Implemented nth Fibonacci number using different methods #7
Conversation
There was a problem hiding this comment.
Please remove the unrelated changes (Sieve of Eratosthenes which we btw already have, albeit with a slightly different interface, package-lock.json).
The structure I envision would be files src/math/fibonacci/recursive.lua, .../fibonacci/binet.lua etc, though packing them up in a table is fine too. Do not use global variables however, use local variables and return "exported" functions or tables appropriately.
The tests effectively all test the same thing (because the functions all fulfill the same spec). Deduplicate them (by extracting their body into a function).
(Note also that they're currently broken: You're not requireing or packing up the functions properly.)
| @@ -0,0 +1,80 @@ | |||
| -- Fibonacci.lua | |||
| -- Fibonacci.lua | ||
|
|
||
| -- Fibonacci Sequence: | ||
| -- The Fibonacci sequence is a series of numbers where each number (after the first two) is the sum of the two preceding ones. |
| -- The Fibonacci sequence is a series of numbers where each number (after the first two) is the sum of the two preceding ones. | ||
| -- More information: https://en.wikipedia.org/wiki/Fibonacci_number | ||
|
|
||
| -- Author: Gyandeep |
There was a problem hiding this comment.
Not useful to readers of the code. Your name will be in the commit history if/when this is merged.
|
|
||
| -- Author: Gyandeep | ||
|
|
||
| -- Implemented nth Fibonacci number using different approaches in O(2^N) , O(N) , O(logN) , O(1) . |
There was a problem hiding this comment.
This comment is effectively redundant.
|
|
||
|
|
||
| -- Function to calculate Fibonacci numbers using recursion | ||
| -- Time Complexity: O(2^n) |
There was a problem hiding this comment.
Inaccurate. Exponential, but not 2^n (it grows with the golden ratio). I'd just use --! exponential time complexity, just for illustrative purposes here.
| function fibonacci_binet(n) | ||
| local phi = (1 + math.sqrt(5)) / 2 | ||
| local psi = (1 - math.sqrt(5)) / 2 | ||
| return math.floor((math.pow(phi, n) - math.pow(psi, n)) / math.sqrt(5)) |
There was a problem hiding this comment.
Don't use math.pow, use ^ instead.
| function fibonacci_matrix(n) | ||
| if n <= 0 then | ||
| return 0 | ||
| else |
|
|
||
| -- Function to raise a 2x2 matrix to a power n using divide and conquer | ||
| -- Time Complexity: O(log(n)) | ||
| function matrix_power(matrix, n) |
There was a problem hiding this comment.
This is effectively exponentiation by squaring, which we already have and could use with a proper matrix class which provides multiplication. I'm not very keen on duplicating this.
|
|
||
| -- Function to multiply two 2x2 matrices | ||
| -- Time Complexity: O(1) | ||
| function matrix_multiply(a, b) |
There was a problem hiding this comment.
Ideally this should not need to be here if I had finished and pushed my matrix "class" yet :P
There was a problem hiding this comment.
| if n <= 0 then | ||
| return 0 | ||
| else | ||
| local matrix = {1, 1, 1, 0} |
There was a problem hiding this comment.
This def. warrants a short comment, IMO. The crucial point here is that this matrix maps a vector (a, b) to (b, a + b).
This PR introduces enhancements to the Fibonacci sequence calculation in the "Fibonacci.lua" file. It provides implementations for calculating the nth Fibonacci number using four different approaches with varying time complexities:
fibonacci_recursive(n)- Recursive approach.fibonacci_dp(n)- Dynamic programming approach.fibonacci_matrix(n)- Matrix exponentiation approach.fibonacci_binet(n)- Binet's formula approach.Details
Please review and merge this PR to enhance the Fibonacci calculations in codebase.
Thank you!