Given three integers A, B and N. A Custom Fibonacci series is defined as F(x) = F(x – 1) + F(x + 1) where F(1) = A and F(2) = B. Now the task is to find the Nth term of this series.
Examples:
Input: A = 10, B = 17, N = 3
Output: 7
10, 17, 7, -10, -17, …
Input: A = 50, B = 12, N = 10
Output: -50
Approach: It can be observed that the series will go on like A, B, B – A, -A, -B, A – B, A, B, B – A, …
Below is the implementation of the above approach:
C++
// C++ implementation of the Custom Fibonacci series#include <bits/stdc++.h>using namespace std;// Function to return the nth term// of the required sequenceint nth_term(int a, int b, int n){ int z = 0; if (n % 6 == 1) z = a; else if (n % 6 == 2) z = b; else if (n % 6 == 3) z = b - a; else if (n % 6 == 4) z = -a; else if (n % 6 == 5) z = -b; if (n % 6 == 0) z = -(b - a); return z;}// Driver codeint main(){ int a = 10, b = 17, n = 3; cout << nth_term(a, b, n); return 0;} |
Java
// Java implementation of the// Custom Fibonacci seriesclass GFG{// Function to return the nth term// of the required sequencestatic int nth_term(int a, int b, int n){ int z = 0; if (n % 6 == 1) z = a; else if (n % 6 == 2) z = b; else if (n % 6 == 3) z = b - a; else if (n % 6 == 4) z = -a; else if (n % 6 == 5) z = -b; if (n % 6 == 0) z = -(b - a); return z;}// Driver codepublic static void main(String[] args){ int a = 10, b = 17, n = 3; System.out.println(nth_term(a, b, n));}}// This code is contributed by Rajput-Ji |
Python 3
# Python 3 implementation of the# Custom Fibonacci series# Function to return the nth term# of the required sequencedef nth_term(a, b, n): z = 0 if (n % 6 == 1): z = a elif (n % 6 == 2): z = b elif (n % 6 == 3): z = b - a elif (n % 6 == 4): z = -a elif (n % 6 == 5): z = -b if (n % 6 == 0): z = -(b - a) return z# Driver codeif __name__ == '__main__': a = 10 b = 17 n = 3 print(nth_term(a, b, n)) # This code is contributed by Surendra_Gangwar |
C#
// C# implementation of the// Custom Fibonacci seriesusing System;class GFG{ // Function to return the nth term// of the required sequencestatic int nth_term(int a, int b, int n){ int z = 0; if (n % 6 == 1) z = a; else if (n % 6 == 2) z = b; else if (n % 6 == 3) z = b - a; else if (n % 6 == 4) z = -a; else if (n % 6 == 5) z = -b; if (n % 6 == 0) z = -(b - a); return z;}// Driver codestatic public void Main (){ int a = 10, b = 17, n = 3; Console.Write(nth_term(a, b, n));}}// This code is contributed by ajit. |
Javascript
<script>// javascript implementation of the// Custom Fibonacci series // Function to return the nth term // of the required sequence function nth_term(a , b , n) { var z = 0; if (n % 6 == 1) z = a; else if (n % 6 == 2) z = b; else if (n % 6 == 3) z = b - a; else if (n % 6 == 4) z = -a; else if (n % 6 == 5) z = -b; if (n % 6 == 0) z = -(b - a); return z; } // Driver code var a = 10, b = 17, n = 3; document.write(nth_term(a, b, n));// This code is contributed by Rajput-Ji </script> |
Output:
7
Time Complexity: O(1)
Auxiliary Space: O(1)
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