Develop Reference

System.DivideByZeroException on high numbers in C#

So I've been trying to write a program in C# that returns all factors for a given number (I will implement user input later). The program looks as follows:
//Number to divide
long num = 600851475143;
//initializes list
List<long> list = new List<long>();
//Defines combined variable for later output
var combined = string.Join(", ", list);
for (int i = 1; i < num; i++)
{
if (num % i == 0)
{
list.Add(i);
Console.WriteLine(i);
}
}
However, after some time the program starts to also try to divide negative numbers, which after some time ends in a System.DivideByZeroException. It's not clear to me why it does this. It only starts to do this after the "num" variable contains a number with 11 digits or more. But since I need such a high number, a fix or similiar would be highly appreciated. I am still a beginner.
Thank you!

I strongly suspect the problem is integer overflow. num is a 64-bit integer, whereas i is a 32-bit integer. If num is more than int.MaxValue, then as you increment i it will end up overflowing back to negative values and then eventually 0... at which point num % i will throw.
The simplest option is just to change i to be a long instead:
for (long i = 1; i < num; i++)
It's unfortunate that there'd be no warning in your original code - i is promoted to long where it needs to be, because there's an implicit conversion from int to long. It's not obvious to me what would need to change for this to be spotted in the language itself. It would be simpler for a Roslyn analyzer to notice this sort of problem.

Simple program using Tasks

I got homework to create a program using Tasks.
The program should generate 100,000 numbers in the range from 100,000 to 100,000,000
Then check whether the number is a prime number and if that number is Fibonacci number.
There are strict requirements for this program:
1) The first task should generate the number.
2) Second task should check if the number is prime.
3) The third task should check if the number is fibonacci.
!! Only after the third action program should generate a new number. !!
I have written a program, but it takes a very long time before all the numbers is generated. What I'm doing wrong? Is there any other way to do it faster ? Because it takes about 25 minutes to generate all the numbers. (I'm using MS VStudio 2010, Framework 4)
Sorry for my English..
Code:
for (int i = 0; i < 100000; i++)
{
Task<int> t1 = Task<int>.Factory.StartNew(() => RandomGen1.Next()); // Generate Number
Task<string> t2 = Task<string>.Factory.StartNew(() => is_prime(t1.Result)); // Return Yes or No
Task<string> t3 = Task<string>.Factory.StartNew(() => IsFibonacci(t1.Result)); // Return Yes or No
Task.WaitAll(new Task[] {t1,t2,t3});
this.dataGridView1.Rows.Add(t1.Result, t2.Result, t3.Result);
}
Update:
Here's my is_prime and isFibonacci functions:
public string is_prime(int number)
{
for (int i = 2; i < number; ++i)
{
if (number % i == 0)
{
return "";
}
}
return "Yes";
}
static string IsFibonacci(int number)
{
double fi = (1 + Math.Sqrt(5)) / 2.0; //Golden ratio
int n = (int)Math.Floor(Math.Log(number * Math.Sqrt(5) + 0.5, fi)); //Find's the index (n) of the given number in the fibonacci sequence
int actualFibonacciNumber = (int)Math.Floor(Math.Pow(fi, n) / Math.Sqrt(5) + 0.5); //Finds the actual number corresponding to given index (n)
if (actualFibonacciNumber == number)
{
return "Yes";
}
return "";
}

Whilst I don't usually do homework for people, I found this a nice problem to solve, and I had a some code laying around from solving Project Euler questions that I could put to use.
I agree with one of the comments that this is a strange requirement to use to Tasks for, seems to be using Tasks for just for the sake of it.
The console app I put together runs in about 15 seconds. No, I'm not going to post the code, because you won't learn anything.
Without seeing the code behind your is_prime and IsFibonacci methods, it's hard to say what could be wrong. I hope you aren't doing something silly like calculating a list of all the fibonacci numbers up to the random number on each iteration through the loop, as that is going to be dreadfully slow.
Remember: A number is Fibonacci if and only if one or both of (5*n2 + 4) or (5*n2 – 4) is a perfect square.

Cartesian product subset returning set of mostly 0

I'm trying to calculate
If we calculated every possible combination of numbers from 0 to (c-1)
with a length of x
what set would occur at point i
For example:
c = 4
x = 4
i = 3
Would yield:
[0000]
[0001]
[0002]
[0003] <- i
[0010]
....
[3333]
This is very nearly the same problem as in the related question Logic to select a specific set from Cartesian set. However, because x and i are large enough to require the use of BigInteger objects, the code has to be changed to return a List, and take an int, instead of a string array:
int PossibleNumbers;
public List<int> Get(BigInteger Address)
{
List<int> values = new List<int>();
BigInteger sizes = new BigInteger(1);
for (int j = 0; j < PixelArrayLength; j++)
{
BigInteger index = BigInteger.Divide(Address, sizes);
index = (index % PossibleNumbers);
values.Add((int)index);
sizes *= PossibleNumbers;
}
return values;
}
This seems to behave as I'd expect, however, when I start using values like this:
c = 66000
x = 950000
i = (66000^950000)/2
So here, I'm looking for the ith value in the cartesian set of 0 to (c-1) of length 950000, or put another way, the halfway point.
At this point, I just get a list of zeroes returned. How can I solve this problem?
Notes: It's quite a specific problem, and I apologise for the wall-of-text, I do hope it's not too much, I was just hoping to properly explain what I meant. Thanks to you all!
Edit: Here are some more examples: http://pastebin.com/zmSDQEGC

Here is a generic base converter... it takes a decimal for the base10 value to convert into your newBase and returns an array of int's. If you need a BigInteger this method works perfectly well with just changing the base10Value to BigInteger.
EDIT: Converted method to BigInteger since that's what you need.
EDIT 2: Thanks phoog for pointing out BigInteger is base2 so changing the method signature.
public static int[] ConvertToBase(BigInteger value, int newBase, int length)
{
var result = new Stack<int>();
while (value > 0)
{
result.Push((int)(value % newBase));
if (value < newBase)
value = 0;
else
value = value / newBase;
}
for (var i = result.Count; i < length; i++)
result.Push(0);
return result.ToArray();
}
usage...
int[] a = ConvertToBase(13, 4, 4) = [0,0,3,1]
int[] b = ConvertToBase(0, 4, 4) = [0,0,3,1]
int[] c = ConvertToBase(1234, 12, 4) = [0,8,6,10]
However the probelm you specifically state is a bit large to test it on. :)
Just calculating 66000 ^ 950000 / 2 is a good bit of work as Phoog mentioned. Unless of course you meant ^ to be the XOR operator. In which case it's quite fast.
EDIT: From the comments... The largest base10 number that can be represented given a particular newBase and length is...
var largestBase10 = BigInteger.Pow(newBase, length)-1;

The first expression of the problem boils down to "write 3 as a 4-digit base-4 number". So, if the problem is "write i as an x-digit base-c number", or, in this case, "write (66000^950000)/2 as a 950000-digit base 66000 number", then does that make it easier?
If you're specifically looking for the halfway point of the cartesian product, it's not so hard. If you assume that c is even, then the most significant digit is c / 2, and the rest of the digits are zero. If your return value is all zeros, then you may have an off-by-one error, or the like, since actually only one digit is incorrect.

Efficient algorithm to get primes between two large numbers

I'm a beginner in C#, I'm trying to write an application to get primes between two numbers entered by the user. The problem is: At large numbers (valid numbers are in the range from 1 to 1000000000) getting the primes takes long time and according to the problem I'm solving, the whole operation must be carried out in a small time interval. This is the problem link for more explanation:
SPOJ-Prime
And here's the part of my code that's responsible of getting primes:
public void GetPrime()
{
int L1 = int.Parse(Limits[0]);
int L2 = int.Parse(Limits[1]);
if (L1 == 1)
{
L1++;
}
for (int i = L1; i <= L2; i++)
{
for (int k = L1; k <= L2; k++)
{
if (i == k)
{
continue;
}
else if (i % k == 0)
{
flag = false;
break;
}
else
{
flag = true;
}
}
if (flag)
{
Console.WriteLine(i);
}
}
}
Is there any faster algorithm?
Thanks in advance.

I remember solving the problem like this:
Use the sieve of eratosthenes to generate all primes below sqrt(1000000000) = ~32 000 in an array primes.
For each number x between m and n only test if it's prime by testing for divisibility against numbers <= sqrt(x) from the array primes. So for x = 29 you will only test if it's divisibile by 2, 3 and 5.
There's no point in checking for divisibility against non-primes, since if x divisible by non-prime y, then there exists a prime p < y such that x divisible by p, since we can write y as a product of primes. For example, 12 is divisible by 6, but 6 = 2 * 3, which means that 12 is also divisible by 2 or 3. By generating all the needed primes in advance (there are very few in this case), you significantly reduce the time needed for the actual primality testing.
This will get accepted and doesn't require any optimization or modification to the sieve, and it's a pretty clean implementation.
You can do it faster by generalising the sieve to generate primes in an interval [left, right], not [2, right] like it's usually presented in tutorials and textbooks. This can get pretty ugly however, and it's not needed. But if anyone is interested, see:
http://pastie.org/9199654 and this linked answer.

You are doing a lot of extra divisions that are not needed - if you know a number is not divisible by 3, there is no point in checking if it is divisible by 9, 27, etc. You should try to divide only by the potential prime factors of the number. Cache the set of primes you are generating and only check division by the previous primes. Note that you do need to generate the initial set of primes below L1.
Remember that no number will have a prime factor that's greater than its own square root, so you can stop your divisions at that point. For instance, you can stop checking potential factors of the number 29 after 5.
You also do can increment by 2 so you can disregard checking if an even number is prime altogether (special casing the number 2, of course.)
I used to ask this question during interviews - as a test I compared an implementation similar to yours with the algorithm I described. With the optimized algorithm, I could generate hundreds of thousands of primes very fast - I never bothered waiting around for the slow, straightforward implementation.

You could try the Sieve of Eratosthenes. The basic difference would be that you start at L1 instead of starting at 2.

Let's change the question a bit: How quickly can you generate the primes between m and n and simply write them to memory? (Or, possibly, to a RAM disk.) On the other hand, remember the range of parameters as described on the problem page: m and n can be as high as a billion, while n-m is at most a million.
IVlad and Brian most of a competitive solution, even if it is true that a slower solution could be good enough. First generate or even precompute the prime numbers less than sqrt(billion); there aren't very many of them. Then do a truncated Sieve of Eratosthenes: Make an array of length n-m+1 to keep track of the status of every number in the range [m,n], with initially every such number marked as prime (1). Then for each precomputed prime p, do a loop that looks like this:
for(k=ceil(m/p)*p; k <= n; k += p) status[k-m] = 0;
This loop marks all of the numbers in the range m <= x <= n as composite (0) if they are multiple of p. If this is what IVlad meant by "pretty ugly", I don't agree; I don't think that it's so bad.
In fact, almost 40% of this work is just for the primes 2, 3, and 5. There is a trick to combine the sieve for a few primes with initialization of the status array. Namely, the pattern of divisibility by 2, 3, and 5 repeats mod 30. Instead of initializing the array to all 1s, you can initialize it to a repeating pattern of 010000010001010001010001000001. If you want to be even more cutting edge, you can advance k by 30*p instead of by p, and only mark off the multiples in the same pattern.
After this, realistic performance gains would involve steps like using a bit vector rather than a char array to keep the sieve data in on-chip cache. And initializing the bit vector word by word rather than bit by bit. This does get messy, and also hypothetical since you can get to the point of generating primes faster than you can use them. The basic sieve is already very fast and not very complicated.

One thing no one's mentioned is that it's rather quick to test a single number for primality. Thus, if the range involved is small but the numbers are large (ex. generate all primes between 1,000,000,000 and 1,000,100,000), it would be faster to just check every number for primality individually.

There are many algorithms finding prime numbers. Some are faster, others are easier.
You can start by making some easiest optimizations. For example,
why are you searching if every number is prime? In other words, are you sure that, given a range of 411 to 418, there is a need to search if numbers 412, 414, 416 and 418 are prime? Numbers which divide by 2 and 3 can be skipped with very simple code modifications.
if the number is not 5, but ends by a digit '5' (1405, 335), it is not prime bad idea: it will make the search slower.
what about caching the results? You can then divide by primes rather by every number. Moreover, only primes less than square root of the number you search are concerned.
If you need something really fast and optimized, taking an existing algorithm instead of reinventing the wheel can be an alternative. You can also try to find some scientific papers explaining how to do it fast, but it can be difficult to understand and to translate to code.

int ceilingNumber = 1000000;
int myPrimes = 0;
BitArray myNumbers = new BitArray(ceilingNumber, true);
for(int x = 2; x < ceilingNumber; x++)
if(myNumbers[x])
{
for(int y = x * 2; y < ceilingNumber; y += x)
myNumbers[y] = false;
}
for(int x = 2; x < ceilingNumber; x++)
if(myNumbers[x])
{
myPrimes++;
Console.Out.WriteLine(x);
}
Console.Out.WriteLine("======================================================");
Console.Out.WriteLine("There is/are {0} primes between 0 and {1} ",myPrimes,ceilingNumber);
Console.In.ReadLine();

I think i have a very fast and efficient(generate all prime even if using type BigInteger) algorithm to getting prime number,it much more faster and simpler than any other one and I use it to solve almost problem related to prime number in Project Euler with just a few seconds for complete solution(brute force)
Here is java code:
public boolean checkprime(int value){ //Using for loop if need to generate prime in a
int n, limit;
boolean isprime;
isprime = true;
limit = value / 2;
if(value == 1) isprime =false;
/*if(value >100)limit = value/10; // if 1 number is not prime it will generate
if(value >10000)limit = value/100; //at lest 2 factor (not 1 or itself)
if(value >90000)limit = value/300; // 1 greater than average 1 lower than average
if(value >1000000)limit = value/1000; //ex: 9997 =13*769 (average ~ sqrt(9997) is 100)
if(value >4000000)limit = value/2000; //so we just want to check divisor up to 100
if(value >9000000)limit = value/3000; // for prime ~10000
*/
limit = (int)Math.sqrt(value); //General case
for(n=2; n <= limit; n++){
if(value % n == 0 && value != 2){
isprime = false;
break;
}
}
return isprime;
}

import java.io.*;
import java.util.Scanner;
class Test{
public static void main(String args[]){
Test tt=new Test();
Scanner obj=new Scanner(System.in);
int m,n;
System.out.println(i);
m=obj.nextInt();
n=obj.nextInt();
tt.IsPrime(n,m);
}
public void IsPrime(int num,int k)
{
boolean[] isPrime = new boolean[num+1];
// initially assume all integers are prime
for (int i = 2; i <= num; i++) {
isPrime[i] = true;
}
// mark non-primes <= N using Sieve of Eratosthenes
for (int i = 2; i*i <= num; i++) {
// if i is prime, then mark multiples of i as nonprime
// suffices to consider mutiples i, i+1, ..., N/i
if (isPrime[i]) {
for (int j = i; i*j <=num; j++) {
isPrime[i*j] = false;
}
}
}
for (int i =k; i <= num; i++) {
if (isPrime[i])
{
System.out.println(i);
}
}
}
}

List<int> prime(int x, int y)
{
List<int> a = new List<int>();
int b = 0;
for (int m = x; m < y; m++)
{
for (int i = 2; i <= m / 2; i++)
{
b = 0;
if (m % i == 0)
{
b = 1;
break;
}
}
if (b == 0) a.Add(m)`
}
return a;
}

How to simplify fractions in C#?

I'm looking for a library or existing code to simplify fractions.
Does anyone have anything at hand or any links?
P.S. I already understand the process but really don't want to rewrite the wheel
Update
Ok i've checked out the fraction library on the CodeProject
BUT the problem I have is a little bit tricker than simplifying a fraction.
I have to reduce a percentage split which could be 20% / 50% / 30% (always equal to 100%)

I think you just need to divide by the GCD of all the numbers.
void Simplify(int[] numbers)
{
int gcd = GCD(numbers);
for (int i = 0; i < numbers.Length; i++)
numbers[i] /= gcd;
}
int GCD(int a, int b)
{
while (b > 0)
{
int rem = a % b;
a = b;
b = rem;
}
return a;
}
int GCD(int[] args)
{
// using LINQ:
return args.Aggregate((gcd, arg) => GCD(gcd, arg));
}
I haven't tried the code, but it seems simple enough to be right (assuming your numbers are all positive integers and you don't pass an empty array).

You can use Microsoft.FSharp.Math.BigRational, which is in the free F# Power Pack library. Although it depends on F# (which is gratis and included in VS2010), it can be used from C#.
BigRational reduced = BigRational.FromInt(4)/BigRational.FromInt(6);
Console.WriteLine(reduced);
2/3
Console.WriteLine(reduced.Numerator);
2
Console.WriteLine(reduced.Denominator);
3

This library looks like it might be what you need:
var f = new Fraction(numerator, denominator);
numerator = f.Numerator;
denominator = f.Denominator;
Although, I haven't tested it, so it looks like you may need to play around with it to get it to work.

The best example of Fraction (aka Rational) I've seen is in Timothy Budd's "Classic Data Structures in C++". His implementation is very good. It includes a simple implementation of GCD algorithm.
It shouldn't be hard to adapt to C#.

A custom solution:
void simplify(int[] numbers)
{
for (int divideBy = 50; divideBy > 0; divideBy--)
{
bool divisible = true;
foreach (int cur in numbers)
{
//check for divisibility
if ((int)(cur/divideBy)*divideBy!=cur){
divisible = false;
break;
}
}
if (divisible)
{
for (int i = 0; i < numbers.GetLength(0);i++ )
{
numbers[i] /= divideBy;
}
}
}
}
Example usage:
int [] percentages = {20,30,50};
simplify(percentages);
foreach (int p in percentages)
{
Console.WriteLine(p);
}
Outupts:
2
3
5
By the way, this is my first c# program. Thought it would simply be a fun problem to try a new language with, and now I'm in love! It's like Java, but everything I wish was a bit different is exactly how I wanted it
<3 c#
Edit: Btw don't forget to make it static void if it's for your Main class.