# 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++

`// 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; ` `} ` |

*chevron_right*

*filter_none*

## 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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