fibonacci(arr);
}
}
def is_fibonacci(N):
if N == 0 or N == 1:
return True
a, b = 0, 1
while True:
c = a + b
a = b
b = c
if c == N:
return True
elif c >= N:
return False
def find_fibonacci_min_max(arr):
minimum = float('inf') # Initialize the minimum as positive infinity
maximum = float('-inf') # Initialize the maximum as negative infinity
for num in arr:
if is_fibonacci(num): # Check if the current number is a Fibonacci number
minimum = min(minimum, num) # Update the minimum if needed
maximum = max(maximum, num) # Update the maximum if needed
return minimum, maximum
arr = [1, 2, 3, 4, 5, 6, 7]
minimum, maximum = find_fibonacci_min_max(arr)
print(f"{minimum}, {maximum}")
using System;
class Program {
// Function to check Fibonacci number
static bool IsFibonacci(int N)
{
if (N == 0 || N == 1)
return true;
int a = 0, b = 1, c;
while (true) {
c = a + b;
a = b;
b = c;
if (c == N)
return true;
else if (c >= N)
return false;
}
}
// Function to find minimum and maximum
// Fibonacci number in given array
static void Fibonacci(int[] arr, int n)
{
// 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 the current element is a Fibonacci
// number
if (IsFibonacci(arr[i])) {
// Update the maximum and minimum
// accordingly
minimum = Math.Min(minimum, arr[i]);
maximum = Math.Max(maximum, arr[i]);
}
}
Console.WriteLine(minimum + ", " + maximum);
}
// Driver code
static void Main()
{
int[] arr = { 1, 2, 3, 4, 5, 6, 7 };
int n = arr.Length;
Fibonacci(arr, n);
}
}
// Function to check if a number is a Fibonacci number
function isFibonacci(N) {
if (N === 0 || N === 1) {
return true;
}
let a = 0, b = 1, c;
while (true) {
c = a + b;
a = b;
b = c;
if (c === N) {
return true;
} else if (c >= N) {
return false;
}
}
}
// Function to find the minimum and maximum Fibonacci numbers in the given array
function fibonacci(arr) {
// For storing the minimum and maximum Fibonacci numbers
let minimum = Infinity;
let maximum = -Infinity;
for (let i = 0; i < arr.length; i++) {
// Check if the current element is a Fibonacci number
if (isFibonacci(arr[i])) {
// Update the minimum and maximum accordingly
minimum = Math.min(minimum, arr[i]);
maximum = Math.max(maximum, arr[i]);
}
}
console.log(minimum + ', ' + maximum);
}
// Driver code
const arr = [1, 2, 3, 4, 5, 6, 7];
fibonacci(arr);
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(1)
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Print the Fibonacci sequence - PythonTo print the Fibonacci sequence in Python, we need to generate a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. The Fibonacci sequence follows a specific pattern that begins with 0 and 1, and every subsequent number is the sum of the two previous num
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C Program to Print Fibonacci SeriesThe Fibonacci series is the sequence where each number is the sum of the previous two numbers of the sequence. The first two numbers are 0 and 1 which are used to generate the whole series.ExampleInput: n = 5Output: 0 1 1 2 3Explanation: The first 5 terms of the Fibonacci series are 0, 1, 1, 2, 3.In
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JavaScript Program to print Fibonacci SeriesThe Fibonacci sequence is the integer sequence where the first two terms are 0 and 1. After that, the next term is defined as the sum of the previous two terms. The recurrence relation defines the sequence Fn of Fibonacci numbers:Fn = Fn-1 + Fn-2 with seed values F0 = 0 and F1 = 1Examples:Input : 5
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Length of longest subsequence of Fibonacci Numbers in an ArrayGiven an array arr containing non-negative integers, the task is to print the length of the longest subsequence of Fibonacci numbers in this array.Examples: Input: arr[] = { 3, 4, 11, 2, 9, 21 } Output: 3 Here, the subsequence is {3, 2, 21} and hence the answer is 3.Input: arr[] = { 6, 4, 10, 13, 9,
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Last digit of sum of numbers in the given range in the Fibonacci seriesGiven two non-negative integers M, N which signifies the range [M, N] where M ? N, the task is to find the last digit of the sum of FM + FM+1... + FN where FK is the Kth Fibonacci number in the Fibonacci series. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... Examples: Input: M = 3, N = 9 Output:
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K- Fibonacci seriesGiven integers 'K' and 'N', the task is to find the Nth term of the K-Fibonacci series. In K - Fibonacci series, the first 'K' terms will be '1' and after that every ith term of the series will be the sum of previous 'K' elements in the same series. Examples: Input: N = 4, K = 2 Output: 3 The K-Fibo
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Fibonacci Series in BashPrerequisite: Fibonacci Series Write a program to print the Fibonacci sequence up to nth digit using Bash. Examples: Input : 5 Output : Fibonacci Series is : 0 1 1 2 3 Input :4 Output : Fibonacci Series is : 0 1 1 2 The Fibonacci numbers are the numbers in the following integer sequence . 0, 1, 1, 2
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R Program to Print the Fibonacci SequenceThe Fibonacci sequence is a series of numbers in which each number (known as a Fibonacci number) is the sum of the two preceding ones. The sequence starts with 0 and 1, and then each subsequent number is the sum of the two previous numbers. The Fibonacci sequence has many applications in various fie
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