Non Fibonacci Numbers

Difficulty Level : Medium
Last Updated : 10 Mar, 2021

Given a positive integer n, the task is to print the n’th 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

A naive solution is to find find Fibonacci numbers and then print first n numbers not present in the found Fibonacci numbers.
A better solution is to use the formula of Fibonacci numbers and keep adding of gap between two consecutive Fibonacci numbers. Value of sum of gap is count of non-fibonacci numbers seen so far. Below is implementation of 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;
}

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

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
?>

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>

Output :

Time Complexity : O(n)
Auxiliary Space : O(1)
The above problem and solution are contributed by Hemang Sarkar. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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