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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Java

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// 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

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Python3

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# 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 +
        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

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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 
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

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Output:

2


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