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