144
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 ...
- 18.8k
76
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 ...
- 14.6k
44
votes
Accepted
Checking if a number is divisible by 9
I see some things that you might want to use to improve your code.
Use an early bailout
If the passed number x is less than 9, the routine can immediately return <...
- 64.1k
41
votes
Accepted
Solving the Lazy Hobo Riddle
Notice how the square of a number 15 or greater exceeds 200? What you can do, is set the interval from 1 to ...
- 2,599
40
votes
Solving the Lazy Hobo Riddle
One thing you should note is that the fourth iteration is useless. Once you fixed the first 3 variables, you need to find the value for the fourth one that equals to 200 minus the sum of squares of ...
- 667
32
votes
Beehive numbers - using goto in C++
Your use of goto is wholly unjustified, not just because goto is taboo, but because your code has flow-of-control that is hard ...
- 142k
31
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,...
- 441
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:
...
- 3,363
30
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 ...
- 401
30
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 ...
- 691
26
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 ...
- 621
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 ...
- 18.8k
24
votes
Accepted
Greatest common divisor
A more elegant implementation of the gcd function:
int gcd(int a, int b) {
return b == 0 ? a : gcd(b, a % b);
}
To ensure ...
- 107k
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 ...
- 40.5k
22
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 ...
21
votes
Checking if a number is divisible by 9
After reading gnasher729 and Simon's answers, I was inspired to find the fastest possible way to do this.
Analysis of original function
The main problem with the original function is that it only ...
- 28.4k
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 ...
- 41.6k
21
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\$. ...
- 32.4k
20
votes
Accepted
Finding divisors of a number
This code could do with some editing...
First of all is the spacing. It is absolutely horrible (we will fix that after the edits).
Also, the naming is horrible. ...
- 9,414
20
votes
Accepted
Calculate square of a number without multiplication
A more efficient way to do this is to keep doubling the product while you can....
So, for example, \$5^2\$ is:
$$\begin{eqnarray*}
5 +& 5 &\longrightarrow 10 \\
10 +& 10 &\...
- 96.7k
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:
...
- 5,487
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 ...
- 40.5k
18
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 ...
- 53k
17
votes
Accepted
Wow that's a big integer! What's its largest prime factor?
What a fascinating solution! It seems that for every smart decision you made, you also threw in a poor decision or two.
Smart decision: In PrimeFactors(), you ...
- 142k
17
votes
Solving the Lazy Hobo Riddle
Some minor things, but may still be worth mentioning:
Whenever std::endl is used, the buffer gets flushed, which can add to performance a bit, especially if it's ...
- 34.7k
17
votes
Checking if a number is divisible by 9
I did not check if your code works, I assume it does since you say so.
Your code lacks consistency
if(divby8 == (orgx - (olddivby8 << 3)))
{
//...
}
...
- 4,481
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
...
- 11.4k
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
16
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 ...
- 568
14
votes
Solving the Lazy Hobo Riddle
As well as the excellent information from @EngieOP, you could also think about taking some repeated calculations out of the inner loop at the cost of an extra int per 'for' loop. These might be ...
- 241
Only top scored, non community-wiki answers of a minimum length are eligible