712058. Fibonacci series up to Nth term
Fibonacci series up to Nth term
Summary
The problem is about generating the Fibonacci series up to the Nth term. The Fibonacci sequence is a well-known series where each number is the sum of the two preceding ones, usually starting with 0 and 1. We need to find the Nth term in this sequence.
Detailed Explanation
To solve this problem, we can use a recursive approach or dynamic programming. Both approaches have their advantages, but we'll start with the simple recursive solution.
The recursive function will take an integer n as input and return the n-th Fibonacci number. The base cases are when n is 0 or 1, in which case the result is n. For larger values of n, we need to calculate the (n-1)-th and (n-2)-th Fibonacci numbers and add them together.
Here's a step-by-step breakdown:
- If
nis 0 or 1, returnn. - Calculate the
(n-1)-th Fibonacci number using the recursive function. - Calculate the
(n-2)-th Fibonacci number using the recursive function. - Return the sum of the two calculated numbers.
This approach has a time complexity of O(2^n) because we're recalculating the same Fibonacci numbers multiple times. To optimize this, we can use dynamic programming to store the previously calculated values and avoid redundant calculations.
Here's an example of how you could represent the Fibonacci sequence using an array:
0 1 2 3 4
Fib(0) | 0
Fib(1) | 1
Fib(2) | 1
Fib(3) | 2
Fib(4) | 3
Fib(n) |
Optimized Solutions
Java
public class Main {
public static void main(String[] args) {
int n = 10; // Change this to the desired Nth term
System.out.println(fibonacci(n));
}
public static int fibonacci(int n) {
if (n <= 1) return n;
int[] fib = new int[n + 1];
fib[0] = 0;
fib[1] = 1;
for (int i = 2; i <= n; i++) {
fib[i] = fib[i - 1] + fib[i - 2];
}
return fib[n];
}
}