Fibonacci Sequence

Generates the first n numbers in the Fibonacci sequence

Problem Overview

🌀 Nature's Mathematical Pattern
The Fibonacci sequence is one of nature's most beautiful mathematical patterns! Starting with 0 and 1, each subsequent number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13...

🌿 Found Everywhere in Nature:

Spiral patterns in sunflower seeds and pinecones
Branch arrangements in trees and leaf patterns
Shell spirals and galaxy formations
Proportions in art and architecture (Golden Ratio)

🧮 How the Generation Works:

Start with base cases: F(0) = 0, F(1) = 1
For n ≥ 2: F(n) = F(n-1) + F(n-2)
Build sequence iteratively for optimal performance
Use memoization to optimize recursive approaches
Two Efficient Approaches:
Iterative Method: Linear time with simple loop construction
Memoized Recursive: Elegant recursion with caching optimization

💡 Learning & Interview Value:

Classic dynamic programming introduction
Demonstrates iteration vs recursion trade-offs
Foundation for understanding optimization techniques
Common technical interview warm-up question
Real-World Applications:
Computer graphics and spiral generation
Financial modeling and market analysis
Algorithm optimization and performance testing
Mathematical research and golden ratio calculations

Concepts

iterationrecursionmemoizationarray manipulation

Complexity Analysis

Time:O(n) for iterative/memoized

Space:O(n)

Solutions

FibonacciSeq

Time: O(n) | Space: O(n)

export function FibonacciSeq(count: number): number[] {
  if (!Number.isInteger(count)) throw new Error("Input must be an integer");
  if (count < 0) throw new Error("Input must be non-negative");
  if (count === 0) return [];
  if (count === 1) return [0];
  if (count === 2) return [0, 1];

  const fibSeq: number[] = [0, 1];
  for (let i = 2; i < count; i++) fibSeq[i] = fibSeq[i - 1] + fibSeq[i - 2];
  return fibSeq;
}

Examples & Test Cases

#1n=7

Input:7

Output:

[
  0,
  1,
  1,
  2,
  3,
  5,
  8
]

#2n=0

Input:0

Output:[]

#3n=1

Input:1

Output:

[
  0
]

#4n=2

Input:2

Output:

[
  0,
  1
]

#5Negative error

Input:-1

Output:{}

#6Non-integer error

Input:3.5

Output:{}