Skip to content
Related Articles

Related Articles

Save Article
Improve Article
Save Article
Like Article

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

  • Difficulty Level : Basic
  • Last Updated : 09 Jun, 2021

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:
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:
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#




// 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: 
2

 




My Personal Notes arrow_drop_up