Largest subset whose all elements are Fibonacci numbers

Given an array with positive number the task is that we find largest subset from array that contain elements which are Fibonacci numbers.

Asked in Facebook

Examples :

Input : arr[] = {1, 4, 3, 9, 10, 13, 7};
Output : subset[] = {1, 3, 13}
The output three numbers are Fibonacci
numbers.

Input  : arr[] = {0, 2, 8, 5, 2, 1, 4, 
                  13, 23};
Output : subset[] = {0, 2, 8, 5, 2, 1, 
                    13, 23}

A simple solution is to iterate through all elements of given array. For every number, check if it is Fibonacci or not. If yes, add it to the result.

Below is an efficient solution based on hashing.

  1. Find max in the array
  2. Generate Fibonacci numbers till the max and store it in hash table.
  3. Traverse array again if the number is present in hash table then add it to the result.

C++


[sourcecode language=”CPP” highlight=”5-32″]
// C++ program to find largest Fibonacci subset
#include<bits/stdc++.h>
using namespace std;

// Prints largest subset of an array whose
// all elements are fibonacci numbers
void findFibSubset(int arr[], int n)
{
// Find maximum element in arr[]
int max = *std::max_element(arr, arr+n);

// Generate all Fibonacci numbers till
// max and store them in hash.
int a = 0, b = 1;
unordered_set<int> hash;
hash.insert(a);
hash.insert(b);
while (b < max)
{
int c = a + b;
a = b;
b = c;
hash.insert(b);
}

// Npw iterate through all numbers and
// quickly check for Fibonacci using
// hash.
for (int i=0; i<n; i++)
if (hash.find(arr[i]) != hash.end())
printf("%d ", arr[i]);
}

// Driver code
int main()
{
int arr[] = {4, 2, 8, 5, 20, 1, 40, 13, 23};
int n = sizeof(arr)/sizeof(arr[0]);
findFibSubset(arr, n);
return 0;
}
[/sourcecode]

Java


[sourcecode language=”Java” highlight=”7-34″]
// Java program to find
// largest Fibonacci subset
import java.util.*;

class GFG
{
// Prints largest subset of an array whose
// all elements are fibonacci numbers
public static void findFibSubset(Integer[] x)
{
Integer max = Collections.max(Arrays.asList(x));
List<Integer> fib = new ArrayList<Integer>();
List<Integer> result = new ArrayList<Integer>();

// Generate all Fibonacci numbers
// till max and store them
Integer a = 0;
Integer b = 1;
while (b < max){
Integer c = a + b;
a=b;
b=c;
fib.add(c);
}

// Now iterate through all numbers and
// quickly check for Fibonacci
for (Integer i = 0; i < x.length; i++){
if(fib.contains(x[i])){
result.add(x[i]);
}
}
System.out.println(result);
}

// Driver code
public static void main(String args[])
{
Integer[] a = {4, 2, 8, 5, 20, 1, 40, 13, 23};
findFibSubset(a);
}
}

// This code is contributed by prag93

[/sourcecode]


Output:

2 8 5 1 13 

Asked in: Facebook

Reference :
https://www.careercup.com/question?id=5154130839470080

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Improved By : prag93, Ita_c