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.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 

Output:

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

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