Minimum number of elements to be replaced to make the given array a Fibonacci Sequence

Given an array arr containing N integer elements, the task is to count the minimum number of elements that need to be changed such that all the elements (after proper rearrangement) make first N terms of Fibonacci Series.

Examples:

Input: arr[] = {4, 1, 2, 1, 3, 7}
Output: 2
4 and 7 must be changed to 5 and 8 to make first N(6) terms of Fibonacci series.

Input: arr[] = {5, 3, 1, 1, 2, 8, 11}
Output: 1
11 must be changed to 13.



Approach:

  • Insert first N elements of Fibonacci series into a multi set.
  • Then, traverse the array from left to right and check if the current element is present in multi set.
  • If element is present in the multi set then remove it.
  • Final answer will be the size of final multi set.

Below is the implementation of the above approach:

C++

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// C++ program to find the minimum number
// of elements the need to be changed
// to get first N numbers of Fibonacci series
#include <bits/stdc++.h>
using namespace std;
  
// Function that finds minimum changes required
int fibonacciArray(int arr[], int n)
{
    multiset<int> s;
  
    // a and b are first two
    // fibonacci numbers
    int a = 1, b = 1;
    int c;
  
    // insert first n fibonacci elements to set
    s.insert(a);
    if (n >= 2)
        s.insert(b);
  
    for (int i = 0; i < n - 2; i++) {
        c = a + b;
        s.insert(c);
        a = b;
        b = c;
    }
  
    multiset<int>::iterator it;
    for (int i = 0; i < n; i++) {
  
        // if fibonacci element is present
        // in the array then remove it from set
        it = s.find(arr[i]);
        if (it != s.end())
            s.erase(it);
    }
  
    // return the remaining number of
    // elements in the set
    return s.size();
}
  
// Driver code
int main()
{
    int arr[] = { 3, 1, 21, 4, 2, 1, 8, 9 };
    int n = sizeof(arr) / sizeof(arr[0]);
  
    cout << fibonacciArray(arr, n);
  
    return 0;
}

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Python3





# Python3 program to find the minimum number

# of elements the need to be changed

# to get first N numbers of Fibonacci series 


# Function that finds minimum changes required

def fibonacciArray(arr, n): 


	s = set() 


	# a and b are first two

	# fibonacci numbers

	a, b = 1, 1


	# insert first n fibonacci elements to set

	s.add(a)

	if n >= 2:

		s.add(b) 


	for i in range(0, n – 2):

		c = a + b

		s.add(c)

		a, b = b, c 


	for i in range(0, n): 


		# if fibonacci element is present in

		# the array then remove it from set

		if arr[i] in s:

			s.remove(arr[i]) 


	# return the remaining number

	# of elements in the set

	return len(s) 


# Driver code

if __name__ == “__main__”: 


	arr = [3, 1, 21, 4, 2, 1, 8, 9]

	n = len(arr) 


	print(fibonacciArray(arr, n))


# This code is contributed by Rituraj Jain





Output:


2






          
          
          
          

            

    

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