153
votes
Accepted
Disproving Euler proposition by brute force in C
Note: At some point, this review drifted into the realm of assembler and GMP. An actual review is at the end of this post, whereas the first section discusses the runtime-problems concerning ...
- 19.3k
80
votes
Disproving Euler proposition by brute force in C
Well let's start with this:
for (a = 1; a < 100000; a++) {
for (b = 1; b < 300000; b++) {
for (c = 1; c < 500000; c++) {
let's ignore ...
- 14.9k
34
votes
Disproving Euler proposition by brute force in C
All of the answers given (when this 'answer' was first written) ignore an important constraint: native types. In C, a long int is a 32-bit (or greater) signed type,...
- 471
33
votes
Disproving Euler proposition by brute force in C
Some interesting things no one have mentioned about this, but it is an improvement when looking for the smallest solution:
If the \$\gcd(a,b,c) \neq 1\$ then \$a^4\$,\$b^4\$,\$c^4\$ and \$d^4\$ are ...
- 431
33
votes
Disproving Euler proposition by brute force in C
I'm not able to comment on vnp's solution, but vnp was right the first time: you can brute force it in \$O(n^2\log(n))\$ time and \$O(n)\$ space. You don't need \$O(n^2)\$ space because you don't have ...
- 751
31
votes
Python program to calculate GCD
Bug:
When I input -6 and -3 I expect the result to be 3 but I get a RecursionError exception instead:
...
- 3,392
27
votes
Disproving Euler proposition by brute force in C
Read the source
Since you've already identified the author, why not read the original paper?
Some misconceptions
In fact, the numbers found by Elkies were not the ones cited in the question. They ...
26
votes
Accepted
A math engine with support for complex numbers, calculus, and fractions
using namespace std
Given that you're using template and declare your class, you're working ...
- 19.3k
26
votes
Accepted
Arcsine function for a real-time control program
Use a namespace instead of a class
There is no reason to use a class if you only have static ...
- 61.7k
24
votes
Implementation of the trigonometric functions for real time application
Your implementation is going to be slow, and the excuse "I need it to take a fixed amount of time" does not justify this. Using plain tables smells like cargo culting as well.
So I'm not ...
- 641
23
votes
Accepted
Large Number Limit Extravaganza
Your method of generating primes is horribly slow. Running your code takes on the order of 5 minutes on my machine.
Consider as an alternative a prime sieve, even a simple one like the Sieve of ...
- 41.1k
22
votes
Disproving Euler proposition by brute force in C
I recommend to rewrite a problem as finding \$a,b,c,d\$ such that \$a^4 + b^4 = d^4 - c^4\$. Now you may only operate in pairs of powers. Building a table of sums takes \$O(n^2)\$. Building the table ...
- 57.3k
21
votes
Check if a given number N is a power of k
I'd follow Ludisposed's answer.
Except, there's a simple way to do this. Use logarithms.
Since the equation is \$N = k^a\$ you can change it to \$a = \log_k N\$.
And so if \$a\$ is an integer, then ...
- 43.5k
20
votes
Accepted
Efficiently find all the Pythagorean triplets where all numbers less than 1000
Some optimizations and style suggestions:
After finding a solution you can break:
...
- 5,664
20
votes
Sine function calculated via look-up table and linear interpolation
You only need to store values for \$\left[0, \frac{1}{2}\pi\right)\$
You can exploit the structure of the sine function, and only store values in the table for inputs between 0 and \$\frac{1}{2}\pi\$. ...
- 61.7k
19
votes
Python program to calculate GCD
Python has an official style-guide, PEP8. It recommends (among other things) the following:
Use whitespace around operators (so a = input(...)).
Don't use ...
- 41.1k
17
votes
Accepted
Check if a given number N is a power of k
Major
print " True "
Don't print but return variables from functions, that makes them usable later on
...
- 11.6k
17
votes
Newton Fractal writen in C
Use complex numbers
Since C99, C supports complex numbers, and has many mathematical functions that work on complex numbers. I would rewrite all your code to use ...
- 61.7k
16
votes
Accepted
Searching for three positive integers as a solution to an equation
Here are some simple optimizations you can make that can push your limit a bit higher:
Don't use floating point arithmetic. Floating point arithmetic is slow compared to integer arithmetic (this is ...
- 736
15
votes
Disproving Euler proposition by brute force in C
This is a different method from the other (priority queue) answer I submitted earlier. It is simpler and achieves \$O(n^2\log(n))\$ time and \$O(n)\$ memory with a better constant factor. You choose ...
- 751
15
votes
Efficiently find all the Pythagorean triplets where all numbers less than 1000
My "review" will have to be "If you really want it fast, you need a completely different approach". The following ~ O(N log N) approach is about ...
- 566
14
votes
C++ determinant calculator - follow-up
if(dimension == 0) {
return 0;
}
Mathematically, that is not correct. The determinant of an empty (i.e. zero-dimensional) matrix is one, see for example What ...
- 23.5k
13
votes
Accepted
RSA algorithm implementation in Python 3
I think your Modular Inverse implementation is slow. We can apply this Extended GCD algorithm recursive implementation which shows quite a dramatic speed improvement (at least on my machine):
...
- 17.3k
13
votes
Python program to calculate GCD
If you want to know whether there are more efficient algorithms than Euclid's, this is probably the wrong place to ask. Even Wikipedia would be a better starting point. The answer is yes but they are ...
- 6,016
13
votes
Plotting the Mandelbrot set efficiently
Unnecessary use of OpenGL
Using OpenGL to draw individual pixels is the completely wrong thing to do. Apart from requiring OpenGL support which might not be present on all systems, this has a huge ...
- 61.7k
12
votes
Disproving Euler proposition by brute force in C
Multiplication is not needed.
Consider how to calculate a series of squares 1,4,9,16
...
- 33.6k
12
votes
Accepted
Calculator in C++
I have some suggestions here:
Using switch/case instead of if/else looks a little better and slightly faster as also mentioned in the comments.
You could definitely work on formatting your code it ...
12
votes
Accepted
Count numbers that are the sum of three perfect cubes
Optimization: Code movement
You are repeatedly doing the same computations over and over. How many times is \$i^3\$ computed?
...
- 34k
12
votes
Dividing two numbers then handle the divide by zero exception with try/catch
If you know that you want to divide two numbers then IMHO it would make more sense to perform a pre-liminary check.
In other words, rather than executing the operation "blindly" by trusting ...
- 9,849
11
votes
Disproving Euler proposition by brute force in C
The solution you are talking about was not found by Elkies but by Frye. This is described in [Elkies]:
Euler conjectured in 1769 that the Diophantine equation
\$A^4 + B^4 + C^4 = D^4\$,(...)has no ...
- 1,348
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