Generate Fibonacci Sequence

Generate Fibonacci Sequence - Problem

JavaScript Easy

Write a generator function that returns a generator object which yields the Fibonacci sequence.

The Fibonacci sequence is defined by the relation Xn = Xn-1 + Xn-2.

The first few numbers of the series are: 0, 1, 1, 2, 3, 5, 8, 13...

Your generator should yield numbers indefinitely when called repeatedly.

Input & Output

Example 1 — First 6 Numbers

$ Input: n = 6

› Output: [0,1,1,2,3,5]

💡 Note: The first 6 Fibonacci numbers: F(0)=0, F(1)=1, F(2)=0+1=1, F(3)=1+1=2, F(4)=1+2=3, F(5)=2+3=5

Example 2 — First 8 Numbers

$ Input: n = 8

› Output: [0,1,1,2,3,5,8,13]

💡 Note: Extending further: F(6)=3+5=8, F(7)=5+8=13. Each number is sum of previous two.

Example 3 — Edge Case

$ Input: n = 1

› Output: [0]

💡 Note: Only the first Fibonacci number, which is 0 by definition.

Constraints

1 ≤ n ≤ 50
Generated numbers will fit in 64-bit integer

Visualization

Tap to expand

Asked in

G Google 15 f Facebook 12 a Amazon 8 M Microsoft 6

The key insight is that each Fibonacci number only depends on the previous two numbers. The optimal approach uses an iterative generator that maintains only two variables, achieving O(n) time and O(1) space complexity.

Common Approaches

✓ Iterative Generator

⏱️ Time: O(n) Space: O(1)

Use an iterative approach to generate Fibonacci numbers by maintaining only the last two values. This eliminates redundant calculations and provides linear time complexity.

Memoized Generator

⏱️ Time: O(n) Space: O(n)

Combine recursion with memoization to avoid recalculating the same Fibonacci numbers. Store results in a cache for O(1) lookup of previously computed values.

Recursive Generator

⏱️ Time: O(2^n) Space: O(n)

Calculate each Fibonacci number using the classic recursive formula F(n) = F(n-1) + F(n-2). This approach recalculates values multiple times.

Iterative Generator — Algorithm Steps

Initialize first two Fibonacci numbers (0, 1)
For each subsequent number, calculate sum of previous two
Update the two tracking variables
Yield the current number

Visualization

Tap to expand

Step-by-Step Walkthrough

Initialize

Start with a=0, b=1

Generate Next

Calculate c = a + b, then shift: a=b, b=c

Result

Each number calculated exactly once in O(1) time

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

void solution(int n, long long* result) {
    if (n <= 0) return;
    
    long long a = 0, b = 1;
    for (int i = 0; i < n; i++) {
        if (i == 0) {
            result[i] = a;
        } else if (i == 1) {
            result[i] = b;
        } else {
            long long c = a + b;
            result[i] = c;
            a = b;
            b = c;
        }
    }
}

int main() {
    int n;
    scanf("%d", &n);
    
    if (n <= 0) {
        printf("[]\n");
        return 0;
    }
    
    long long* result = (long long*)malloc(n * sizeof(long long));
    solution(n, result);
    
    printf("[");
    for (int i = 0; i < n; i++) {
        printf("%lld", result[i]);
        if (i < n - 1) printf(",");
    }
    printf("]\n");
    
    free(result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single loop that runs n times to generate n Fibonacci numbers

⚠ Quadratic Growth

Space Complexity

O(1)

Only uses two variables to track previous Fibonacci numbers

⚡ Linearithmic Space

25.0K Views

Medium Frequency

~15 min Avg. Time

850 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Iterative Generator — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler