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

Last Updated : 09 Sep, 2022

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;
}

Java

// Java program to find the minimum number 
// of elements the need to be changed 
// to get first N numbers of Fibonacci series 
import java.util.*;

class geeks
{

    // Function that finds minimum changes required
    public static int fibonacciArray(int[] arr, int n) 
    {
        Set<Integer> s = new HashSet<Integer>();

        // a and b are first two
        // fibonacci numbers
        int a = 1, b = 1;
        int c;

        // insert first n fibonacci elements to set
        s.add(a);
        if (n > 2)
            s.add(b);

        for (int i = 0; i < n - 2; i++)
        {
            c = a + b;
            s.add(c);
            a = b;
            b = c;
        }

        for (int i = 0; i < n; i++)
        {

            // if fibonacci element is present
            // in the array then remove it from set
            if (s.contains(arr[i]))
                s.remove(arr[i]);
        }

        // return the remaining number of
        // elements in the set
        return s.size();
    }

    // Driver Code
    public static void main(String[] args) 
    {
        int[] arr = { 3, 1, 21, 4, 2, 1, 8, 9 };
        int n = arr.length;

        System.out.print(fibonacciArray(arr, n));
    }
}

// This code is contributed by
// sanjeev2552

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

// C# program to find the minimum number 
// of elements the need to be changed 
// to get first N numbers of Fibonacci series 
using System;
using System.Collections.Generic;
    
public class geeks
{

    // Function that finds minimum changes required
    public static int fibonacciArray(int[] arr, int n) 
    {
        HashSet<int> s = new HashSet<int>();

        // a and b are first two
        // fibonacci numbers
        int a = 1, b = 1;
        int c;

        // insert first n fibonacci elements to set
        s.Add(a);
        if (n > 2)
            s.Add(b);

        for (int i = 0; i < n - 2; i++)
        {
            c = a + b;
            s.Add(c);
            a = b;
            b = c;
        }

        for (int i = 0; i < n; i++)
        {

            // if fibonacci element is present
            // in the array then remove it from set
            if (s.Contains(arr[i]))
                s.Remove(arr[i]);
        }

        // return the remaining number of
        // elements in the set
        return s.Count;
    }

    // Driver Code
    public static void Main(String[] args) 
    {
        int[] arr = { 3, 1, 21, 4, 2, 1, 8, 9 };
        int n = arr.Length;

        Console.WriteLine(fibonacciArray(arr, n));
    }
}

// This code is contributed by Rajput-Ji

JavaScript

<script>
// Javascript 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
function fibonacciArray(arr, n) {
    let s = new Set();

    // a and b are first two
    // fibonacci numbers
    let a = 1, b = 1;
    let c;

    // insert first n fibonacci elements to set
    s.add(a);
    if (n > 2)
        s.add(b);

    for (let i = 0; i < n - 2; i++) {
        c = a + b;
        s.add(c);
        a = b;
        b = c;
    }

    for (let i = 0; i < n; i++) {

        // if fibonacci element is present
        // in the array then remove it from set
        if (s.has(arr[i]))
            s.delete(arr[i]);
    }

    // return the remaining number of
    // elements in the set
    return s.size;
}

// Driver Code

let arr = [3, 1, 21, 4, 2, 1, 8, 9];
let n = arr.length;

document.write(fibonacciArray(arr, n));

// This code is contributed by _saurabh_jaiswal
</script>

Output

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

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