Fibonacci Series upto nth term
Detailed guide and Python implementation for the 'Fibonacci Series upto nth term' problem.
1. Concept Overview
The 'Fibonacci Series upto nth term' problem is a key challenge in the Basics section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Fibonacci Series upto nth term.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Fibonacci Series upto nth term carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Write a function fibonacci_series(n) that takes a non-negative integer n and returns a list containing the first n terms of the Fibonacci series. The Fibonacci series starts with 0 and 1, and each subsequent term is the sum of the two preceding terms. If n is 0, return an empty list.
- •0 <= n <= 50
Examples
n = 6
[0, 1, 1, 2, 3, 5]
The first 6 Fibonacci terms: 0, 1, 1 (0+1), 2 (1+1), 3 (1+2), 5 (2+3).
n = 1
[0]
The first 1 term of the Fibonacci series is just [0].
n = 0
[]
With n=0, there are no terms to return.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def fib_series_opt(n: int) -> list:
if n <= 0: return []
if n == 1: return [0]
res = [0, 1]
while len(res) < n:
res.append(res[-1] + res[-2])
return resBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def fib_series_brute(n: int) -> list:
if n <= 0: return []
def fib(k):
if k <= 1: return k
return fib(k-1) + fib(k-2)
return [fib(i) for i in range(n)]Algorithm Pattern Checklist
When dealing with Basics data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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