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How do you do this in C# without using List?

I am new to C#. The following code was a solution I came up to solve a challenge. I am unsure how to do this without using List since my understanding is that you can't push to an array in C# since they are of fixed size.
Is my understanding of what I said so far correct?
Is there a way to do this that doesn't involve creating a new array every time I need to add to an array? If there is no other way, how would I create a new array when the size of the array is unknown before my loop begins?
Return a sorted array of all non-negative numbers less than the given n which are divisible both by 3 and 4. For n = 30, the output should be
threeAndFour(n) = [0, 12, 24].
int[] threeAndFour(int n) {
List<int> l = new List<int>(){ 0 };
for (int i = 12; i < n; ++i)
if (i % 12 == 0)
l.Add(i);
return l.ToArray();
}
EDIT: I have since refactored this code to be..
int[] threeAndFour(int n) {
List<int> l = new List<int>(){ 0 };
for (int i = 12; i < n; i += 12)
l.Add(i);
return l.ToArray();
}

A. Lists is OK
If you want to use a for to find out the numbers, then List is the appropriate data structure for collecting the numbers as you discover them.
B. Use more maths
static int[] threeAndFour(int n) {
var a = new int[(n / 12) + 1];
for (int i = 12; i < n; i += 12) a[i/12] = i;
return a;
}
C. Generator pattern with IEnumerable<int>
I know that this doesn't return an array, but it does avoid a list.
static IEnumerable<int> threeAndFour(int n) {
yield return 0;
for (int i = 12; i < n; i += 12)
yield return i;
}
D. Twist and turn to avoid a list
The code could for twice. First to figure the size or the array, and then to fill it.
int[] threeAndFour(int n) {
// Version: A list is really undesirable, arrays are great.
int size = 1;
for (int i = 12; i < n; i += 12)
size++;
var a = new int[size];
a[0] = 0;
int counter = 1;
for (int i = 12; i < n; i += 12) a[counter++] = i;
}

if (i % 12 == 0)
So you have figured out that the numbers which divides both 3 and 4 are precisely those numbers that divides 12.
Can you figure out how many such numbers there are below a given n? - Can you do so without counting the numbers - if so there is no need for a dynamically growing container, you can just initialize the container to the correct size.
Once you have your array just keep track of the next index to fill.

You could use Linq and Enumerable.Range method for the purpose. For example,
int[] threeAndFour(int n)
{
return Enumerable.Range(0,n).Where(x=>x%12==0).ToArray();
}
Enumerable.Range generates a sequence of integral numbers within a specified range, which is then filtered on the condition (x%12==0) to retrieve the desired result.

Since you know this goes in steps of 12 and you know how many there are before you start, you can do:
Enumerable.Range(0,n/12+1).Select(x => x*12).ToArray();

I am unsure how to do this without using List since my understanding is that you can't push to an array in C# since they are of fixed size.
It is correct that arrays can not grow. List were invented as a wrapper around a array that automagically grows whenever needed. Note that you can give List a integer via the Constructor, wich will tell it the minimum size it should expect. It will allocate at least that much the first time. This can limit growth related overhead.
And dictionaries are just a variation of the list mechanics, with Hash Table key search speed.
There is only 1 other Collection I know of that can grow. However it is rarely mentioned outside of theory and some very specific cases:
Linked Lists. The linked list has a unbeatable growth performance and the lowest issue of running into OutOfMemory Exceptions due to Fragmentation. Unfortunately, their random access times are the worst as a result. Unless you can process those collections exclusively sequentally from the start (or sometimes the end), their performance will be abysmal. Only stacks and queues are likely to use them. There is however still a implementation you could use in .NET: https://learn.microsoft.com/en-us/dotnet/api/system.collections.generic.linkedlist-1
Your code holds some potential too:
for (int i = 12; i < n; ++i)
if (i % 12 == 0)
l.Add(i);
It would way more effective to count up by 12 every itteration - you are only interested in every 12th number after all. You may have to change the loop, but I think a do...while would do. Also the array/minimum List size is easily predicted: Just divide n by 12 and add 1. But I asume that is mostly mock-up code and it is not actually that deterministic.

List generally works pretty well, as I understand your question you have challenged yourself to solve a problem without using the List class. An array (or List) uses a contiguous block of memory to store elements. Arrays are of fixed size. List will dynamically expand to accept new elements but still keeps everything in a single block of memory.
You can use a linked list https://learn.microsoft.com/en-us/dotnet/api/system.collections.generic.linkedlist-1?view=netframework-4.8 to produce a simulation of an array. A linked list allocates additional memory for each element (node) that is used to point to the next (and possibly the previous). This allows you to add elements without large block allocations, but you pay a space cost (increased use of memory) for each element added. The other problem with linked lists are you can't quickly access random elements. To get to element 5, you have to go through elements 0 through 4. There's a reason arrays and array like structures are favored for many tasks, but it's always interesting to try to do common things in a different way.

Pre-decrement of value in a for loop is not correctly decreasing value on first loop

I have the following for loop in my code (using C#)
for (int i = 150; i >= 75; --i)
{
print("I holds " + i);
images[i].gameObject.SetActive(false);
}
trying to run through each item in a list, and disable the object. The list holds 150 objects (but since it starts at value zero, the final reference position is 149)
So, I figured a for loop was a good way to iterate through them all. Yet, I try to decrease the value of i to 149 for the first run of the loop, but it still passes a value of 150 into the loop in the first run, which throws the expected ("Argument is out of range") error.
Can anyone work out why the decreased value isn't correctly being passed to the loop?
I tried both decreasing it before and after the first run of the loop, but both times it passes a value of 150 into the loop.
I feel this should be a relatively simple issue to solve, yet it's not working as I expected it to do!

for (int i = 10; i >= 0; --i)
is the same as
for (int i = 10; i >= 0; i--)
i does not decrease/increase on the first loop. This is for many languages. Just start with 149 and it works.
Answer for "Can anyone work out why the decreased value isn't correctly being passed to the loop?"

Another way to loop through all items of an array without caring of actual indices is to make use of a foreach statement:
foreach(var image in images)
{
image.gameObject.SetActive(false);
}
If you want to use a for statement. I would suggest you write it as below:
for(var i=0; i<images.Length; i++)
{
image[i].gameObject.SetActive(false);
}
Doing so, you are pretty confident that you are not going to be out of the array's size. You start at the element at the position with index of 0 and you read the last item stored in the array, in the position of images.Length-1.
Update
If you want to update only the first 75 items (where 75 is half the total items in the array) in your array you could try this:
for(var i=0; i<images.Length/2; i++)
{
image[i].gameObject.SetActive(false);
}

C# Trial division - first n primes. Error in logic?

In a course a problem was to list the first n primes. Apparently we should implement trial division while saving primes in an array to reduce the number of divisions required. Initially I misunderstood, but got a working if slower solution using a separate function to test for primality but I would like to implement it the way I should have done.
Below is my attempt, with irrelevant code removed, such as the input test.
using System;
namespace PrimeNumbers
{
class MainClass
{
public static void Main (string[] args)
{
Console.Write("How many primes?\n");
string s = Console.ReadLine();
uint N;
UInt32.TryParse(s, out N)
uint[] PrimeTable = new uint[N];
PrimeTable[0] = 2;
for (uint i=1; i < N; i++)//loop n spaces in array, [0] set already so i starts from 1
{
uint j = PrimeTable[i -1] + 1;//sets j bigger than biggest prime so far
bool isPrime = false;// Just a condition to allow the loop to break???(Is that right?)
while (!isPrime)//so loop continues until a break is hit
{
isPrime = true;//to ensure that the loop executes
for(uint k=0; k < i; k++)//want to divide by first i primes
{
if (PrimeTable[k] == 0) break;//try to avoid divide by zero - unnecessary
if (j % PrimeTable[k] == 0)//zero remainder means not prime so break and increment j
{
isPrime = false;
break;
}
}
j++;//j increment mentioned above
}
PrimeTable[i] = j; //not different if this is enclosed in brace above
}
for (uint i = 0; i < N; i++)
Console.Write(PrimeTable[i] + " ");
Console.ReadLine();
}
}
}
My comments are my attempt to describe what I think the code is doing, I have tried very many small changes, often they would lead to divide by zero errors when running so I added in a test, but I don't think it should be necessary. (I also got several out of range errors when trying to change the loop conditions.)
I have looked at several questions on stack exchange, in particular:
Program to find prime numbers
The first answer uses a different method, the second is close to what I want, but the exact thing is in this comment from Nick Larsson:
You could make this faster by keeping track of the primes and only
trying to divide by those.
C# is not shown on here: http://rosettacode.org/wiki/Sequence_of_primes_by_Trial_Division#Python
I have seen plenty of other methods and algorithms, such as Eratosthenes sieve and GNF, but really only want to implement it this way, as I think my problem is with the program logic and I don't understand why it doesn't work. Thanks

The following should solve your problem:
for (uint i = 1; i < numberOfPrimes; i++)//loop n spaces in array, [0] set already so i starts from 1
{
uint j = PrimeTable[i - 1] + 1;//sets j bigger than biggest prime so far
bool isPrime = false;// Just a condition to allow the loop to break???(Is that right?)
while (!isPrime)//so loop continues until a break is hit
{
isPrime = true;//to ensure that the loop executes
for (uint k = 0; k < i; k++)//want to divide by first i primes
{
if (PrimeTable[k] == 0) break;//try to avoid divide by zero - unnecessary
if (j % PrimeTable[k] == 0)//zero remainder means not prime so break and increment j
{
isPrime = false;
j++;
break;
}
}
}
PrimeTable[i] = j;
}
The major change that I did was move the incrementation of the variable j to inside the conditional prime check. This is because, the current value is not prime, so we want to check the next prime number and must move to the next candidate before breaking in the loop.
Your code was incrementing after the check was made. Which means that when you found a prime candidate, you would increment to the next candidate and assign that as your prime. For example, when j = 3, it would pass the condition, isPrime would still = true, but then j++ would increment it to 4 and that would add it to the PrimeTable.
Make sense?

This might not be a very good answer to your question, but you might want to look at this implementation and see if you can spot where yours differs.
int primesCount = 10;
List<uint> primes = new List<uint>() { 2u };
for (uint n = 3u;; n += 2u)
{
if (primes.TakeWhile(u => u * u <= n).All(u => n % u != 0))
{
primes.Add(n);
}
if (primes.Count() >= primesCount)
{
break;
}
}
This correctly and efficiently computes the first primesCount primes.

Random selection for a variable set with a guarantee of every item at least once

I am working on a game in c# but that detail is not really neccessary to solve my problem.
At I high level here is what I want:
I have a set that could have any number of items in it.
I want to randomly select 10 items from that set.
If the set has less than 10 items in then I expect to select the same
item more than once.
I want to ensure every item is selected at least once.
What would be the algorithm for this?
Sorry I'm not sure if this is an appropriate place to ask, but I've got no pen and paper to hand and I can't quite get my head round what's needed so appreciate the help.
In addition I might also want to add weights to the items to
increase/decrease chance of selection, so if you are able to
incorporate that into your answer that would be fab.
Finally thought I should mention that my set is actually a List<string>, which might be relevent if you prefer to give a full answer rather than psuedo code.

This is what I use to randomize an array. It takes an integer array and randomly sorts that list a certain amount of times determined by the random number (r).
private int[] randomizeArray(int[] i)
{
int L = i.Length - 1;
int c = 0;
int r = random.Next(L);
int prev = 0;
int curr = 0;
int temp;
while (c < r)
{
curr = random.Next(0, L);
if (curr != prev)
{
temp = i[prev];
i[prev] = i[curr];
i[curr] = temp;
c++;
}
}
return i;
}

If you look for effective code, my answer isnt it. In theory, create some collection you can remove from that will mirror your set. Then select random member of the object from it ...and remove, this will garantee items wont repeat(if possible).
Random rnd = new Random();
List<int> indexes = new List<int>(items.Count);
for (int i = 0; i < items.Count; i++)
indexes.Add(i);
List<string> selectedItems = new List<string>(10);
int tmp;
for(int i = 0; i < 10; i++)
{
tmp = rnd.Next(1,10000); //something big
if(indexes.Count > 0)
{
selectedItems.Add(yourItems[indexes[tmp%indexes.Count]]);
indexes.RemoveAt(tmp%indexes.Count);
}
else
selectedItems.Add(yourItems[rnd.Next(0,9)]); //you ran out of unique items
}
where items is your list and yourItems is list of selected items, you dont need to store them if you want process them right away

Perhaps shuffle the collection and pick elements from the front until you have the required amount.
Once you've gone through all the elements, you should perhaps shuffle it again, so you don't just repeat the same sequence.
The basic algorithm for shuffling: (in pseudo-code)
for i from n − 1 downto 1 do
j ← random integer with 0 ≤ j ≤ i
exchange a[j] and a[i]
With the above algorithm (or a minor variation), it's possible to just shuffle until you reach the required number of elements, no need to shuffle the whole thing.

Looping and changing a list - remove doesn't always work

I'm trying to go through a loop 40 times and changing a list in the process.
This is the code:
for (int i = 0; i < 40; i++)
{
location = rand.Next(rows.Count);
rank = rand2.Next(pondRanks.Count);
ComputerPonds[rows[location]].Rank = (PondRank)pondRanks[rank];
rows.Remove(location);
pondRanks.Remove(rank);
}
For some reason the remove doesn't happen all the time, and only sometimes. Anyone has a suggestion?
Both of the list are List , they have 40 elements, and I want to remove the element itself.
Even when debugging I can see that the list count isn't the same (they both have the same initial numbers and they both need to do remove at this loop). If it matters, I'm working on windows phone platform..

I'm pretty sure you should be using List.RemoveAt not List.Remove. RemoveAt will remove the item at the specified index, whereas Remove will look for that object you passed in and remove it from the List if it's in there. But I'm pretty sure that looking at your code that location and rank represent the index, not the objects themselves.
for (int i = 0; i < 39; i++)
{
location = rand.Next(rows.Count);
rank = rand2.Next(pondRanks.Count);
ComputerPonds[location].Rank = (PondRank)pondRanks[rank];
rows.RemoveAt(location);
pondRanks.RemoveAt(rank);
}
EDIT: You may also want to consider making sure that your rows and pondRanks have enough elements (39) before starting the loop (or altering the i < 39 to max out at the upper limit of their length)