Given a number N, the task is to find the next Non-Fibonacci number.
Examples:
Input: N = 4
Output: 6
6 is the next non-fibonacci number after 4
Input: N = 6
Output: 7
Approach: As the fibonacci series is given as
0, 1, 1, 2, 3, 5, 8, 13, 21, 34….
It can be observed that there does not exists any 2 consecutive fibonacci numbers. Therefore, inorder to find the next Non-Fibonacci number, the following cases arise:
- If N <= 3, then the next Non-Fibonacci number will be 4
- If N > 3, then we will check if (N + 1) is fibonacci number or not.
- If (N + 1) is a fibonacci number then (N + 2) will be the next Non-Fibonacci number.
- Else (N + 1) will be the answer
- If (N + 1) is a fibonacci number then (N + 2) will be the next Non-Fibonacci number.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to check if a// number is perfect squarebool isPerfectSquare(int x){ int s = sqrt(x); return (s * s == x);}// Function to check if a// number is Fibonacci Numberbool isFibonacci(int N){ // N is Fibonacci if either // (5*N*N + 4), (5*N*N - 4) or both // is a perfect square return isPerfectSquare(5 * N * N + 4) || isPerfectSquare(5 * N * N - 4);}// Function to find// the next Non-Fibonacci Numberint nextNonFibonacci(int N){ // Case 1 // If N<=3, then 4 will be // next Non-Fibonacci Number if (N <= 3) return 4; // Case 2 // If N+1 is Fibonacci, then N+2 // will be next Non-Fibonacci Number if (isFibonacci(N + 1)) return N + 2; // If N+1 is Non-Fibonacci, then N+2 // will be next Non-Fibonacci Number else return N + 1;}// Driver codeint main(){ int N = 3; cout << nextNonFibonacci(N) << endl; N = 5; cout << nextNonFibonacci(N) << endl; N = 7; cout << nextNonFibonacci(N) << endl;} |
C
// C implementation of the approach#include <stdio.h>#include<stdbool.h>#include<math.h>// Function to check if a// number is perfect squarebool isPerfectSquare(int x){ int s = sqrt(x); return (s * s == x);}// Function to check if a// number is Fibonacci Numberbool isFibonacci(int N){ // N is Fibonacci if either // (5*N*N + 4), (5*N*N - 4) or both // is a perfect square return isPerfectSquare(5 * N * N + 4) || isPerfectSquare(5 * N * N - 4);}// Function to find// the next Non-Fibonacci Numberint nextNonFibonacci(int N){ // Case 1 // If N<=3, then 4 will be // next Non-Fibonacci Number if (N <= 3) return 4; // Case 2 // If N+1 is Fibonacci, then N+2 // will be next Non-Fibonacci Number if (isFibonacci(N + 1)) return N + 2; // If N+1 is Non-Fibonacci, then N+2 // will be next Non-Fibonacci Number else return N + 1;}// Driver codeint main(){ int N = 3; printf("%d\n",nextNonFibonacci(N)); N = 5; printf("%d\n",nextNonFibonacci(N)); N = 7; printf("%d",nextNonFibonacci(N)); }// This code is contributed by allwink45. |
Java
// Java implementation of the approachimport java.util.*;class GFG{ // Function to check if a// number is perfect squarestatic boolean isPerfectSquare(int x){ int s = (int) Math.sqrt(x); return (s * s == x);} // Function to check if a// number is Fibonacci Numberstatic boolean isFibonacci(int N){ // N is Fibonacci if either // (5*N*N + 4), (5*N*N - 4) or both // is a perfect square return isPerfectSquare(5 * N * N + 4) || isPerfectSquare(5 * N * N - 4);} // Function to find// the next Non-Fibonacci Numberstatic int nextNonFibonacci(int N){ // Case 1 // If N<=3, then 4 will be // next Non-Fibonacci Number if (N <= 3) return 4; // Case 2 // If N+1 is Fibonacci, then N+2 // will be next Non-Fibonacci Number if (isFibonacci(N + 1)) return N + 2; // If N+1 is Non-Fibonacci, then N+2 // will be next Non-Fibonacci Number else return N + 1;} // Driver codepublic static void main(String[] args){ int N = 3; System.out.print(nextNonFibonacci(N) +"\n"); N = 5; System.out.print(nextNonFibonacci(N) +"\n"); N = 7; System.out.print(nextNonFibonacci(N) +"\n");}}// This code is contributed by 29AjayKumar |
Python 3
# Python 3 implementation of the approachfrom math import sqrt# Function to check if a# number is perfect squaredef isPerfectSquare(x): s = sqrt(x) return (s * s == x)# Function to check if a# number is Fibonacci Numberdef isFibonacci(N): # N is Fibonacci if either # (5*N*N + 4), (5*N*N - 4) or both # is a perfect square return isPerfectSquare(5 * N * N + 4) or \ isPerfectSquare(5 * N * N - 4)# Function to find# the next Non-Fibonacci Numberdef nextNonFibonacci(N): # Case 1 # If N<=3, then 4 will be # next Non-Fibonacci Number if (N <= 3): return 4 # Case 2 # If N+1 is Fibonacci, then N+2 # will be next Non-Fibonacci Number if (isFibonacci(N + 1)): return N + 2 # If N+1 is Non-Fibonacci, then N+2 # will be next Non-Fibonacci Number else: return N # Driver codeif __name__ == '__main__': N = 3 print(nextNonFibonacci(N)) N = 4 print(nextNonFibonacci(N)) N = 7 print(nextNonFibonacci(N)) # This code is contributed by Surendra_Gangwar |
C#
// C# implementation of the approachusing System;class GFG{ // Function to check if a// number is perfect squarestatic bool isPerfectSquare(int x){ int s = (int) Math.Sqrt(x); return (s * s == x);} // Function to check if a// number is Fibonacci Numberstatic bool isFibonacci(int N){ // N is Fibonacci if either // (5*N*N + 4), (5*N*N - 4) or both // is a perfect square return isPerfectSquare(5 * N * N + 4) || isPerfectSquare(5 * N * N - 4);} // Function to find// the next Non-Fibonacci Numberstatic int nextNonFibonacci(int N){ // Case 1 // If N<=3, then 4 will be // next Non-Fibonacci Number if (N <= 3) return 4; // Case 2 // If N+1 is Fibonacci, then N+2 // will be next Non-Fibonacci Number if (isFibonacci(N + 1)) return N + 2; // If N+1 is Non-Fibonacci, then N+2 // will be next Non-Fibonacci Number else return N + 1;} // Driver codepublic static void Main(String[] args){ int N = 3; Console.Write(nextNonFibonacci(N) +"\n"); N = 5; Console.Write(nextNonFibonacci(N) +"\n"); N = 7; Console.Write(nextNonFibonacci(N) +"\n");}}// This code is contributed by Princi Singh |
Javascript
<script>// Javascript implementation of the approach// Function to check if a// number is perfect squarefunction isPerfectSquare(x){ var s = parseInt(Math.sqrt(x)); return (s * s == x);}// Function to check if a// number is Fibonacci Numberfunction isFibonacci(N){ // N is Fibonacci if either // (5*N*N + 4), (5*N*N - 4) or both // is a perfect square return isPerfectSquare(5 * N * N + 4) || isPerfectSquare(5 * N * N - 4);}// Function to find// the next Non-Fibonacci Numberfunction nextNonFibonacci(N){ // Case 1 // If N<=3, then 4 will be // next Non-Fibonacci Number if (N <= 3) return 4; // Case 2 // If N+1 is Fibonacci, then N+2 // will be next Non-Fibonacci Number if (isFibonacci(N + 1)) return N + 2; // If N+1 is Non-Fibonacci, then N+2 // will be next Non-Fibonacci Number else return N + 1;}// Driver codevar N = 3;document.write(nextNonFibonacci(N)+"<br>");N = 5;document.write(nextNonFibonacci(N)+"<br>");N = 7;document.write(nextNonFibonacci(N)+"<br>");// This code is contributed by rutvik_56.</script> |
Output:
4 6 9
Time Complexity: O(n1/2)
Auxiliary Space: O(1)
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