Non Fibonacci Numbers

Given a positive integer n, the task is to print the nth non-Fibonacci number. The Fibonacci numbers are defined as: 

Fib(0) = 0
Fib(1) = 1
for n >1, Fib(n) = Fib(n-1) + Fib(n-2)

First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 141, ……..

Examples:

Input : n = 2
Output : 6

Input : n = 5
Output : 10

Below is the implementation of the above idea.

C++

// C++ program to find n'th Fibonacci number

#include <bits/stdc++.h>
using namespace std;

// Returns n'th Non-Fibonacci number
int nonFibonacci(int n)
{
    // curr is to keep track of current fibonacci
    // number, prev is previous, prevPrev is
    // previous of previous.
    int prevPrev = 1, prev = 2, curr = 3;

    // While count of non-fibonacci numbers
    // doesn't become negative or zero
    while (n > 0) {
        // Simple Fibonacci number logic
        prevPrev = prev;
        prev = curr;
        curr = prevPrev + prev;

        // (curr - prev - 1) is count of
        // non-Fibonacci numbers between curr
        // and prev.
        n = n - (curr - prev - 1);
    }

    // n might be negative now. Make sure it
    // becomes positive by removing last added
    // gap.
    n = n + (curr - prev - 1);

    // n must be now positive and less than or equal
    // to gap between current and previous, i.e.,
    // (curr - prev - 1);

    // Now add the positive n to previous Fibonacci
    // number to find the n'th non-fibonacci.
    return prev + n;
}

// Driver code
int main()
{
    cout << nonFibonacci(5);
    return 0;
}

C

// C program to find n'th Fibonacci number

#include<stdio.h>


// Returns n'th Non-Fibonacci number
int nonFibonacci(int n)
{
  // curr is to keep track of current fibonacci
  // number, prev is previous, prevPrev is
  // previous of previous.
  int prevPrev=1, prev=2, curr=3;

  // While count of non-fibonacci numbers
  // doesn't become negative or zero
  while (n > 0)
  {
    // Simple Fibonacci number logic
    prevPrev = prev;
    prev = curr;
    curr = prevPrev + prev;

    // (curr - prev - 1) is count of
    // non-Fibonacci numbers between curr
    // and prev.
    n = n - (curr - prev - 1);
  }

  // n might be negative now. Make sure it
  // becomes positive by removing last added
  // gap.
  n = n + (curr - prev - 1);

  // n must be now positive and less than or equal
  // to gap between current and previous, i.e.,
  // (curr - prev - 1);

  // Now add the positive n to previous Fibonacci
  // number to find the n'th non-fibonacci.
  return prev + n;
}

// Driver code
int main()
{
  printf("%d",nonFibonacci(5));
  return 0;
}

// This code is contributed by allwink45.

Java

// Java program to find
// n'th Fibonacci number

import java.io.*;

class GFG {
    // Returns n'th Non-
    // Fibonacci number
    static int nonFibonacci(int n)
    {

        // curr is to keep track of
        // current fibonacci number,
        // prev is previous, prevPrev
        // is previous of previous.
        int prevPrev = 1, prev = 2, curr = 3;

        // While count of non-fibonacci
        // numbers doesn't become
        // negative or zero
        while (n > 0) {
            // Simple Fibonacci number logic
            prevPrev = prev;
            prev = curr;
            curr = prevPrev + prev;

            // (curr - prev - 1) is count
            // of non-Fibonacci numbers
            // between curr and prev.
            n = n - (curr - prev - 1);
        }

        // n might be negative now. Make
        // sure it becomes positive by
        // removing last added gap.
        n = n + (curr - prev - 1);

        // n must be now positive and less
        // than or equal to gap between
        // current and previous, i.e.,
        // (curr - prev - 1);

        // Now add the positive n to
        // previous Fibonacci number
        // to find the n'th non-fibonacci.
        return prev + n;
    }

    // Driver Code
    public static void main(String args[])
    {
        System.out.println(nonFibonacci(5));
    }
}

// This code is contributed by aj_36

Python

# Python program to find n'th
# Fibonacci number

# Returns n'th Non-Fibonacci
# number


def nonFibonacci(n):

    # curr is to keep track of
    # current fibonacci number,
    # prev is previous, prevPrev
    # is previous of previous.
    prevPrev = 1
    prev = 2
    curr = 3

    # While count of non-fibonacci
    # numbers doesn't become
    # negative or zero
    while n > 0:
        prevPrev = prev
        prev = curr
        curr = prevPrev + prev

        # (curr - prev - 1) is
        # count of non-Fibonacci
        # numbers between curr
        # and prev.
        n = n - (curr - prev - 1)

    # n might be negative now.
    # Make sure it becomes positive
    # by removing last added gap.
    n = n + (curr - prev - 1)

    # n must be now positive and
    # less than or equal to gap
    # between current and previous,
    # i.e., (curr - prev - 1)

    # Now add the positive n to
    # previous Fibonacci number to
    # find the n'th non-fibonacci.
    return prev + n


# Driver code
print(nonFibonacci(5))

# This code is contributed by anuj_67.

C#

// C# program to find
// n'th Fibonacci number

using System;

class GFG
{
    // Returns n'th Non-
    // Fibonacci number
    static int nonFibonacci (int n)
    {

    // curr is to keep track of
    // current fibonacci number,
    // prev is previous, prevPrev
    // is previous of previous.
    int prevPrev = 1, prev = 2, curr = 3;

    // While count of non-fibonacci
    // numbers doesn't become
    // negative or zero
    while (n > 0)
    {
        // Simple Fibonacci number logic
        prevPrev = prev;
        prev = curr;
        curr = prevPrev + prev;

        // (curr - prev - 1) is count
        // of non-Fibonacci numbers
        // between curr and prev.
        n = n - (curr - prev - 1);
    }

    // n might be negative now. Make
    // sure it becomes positive by
    // removing last added gap.
    n = n + (curr - prev - 1);

    // n must be now positive and less
    // than or equal to gap between
    // current and previous, i.e.,
    // (curr - prev - 1);

    // Now add the positive n to
    // previous Fibonacci number
    // to find the n'th non-fibonacci.
    return prev + n;
    }

    // Driver Code
    public static void Main ()
    {
    Console.WriteLine (nonFibonacci(5));
    }
}

//This code is contributed by aj_36

Javascript

<script>

// Javascript program to find n'th Fibonacci number

// Returns n'th Non-Fibonacci number
function nonFibonacci(n)
{
    // curr is to keep track of current fibonacci
    // number, prev is previous, prevPrev is
    // previous of previous.
    let prevPrev=1, prev=2, curr=3;

    // While count of non-fibonacci numbers
    // doesn't become negative or zero
    while (n > 0)
    {
        // Simple Fibonacci number logic
        prevPrev = prev;
        prev = curr;
        curr = prevPrev + prev;

        // (curr - prev - 1) is count of
        // non-Fibonacci numbers between curr
        // and prev.
        n = n - (curr - prev - 1);
    }

    // n might be negative now. Make sure it
    // becomes positive by removing last added
    // gap.
    n = n + (curr - prev - 1);

    // n must be now positive and less than or equal
    // to gap between current and previous, i.e.,
    // (curr - prev - 1);

    // Now add the positive n to previous Fibonacci
    // number to find the n'th non-fibonacci.
    return prev + n;
}

// Driver code

    document.write(nonFibonacci(5));

// This code is contributed by Mayank Tyagi

</script>

PHP

<?php
// PHP program to find
// n'th Fibonacci number

// Returns n'th Non-
// Fibonacci number
function nonFibonacci($n)
{
    // curr is to keep track of
    // current fibonacci number,
    // prev is previous, prevPrev
    // is previous of previous.
    $prevPrev = 1;
    $prev = 2;
    $curr = 3;

    // While count of non-fibonacci
    // numbers doesn't become
    // negative or zero
    while ($n > 0)
    {
        // Simple Fibonacci
        // number logic
        $prevPrev = $prev;
        $prev = $curr;
        $curr = $prevPrev + $prev;

        // (curr - prev - 1) is count
        // of non-Fibonacci numbers
        // between curr and prev.
        $n = $n - ($curr - $prev - 1);
    }

    // n might be negative now. Make
    // sure it becomes positive by
    // removing last added gap.
    $n = $n + ($curr - $prev - 1);

    // n must be now positive and
    // less than or equal to gap
    // between current and previous,
    // i.e., (curr - prev - 1);

    // Now add the positive n to
    // previous Fibonacci number
    // to find the n'th non-fibonacci.
    return $prev + $n;
}

// Driver code
echo nonFibonacci(5);

// This code is contributed by m_kit
?>

Output :

10

Time Complexity : O(n) , Auxiliary Space : O(1)

Now geeks you must be wondering what if we were supposed to print Non-Fibonacci Series in a range, then the code is as follows: 

C++

#include <iostream>
using namespace std;

int main()
{
    int i = 0, j = 1, k, m, no, b[10];

    // Range is 10
    no = 10;
    b[1] = 0;
    b[2] = 1;

    // Check if range is less equals to 1
    if (no <= 1) {
        cout << "You have enter a wrong range";
    }

    // check if range is greater than 1
    // and less equals to 5
    else if (no <= 5 && no > 1) {
        cout << "\nThere is not any Non-Fibonacci series "
                "that lies between 1 to "
             << no << " term of Fibonacci Series.";
    }

    // If range is greater than 5
    else {

        // Loop to calculate fibonacci series till
        // range
        for (m = 2; m < no; m++) {
            k = i + j;
            i = j;
            j = k;

            // Store fibonacci series into b[]
            // array
            b[m] = k;
        }
        i = 5;
        cout << "\nThe Non-Fibonacci series that lies "
                "between 1 to "
             << no << " term of Fibonacci Series is: \n";

        // Loop to calculate Non-Fibonacci
        // series
        for (int ans = 4; ans < b[no - 1]; ans++) {
            if (ans != b[i])

                // Print Non-Fibonacci Series
                cout << ans << "  ";
            else
                i++;
        }
    }
    return 0;
}

C

#include <stdio.h>
#include <stdlib.h>
int main()
{
    int i = 0, j = 1, k, m, no, b[10];

    // Range is 10
    no = 10;
    b[1] = 0;
    b[2] = 1;

    // Check if range is less equals to 1
    if (no <= 1) {
        printf("You have enter a wrong range");
    }

    // check if range is greater than 1 and less equals to 5
    else if (no <= 5 && no > 1) {
        printf("\nThere is not any Non-Fibonacci series "
               "that lies between 1 to %d term of "
               "Fibonacci Series.",
               no);
    }

    // If range is greater than 5
    else {

        // Loop to calculate fibonacci series till range
        for (m = 2; m < no; m++) {
            k = i + j;
            i = j;
            j = k;

            // Store fibonacci series into b[] array
            b[m] = k;
        }

        i = 5;
        printf(
            "\nThe Non-Fibonacci series that lies between "
            "1 to %d term of Fibonacci Series is: \n",
            no);

        // Loop to calculate Non-Fibonacci series
        for (int ans = 4; ans < b[no - 1]; ans++) {
            if (ans != b[i])

                // Print Non-Fibonacci Series
                printf("%d  ", ans);
            else
                i++;
        }
    }
    return 0;
}

Java

/*package whatever //do not write package name here */

import java.io.*;

class GFG {
    int[] holes = {21, 3, 6};
    int i = 0, j = 1, k, m, no;
    int[] b = new int[10];

    // Range is 10
    no = 10;
    b[1] = 0;
    b[2] = 1;

    // Check if range is less equals to 1
    if (no <= 1) {
        System.out.print("You have enter a wrong range");
    }

    // check if range is greater than 1
    // and less equals to 5
    else if (no <= 5 && no > 1) {
        System.out.print("\n" + "There is not any Non-Fibonacci series that lies between 1 to" + no +
        " term of Fibonacci Series.");
    }

    // If range is greater than 5
    else {

        // Loop to calculate fibonacci series till
        // range
        for (m = 2; m < no; m++) {
            k = i + j;
            i = j;
            j = k;

            // Store fibonacci series into b[]
            // array
            b[m] = k;
        }
        i = 5;
        System.out.println("\n" + "The Non-Fibonacci series that lies between 1 to "
             + no + " term of Fibonacci Series is: "+ "\n");

        // Loop to calculate Non-Fibonacci
        // series
        for (int ans = 4; ans < b[no - 1]; ans++) {
            if (ans != b[i])

                // Print Non-Fibonacci Series
                System.out.print(ans + "  ");
            else
                i++;
        }
    }
}

// This Solution is contributed by shinjanpatra.

Python3

i = 0
j = 1
b = []
no = 10  # Range is 10
b.append(0)
b.append(1)
if(no <= 1):  # Check if range is less equals to 1
    print("You have enter a wrong range...")
elif(no <= 5 and no > 1):  # check if range is greater than 1 and less equals to 5
    print("\nThere is not any Non-Fibonacci series that lies between 1 to ",
          no, " term of Fibonacci Series.")
else:  # If range is greater than 5
    for m in range(2, no):  # Loop to calculate fibonacci series till range
        k = i+j
        i = j
        j = k
        b.append(k)  # Store fibonacci series into list b
    i = 5
    print("\nThe Non-Fibonacci series that lies between 1 to ",
          no, " term of Fibonacci Series is:")
    for ans in range(4, b[no-1]):  # Loop to calculate Non-Fibonacci series
        if ans != b[i]:
            print(ans, end="  ")  # Print Non-Fibonacci Series
        else:
            i = i+1

C#

// C# code to implement the approach
using System;
class GFG {

  public static void Main(string[] args)
  {
    int[] holes = { 21, 3, 6 };
    int i = 0, j = 1, k, m, no = 10;
    int[] b = new int[10];

    // Range is 10
    b[1] = 0;
    b[2] = 1;

    // Check if range is less equals to 1
    if (no <= 1) {
      Console.Write("You have enter a wrong range");
    }

    // check if range is greater than 1
    // and less equals to 5
    else if (no <= 5 && no > 1) {
      Console.Write(
        "\n"
        + "There is not any Non-Fibonacci series that lies between 1 to"
        + no + " term of Fibonacci Series.");
    }

    // If range is greater than 5
    else {

      // Loop to calculate fibonacci series till
      // range
      for (m = 2; m < no; m++) {
        k = i + j;
        i = j;
        j = k;

        // Store fibonacci series into b[]
        // array
        b[m] = k;
      }
      i = 5;
      Console.WriteLine(
        "\n"
        + "The Non-Fibonacci series that lies between 1 to "
        + no + " term of Fibonacci Series is: ");

      // Loop to calculate Non-Fibonacci
      // series
      for (int ans = 4; ans < b[no - 1]; ans++) {
        if (ans != b[i])

          // Print Non-Fibonacci Series
          Console.Write(ans + "  ");
        else
          i++;
      }
    }
  }
}

// This Solution is contributed by phasing17

Javascript

<script>


// driver code

let i = 0, j = 1, k, m, no, b = new Array(10);

// Range is 10
no = 10;
b[1] = 0;
b[2] = 1;

// Check if range is less equals to 1
if (no <= 1) {
    console.log("You have enter a wrong range");
}

// check if range is greater than 1
// and less equals to 5
else if (no <= 5 && no > 1) {
    document.write("</br>","There is not any Non-Fibonacci series that lies between 1 to " + no + " term of Fibonacci Series.");
}

// If range is greater than 5
else {

    // Loop to calculate fibonacci series till
    // range
    for (m = 2; m < no; m++) {
        k = i + j;
        i = j;
        j = k;

        // Store fibonacci series into b[]
        // array
        b[m] = k;
    }
    i = 5;
    document.write("</br>","The Non-Fibonacci series that lies between 1 to " + no + " term of Fibonacci Series is: ","</br>");

        // Loop to calculate Non-Fibonacci
        // series
    for (let ans = 4; ans < b[no - 1]; ans++) {
        if (ans != b[i])

            // Print Non-Fibonacci Series
            document.write(ans , "  ");
        else
            i++;
    }
}

// This code is contributed by shinjanpatra

</script>

Output

The Non-Fibonacci series that lies between 1 to 10 term of Fibonacci Series is: 
4  6  7  9  10  11  12  14  15  16  17  18  19  20  22  23  24  25  26  27  28  29  30  31  32  33  

Time Complexity : O(n) , Auxiliary Space : O(n)

The above problem and solution are contributed by Hemang Sarkar.