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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Improved By : rituraj_jain