Develop Reference

Every combination of integers between specific range in combination with a list of strings

I have the following problem:
I have three elements a, b and c. And also integers from 0 to 100. How can I get all the possible combinations to look like:
a 0 b 0 c 0
a 1 b 0 c 0
a 0 b 1 c 0
a 0 b 0 c 1
a 1 b 1 c 0
...
a 100 b 100 c 100
and so on? I am using C# but I am rather struggling to find the correct algorithm independently of programming language. Unfortunately I do not really understand carthesian products etc.

You say you want to
find the correct algorithm independently of programming language
So I shall try to answer this using the minimum of programming language features. The example I shall give assumes the programming language has expandable lists, arrays, arrays of arrays and the ability to shallow clone an array. These are common programming features, so hopefully this will be OK.
To solve this problem, you need to produce all the combinations of 3 sets of N integers where each set consists the integers from 0..N-1. (The set of combinations of a set of sets - which is what this is - is called the Cartesian Product of those sets.)
The solution below uses recursion, but we don't need to worry about stack overflow because the stack depth does not exceed the number of sets to combine - in this case, 3. (Normally with recursion you would try to use a stack class to manage it, but that makes the code more complicated.)
How it works:
combine() recursively iterates through all elements of each set, and at each level of recursion it begins processing the elements of the next set.
So the outer level of recursion begins iterating over all the elements of set[0], and for each element it fills in the next item of the current combination with that element.
Then: if that was the last set, the combination is complete and it is output. Otherwise: a recursive call is made to start filling in the elements from the next set.
Once we have all the combinations, we can just iterate through them and intersperse them
with a, b and c as per your requirement.
Putting this together:
using System;
using System.Collections.Generic;
namespace ConsoleApp1
{
class Program
{
static void Main()
{
var sets = createSets(3, 10);
var combinations = Combinations(sets);
foreach (var combination in combinations)
{
Console.WriteLine($"a {combination[0]} b {combination[1]} c {combination[2]}");
}
}
static int[][] createSets(int numSets, int intsPerSet)
{
int[][] sets = new int[numSets][];
// All the sets are the same, so we can just use copies of it rather than create multiples.
int[] oneSet = new int[intsPerSet];
for (int i = 0; i < intsPerSet; ++i)
oneSet[i] = i;
for (int i = 0; i < numSets; ++i)
sets[i] = oneSet;
return sets;
}
public static List<int[]> Combinations(int[][] sets)
{
var result = new List<int[]>();
combine(sets, 0, new int[sets.Length], result);
return result;
}
static void combine(int[][] sets, int set, int[] combination, List<int[]> output)
{
for (int i = 0; i < sets[set].Length; ++i)
{
combination[set] = sets[set][i];
if (set < (sets.Length - 1))
combine(sets, set + 1, combination, output);
else
output.Add((int[])combination.Clone());
}
}
}
}
Notes
This is an inefficient implementation because it returns all the combinations in one huge list. I kept it this way for simplicity (and to reduce the number of program language features required for its implementation). A better solution in C# would be to pass in an Action<int[]> to be called with each combination - then the results wouldn't need to be returned via a huge list.
This doesn't produce the results in the same order as your sample output. I have assumed that this doesn't matter!
A great Linq implementation of the Cartesian Product is presented by Eric Lippert here. I highly recommending reading it!

If the order of the output doesn't matter, this should be enough:
for(int i = 0; i <= 100; i++){
for(int j = 0; j <= 100; j++){
for(int k = 0; k <= 100; k++){
Console.WriteLine($"a {i} b {j} c {k} ");
}
}
}
OUTPUT
a 0 b 0 c 0
a 0 b 0 c 1
a 0 b 0 c 2
a 0 b 0 c 3
...
a 100 b 100 c 100

Best way to choose two random ints to assign values to

I am creating a Dungeons and Dragons Character Creator. There is a randomize feature that is going to create a complete character sheet. There is a part that I have gotten to and I am not quite sure the best way to proceed.
The way I have the racial modifiers set up is with if statements. Here is an example.
if (raceInt == 0 || raceInt == 2 || raceInt == 10)
{
raceStrMod = 2;
}
if (raceInt == 3 || raceInt == 4 || raceInt == 5 || raceInt == 11 || raceInt == 12)
{
raceDexMod = 2;
}
However there are races that have modifiers that let you select two stats to add a modifier to, such as Strength or Dexterity. What would be the best way to select two random ints for just those races?
For example, the half-elf race which would get +2 to Dex and then +1 to two other random stats. So I need to find a way to randomly select two of the remaining ints to make the value = 1.
My race mod ints are initialized as
int raceStrMod = 0;
int raceDexMod = 0;
int raceConMod = 0;
int raceIntMod = 0;
int raceWisMod = 0;
int raceChaMod = 0;
Then the if statements assign a value dependent on which race was randomly selected.
Thank you all for the input! This is how I ended up coding it
if (raceInt == 9)
{
int randomX = rnd.Next(1, 5);
int randomY = rnd.Next(1, 5);
int attempts = 0;
while (randomX == randomY && attempts < 10)
{
randomY = rnd.Next(1, 5);
attempts++;
}
//if they are still not unique after 10 attempts
if (randomX == randomY)
{
if (randomX == 5)
randomY = 1;
else
randomY = randomX + 1;
}
int[] randomNumbers = { randomX, randomY };
foreach (int i in randomNumbers)
{
switch (i)
{
case 1:
raceStrMod = 1;
break;
case 2:
raceDexMod = 1;
break;
case 3:
raceConMod = 1;
break;
case 4:
raceIntMod = 1;
break;
case 5:
raceWisMod = 1;
break;
}
}
}

Has your class introduced you to enum types yet? If not, is there any restriction on your final project with respect to using language features that weren't taught in the class?
Your question is arguably too broad, as there are many different ways to address this sort of thing even in real-world code, and the classroom context introduces potential roadblocks that while might constrain the question, being unknown they make it impossible to know what answer is actually going to work for you.
That said…
Ignoring the classroom aspect and focusing only on the problem itself, I would use enum types and dictionaries for this sort of thing. For example:
enum Attribute
{
Strength,
Dexterity,
Constitution,
Charisma,
Intelligence,
Wisdom,
Count, // must always be last
}
Dictionary<Attribute, int> modifiers = new Dictionary<Attribute, int>();
Then you can pick a random attribute like (assuming you have a random variable referencing a Random object…don't make the classic newbie mistake of creating a new Random object every time you want to pick a new random number):
Attribute attributeToModify = (Attribute)random.Next((int)Attribute.Count);
And you can store that selection like:
modifiers[attributeToModify] = 1;
This can be used to store however many modifiers you like. You can encapsulate that in an object representing the character itself, or you could put it into a separate AttributeModifiers class. One advantage of doing the latter would be that if you have modifiers that come from different sources, you can track that in the character object as a list of AttributeModifier instances, each in turn keeping track of what the actual source of those modifiers are.
This just barely scratches the surface. As I noted, the question itself is fairly broad. But I strongly recommend using the available language features to ensure that your variables represent things in a type-specific way, rather than just using int values for things that aren't really integers, and to use collection classes that more correctly represent the semantics of what your code is intended to do.
Note that this also means you probably should have an enum type for the races. E.g.:
enum Race
{
Dwarf,
Elf,
HalfElf,
Halfling,
HalfOrc,
Human,
// etc.
}
And your chain of if statements is probably better represented as a switch:
Attribute racialMod;
switch (race)
{
case Human:
case Halfling:
// etc.
racialMod = Attribute.Strength;
break;
case Elf:
case HalfElf:
// etc.
racialMod = Attribute.Dexterity;
break;
}
modifiers[racialMod] = 2;
Something like that. The point is to make sure the code reads more like what the original specification would say (if you actually had written one). This will make the code easier to understand, and it will be less likely for you to put bugs in the code (e.g. you accidentally type the wrong magic, unnamed integer).

I am creating a Dungeons and Dragons Character Creator.
That's a fun beginner project; I did the same when I was learning to program.
I need to find a way to randomly select two of the remaining...
You need to find two distinct values, call then x and y. The solution you've arrived at is:
Generate x
Try to generate y ten times
If no attempt succeeded to find a distinct y, hard-code a choice.
That works, and you almost never have to use the hard-coded choice. But I thought you might be interested to know that there is an easier way to generate two distinct numbers. Let's suppose we want two distinct numbers from 0, 1, 2, 3 or 4. (Obviously if you want a different range, say, 1 through 5, you can solve that problem by generating two distinct numbers 0->4 and then adding one to each.)
The improved algorithm is:
Choose x between 0 and 4 as usual.
Choose n between 1 and 4.
y = (x + n) % 5;
Think about it this way. Suppose we make a list like this:
0, 1, 2, 3, 4, 0, 1, 2, 3
We randomly choose x from the first five entries on the list, and then we choose y by stepping forwards between 1 and 4 steps. Since the list does not repeat in one to four steps, we know that we'll get two unique elements. The math does the equivalent of that.
You could similarly have used % in your program:
if (randomX == 5)
randomY = 1;
else
randomY = randomX + 1;
could be written
randomY = randomX % 5 + 1
If you're unfamiliar with %, it is the remainder operator. It is the complement of the / operator. The rule is:
int x = whatever;
int y = whatever;
int r = x % y;
is the same as:
int r = x - (x / y) * y;
That is, it is the remainder when x is divided by y. Keep in mind that the remainder can be negative!

(Disclaimer: I don't love this option, but couldn't think of another way other than reflection which is even nastier)
You could define a class that masks the fact that all of the mods are stored as an array and therefore can be indexed using a random number.
Something like the following:
public class StatMods
{
public int RaceStrMod { get { return this.mods[0]; } set { this.mods[0] = value; } }
public int RaceDexMod { get { return this.mods[1]; } set { this.mods[1] = value; } }
public int RaceConMod { get { return this.mods[2]; } set { this.mods[2] = value; } }
public int RaceIntMod { get { return this.mods[3]; } set { this.mods[3] = value; } }
public int RaceWisMod { get { return this.mods[4]; } set { this.mods[4] = value; } }
public int RaceChaMod { get { return this.mods[5]; } set { this.mods[5] = value; } }
private readonly int[] mods;
private static readonly Random rand = new Random();
public StatMods()
{
this.mods = new int[6];
}
public void ApplyRandomMod(int modification)
{
this.mods[rand.Next(0, 6)] += modification;
}
}

Priority Queue remove items with same priority first one entered

I've got a priority queue created and working that enters items in order and removes them in order. Even if two numbers have the same priority, it removes the one that was entered first.
If there are three numbers that have the same priority, it does not remove the first one. How would I go about doing this, or should it do this?
Dequeue function:
public void deQueue(Animal item)
{
item = items.elements[0];
items.elements[0] = items.elements[numItems - 1];
numItems--;
items.ReheapDown(0, numItems - 1);
}
ReheapDown Function:
public void ReheapDown(int root, int bottom)
{
int maxchild, rightchild, leftchild;
leftchild = root * 2 + 1;
rightchild = root * 2 + 2;
if (leftchild <= bottom)
{
if (leftchild == bottom)
maxchild = leftchild;
else
{
if (elements[leftchild].priority <= elements[rightchild].priority)
maxchild = rightchild;
else
maxchild = leftchild;
}
if (elements[root].priority < elements[maxchild].priority)
{
Swap(elements, root, maxchild);
ReheapDown(maxchild, bottom);
}
}
}

In this line
if (elements[leftchild].priority <= elements[rightchild].priority)
you swap elements if they're equal. So let's say you enter the numbers [2, 2, 1, 3], in that order. Let's call the second 2, "2*", to differentiate it from the first one. The resulting heap is:
1
/ \
2 2*
/
3
Now, you remove 1. So then you replace the 1 with 3:
3
/ \
2 2*
In your ReheapDown method, the parent has two children, and you're selecting the smallest child. When you compare the two 2's, you have this code:
if (elements[leftchild].priority <= elements[rightchild].priority)
maxchild = rightchild;
else
maxchild = leftchild;
Since 2 == 2, it sets maxchild = rightchild, so the new root becomes 2*--the second 2 that was entered. Your heap now looks like this:
2*
/ \
2 3
And the next thing to be removed will be 2*.
You might think, then, that if you change that <= to <, it'll solve your problem. But it won't.
When you consider all the different ways that the heap can mutate, it's impossible to guarantee that equal items will be removed in the same order that they were inserted, unless you supply additional information. Consider what happens if you enter items in the order [1, 3, 2, 2*]. The resulting heap is:
1
/ \
2* 2
/
3
If you remove 1, you end up with:
3
/ \
2* 2
In this case, the <= would help you out. But in the previous case, it wouldn't.
The only way to guarantee removal order of equal items is to add a second condition on your comparison--basically, you have to make those equal items unequal. You either need to add a date stamp or sequential number to the key so that you can identify the insertion order.

Bug in Microsoft's internal PriorityQueue<T>?

In the .NET Framework in PresentationCore.dll, there is a generic PriorityQueue<T> class whose code can be found here.
I wrote a short program to test the sorting, and the results weren't great:
using System;
using System.Collections.Generic;
using System.Diagnostics;
using MS.Internal;
namespace ConsoleTest {
public static class ConsoleTest {
public static void Main() {
PriorityQueue<int> values = new PriorityQueue<int>(6, Comparer<int>.Default);
Random random = new Random(88);
for (int i = 0; i < 6; i++)
values.Push(random.Next(0, 10000000));
int lastValue = int.MinValue;
int temp;
while (values.Count != 0) {
temp = values.Top;
values.Pop();
if (temp >= lastValue)
lastValue = temp;
else
Console.WriteLine("found sorting error");
Console.WriteLine(temp);
}
Console.ReadLine();
}
}
}
Results:
2789658
3411390
4618917
6996709
found sorting error
6381637
9367782
There is a sorting error, and if the sample size is increased, the number of sorting errors increases somewhat proportionally.
Have I done something wrong? If not, where is the bug in the code of the PriorityQueue class located exactly?

The behavior can be reproduced using the initialization vector [0, 1, 2, 4, 5, 3]. The result is:
[0, 1, 2, 4, 3, 5]
(we can see that 3 is incorrectly placed)
The Push algorithm is correct. It builds a min-heap in a straightforward way:
Start from the bottom right
If the value is greater than the parent node then insert it and return
Otherwise, put instead the parent in the bottom right position, then try inserting the value at the parent place (and keep swapping up the tree until the right place has been found)
The resulting tree is:
0
/ \
/ \
1 2
/ \ /
4 5 3
The issue is with the Pop method. It starts by considering the top node as a "gap" to fill (since we popped it):
*
/ \
/ \
1 2
/ \ /
4 5 3
To fill it, it searches for the lowest immediate child (in this case: 1). It then moves the value up to fill the gap (and the child is now the new gap):
1
/ \
/ \
* 2
/ \ /
4 5 3
It then does the exact same thing with the new gap, so the gap moves down again:
1
/ \
/ \
4 2
/ \ /
* 5 3
When the gap has reached the bottom, the algorithm... takes the bottom-rightmost value of the tree and uses it to fill the gap:
1
/ \
/ \
4 2
/ \ /
3 5 *
Now that the gap is at the bottom-rightmost node, it decrements _count to remove the gap from the tree:
1
/ \
/ \
4 2
/ \
3 5
And we end up with... A broken heap.
To be perfectly honest, I don't understand what the author was trying to do, so I can't fix the existing code. At most, I can swap it with a working version (shamelessly copied from Wikipedia):
internal void Pop2()
{
if (_count > 0)
{
_count--;
_heap[0] = _heap[_count];
Heapify(0);
}
}
internal void Heapify(int i)
{
int left = (2 * i) + 1;
int right = left + 1;
int smallest = i;
if (left <= _count && _comparer.Compare(_heap[left], _heap[smallest]) < 0)
{
smallest = left;
}
if (right <= _count && _comparer.Compare(_heap[right], _heap[smallest]) < 0)
{
smallest = right;
}
if (smallest != i)
{
var pivot = _heap[i];
_heap[i] = _heap[smallest];
_heap[smallest] = pivot;
Heapify(smallest);
}
}
Main issue with that code is the recursive implementation, which will break if the number of elements is too large. I strongly recommend using an optimized thirdparty library instead.
Edit: I think I found out what is missing. After taking the bottom-rightmost node, the author just forgot to rebalance the heap:
internal void Pop()
{
Debug.Assert(_count != 0);
if (_count > 1)
{
// Loop invariants:
//
// 1. parent is the index of a gap in the logical tree
// 2. leftChild is
// (a) the index of parent's left child if it has one, or
// (b) a value >= _count if parent is a leaf node
//
int parent = 0;
int leftChild = HeapLeftChild(parent);
while (leftChild < _count)
{
int rightChild = HeapRightFromLeft(leftChild);
int bestChild =
(rightChild < _count && _comparer.Compare(_heap[rightChild], _heap[leftChild]) < 0) ?
rightChild : leftChild;
// Promote bestChild to fill the gap left by parent.
_heap[parent] = _heap[bestChild];
// Restore invariants, i.e., let parent point to the gap.
parent = bestChild;
leftChild = HeapLeftChild(parent);
}
// Fill the last gap by moving the last (i.e., bottom-rightmost) node.
_heap[parent] = _heap[_count - 1];
// FIX: Rebalance the heap
int index = parent;
var value = _heap[parent];
while (index > 0)
{
int parentIndex = HeapParent(index);
if (_comparer.Compare(value, _heap[parentIndex]) < 0)
{
// value is a better match than the parent node so exchange
// places to preserve the "heap" property.
var pivot = _heap[index];
_heap[index] = _heap[parentIndex];
_heap[parentIndex] = pivot;
index = parentIndex;
}
else
{
// Heap is balanced
break;
}
}
}
_count--;
}

Kevin Gosse's answer identifies the problem. Although his re-balancing of the heap will work, it's not necessary if you fix the fundamental problem in the original removal loop.
As he pointed out, the idea is to replace the item at the top of the heap with the lowest, right-most item, and then sift it down to the proper location. It's a simple modification of the original loop:
internal void Pop()
{
Debug.Assert(_count != 0);
if (_count > 0)
{
--_count;
// Logically, we're moving the last item (lowest, right-most)
// to the root and then sifting it down.
int ix = 0;
while (ix < _count/2)
{
// find the smallest child
int smallestChild = HeapLeftChild(ix);
int rightChild = HeapRightFromLeft(smallestChild);
if (rightChild < _count-1 && _comparer.Compare(_heap[rightChild], _heap[smallestChild]) < 0)
{
smallestChild = rightChild;
}
// If the item is less than or equal to the smallest child item,
// then we're done.
if (_comparer.Compare(_heap[_count], _heap[smallestChild]) <= 0)
{
break;
}
// Otherwise, move the child up
_heap[ix] = _heap[smallestChild];
// and adjust the index
ix = smallestChild;
}
// Place the item where it belongs
_heap[ix] = _heap[_count];
// and clear the position it used to occupy
_heap[_count] = default(T);
}
}
Note also that the code as written has a memory leak. This bit of code:
// Fill the last gap by moving the last (i.e., bottom-rightmost) node.
_heap[parent] = _heap[_count - 1];
Does not clear the value from _heap[_count - 1]. If the heap is storing reference types, then the references remain in the heap and cannot be garbage collected until the memory for the heap is garbage collected. I don't know where this heap is used, but if it's large and lives for any significant amount of time, it could cause excess memory consumption. The answer is to clear the item after it's copied:
_heap[_count - 1] = default(T);
My replacement code incorporates that fix.

Not reproducible in .NET Framework 4.8
Trying to reproduce this issue in 2020 with the .NET Framework 4.8 implementation of the PriorityQueue<T> as linked in the question using the following XUnit test ...
public class PriorityQueueTests
{
[Fact]
public void PriorityQueueTest()
{
Random random = new Random();
// Run 1 million tests:
for (int i = 0; i < 1000000; i++)
{
// Initialize PriorityQueue with default size of 20 using default comparer.
PriorityQueue<int> priorityQueue = new PriorityQueue<int>(20, Comparer<int>.Default);
// Using 200 entries per priority queue ensures possible edge cases with duplicate entries...
for (int j = 0; j < 200; j++)
{
// Populate queue with test data
priorityQueue.Push(random.Next(0, 100));
}
int prev = -1;
while (priorityQueue.Count > 0)
{
// Assert that previous element is less than or equal to current element...
Assert.True(prev <= priorityQueue.Top);
prev = priorityQueue.Top;
// remove top element
priorityQueue.Pop();
}
}
}
}
... succeeds in all 1 million test cases:
So it seems like Microsoft fixed the bug in their implementation:
internal void Pop()
{
Debug.Assert(_count != 0);
if (!_isHeap)
{
Heapify();
}
if (_count > 0)
{
--_count;
// discarding the root creates a gap at position 0. We fill the
// gap with the item x from the last position, after first sifting
// the gap to a position where inserting x will maintain the
// heap property. This is done in two phases - SiftDown and SiftUp.
//
// The one-phase method found in many textbooks does 2 comparisons
// per level, while this method does only 1. The one-phase method
// examines fewer levels than the two-phase method, but it does
// more comparisons unless x ends up in the top 2/3 of the tree.
// That accounts for only n^(2/3) items, and x is even more likely
// to end up near the bottom since it came from the bottom in the
// first place. Overall, the two-phase method is noticeably better.
T x = _heap[_count]; // lift item x out from the last position
int index = SiftDown(0); // sift the gap at the root down to the bottom
SiftUp(index, ref x, 0); // sift the gap up, and insert x in its rightful position
_heap[_count] = default(T); // don't leak x
}
}
As the link in the questions only points to most recent version of Microsoft's source code (currently .NET Framework 4.8) it's hard to say what exactly was changed in the code but most notably there's now an explicit comment not to leak memory, so we can assume the memory leak mentioned in #JimMischel's answer has been addressed as well which can be confirmed using the Visual Studio Diagnostic tools:
If there was a memory leak we'd see some changes here after a couple of million Pop() operations...

Get all possible distinct triples using LINQ

I have a List contains these values: {1, 2, 3, 4, 5, 6, 7}. And I want to be able to retrieve unique combination of three. The result should be like this:
{1,2,3}
{1,2,4}
{1,2,5}
{1,2,6}
{1,2,7}
{2,3,4}
{2,3,5}
{2,3,6}
{2,3,7}
{3,4,5}
{3,4,6}
{3,4,7}
{3,4,1}
{4,5,6}
{4,5,7}
{4,5,1}
{4,5,2}
{5,6,7}
{5,6,1}
{5,6,2}
{5,6,3}
I already have 2 for loops that able to do this:
for (int first = 0; first < test.Count - 2; first++)
{
int second = first + 1;
for (int offset = 1; offset < test.Count; offset++)
{
int third = (second + offset)%test.Count;
if(Math.Abs(first - third) < 2)
continue;
List<int> temp = new List<int>();
temp .Add(test[first]);
temp .Add(test[second]);
temp .Add(test[third]);
result.Add(temp );
}
}
But since I'm learning LINQ, I wonder if there is a smarter way to do this?

UPDATE: I used this question as the subject of a series of articles starting here; I'll go through two slightly different algorithms in that series. Thanks for the great question!
The two solutions posted so far are correct but inefficient for the cases where the numbers get large. The solutions posted so far use the algorithm: first enumerate all the possibilities:
{1, 1, 1 }
{1, 1, 2 },
{1, 1, 3 },
...
{7, 7, 7}
And while doing so, filter out any where the second is not larger than the first, and the third is not larger than the second. This performs 7 x 7 x 7 filtering operations, which is not that many, but if you were trying to get, say, permutations of ten elements from thirty, that's 30 x 30 x 30 x 30 x 30 x 30 x 30 x 30 x 30 x 30, which is rather a lot. You can do better than that.
I would solve this problem as follows. First, produce a data structure which is an efficient immutable set. Let me be very clear what an immutable set is, because you are likely not familiar with them. You normally think of a set as something you add items and remove items from. An immutable set has an Add operation but it does not change the set; it gives you back a new set which has the added item. The same for removal.
Here is an implementation of an immutable set where the elements are integers from 0 to 31:
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System;
// A super-cheap immutable set of integers from 0 to 31 ;
// just a convenient wrapper around bit operations on an int.
internal struct BitSet : IEnumerable<int>
{
public static BitSet Empty { get { return default(BitSet); } }
private readonly int bits;
private BitSet(int bits) { this.bits = bits; }
public bool Contains(int item)
{
Debug.Assert(0 <= item && item <= 31);
return (bits & (1 << item)) != 0;
}
public BitSet Add(int item)
{
Debug.Assert(0 <= item && item <= 31);
return new BitSet(this.bits | (1 << item));
}
public BitSet Remove(int item)
{
Debug.Assert(0 <= item && item <= 31);
return new BitSet(this.bits & ~(1 << item));
}
IEnumerator IEnumerable.GetEnumerator() { return this.GetEnumerator(); }
public IEnumerator<int> GetEnumerator()
{
for(int item = 0; item < 32; ++item)
if (this.Contains(item))
yield return item;
}
public override string ToString()
{
return string.Join(",", this);
}
}
Read this code carefully to understand how it works. Again, always remember that adding an element to this set does not change the set. It produces a new set that has the added item.
OK, now that we've got that, let's consider a more efficient algorithm for producing your permutations.
We will solve the problem recursively. A recursive solution always has the same structure:
Can we solve a trivial problem? If so, solve it.
If not, break the problem down into a number of smaller problems and solve each one.
Let's start with the trivial problems.
Suppose you have a set and you wish to choose zero items from it. The answer is clear: there is only one possible permutation with zero elements, and that is the empty set.
Suppose you have a set with n elements in it and you want to choose more than n elements. Clearly there is no solution, not even the empty set.
We have now taken care of the cases where the set is empty or the number of elements chosen is more than the number of elements total, so we must be choosing at least one thing from a set that has at least one thing.
Of the possible permutations, some of them have the first element in them and some of them do not. Find all the ones that have the first element in them and yield them. We do this by recursing to choose one fewer elements on the set that is missing the first element.
The ones that do not have the first element in them we find by enumerating the permutations of the set without the first element.
static class Extensions
{
public static IEnumerable<BitSet> Choose(this BitSet b, int choose)
{
if (choose < 0) throw new InvalidOperationException();
if (choose == 0)
{
// Choosing zero elements from any set gives the empty set.
yield return BitSet.Empty;
}
else if (b.Count() >= choose)
{
// We are choosing at least one element from a set that has
// a first element. Get the first element, and the set
// lacking the first element.
int first = b.First();
BitSet rest = b.Remove(first);
// These are the permutations that contain the first element:
foreach(BitSet r in rest.Choose(choose-1))
yield return r.Add(first);
// These are the permutations that do not contain the first element:
foreach(BitSet r in rest.Choose(choose))
yield return r;
}
}
}
Now we can ask the question that you need the answer to:
class Program
{
static void Main()
{
BitSet b = BitSet.Empty.Add(1).Add(2).Add(3).Add(4).Add(5).Add(6).Add(7);
foreach(BitSet result in b.Choose(3))
Console.WriteLine(result);
}
}
And we're done. We have generated only as many sequences as we actually need. (Though we have done a lot of set operations to get there, but set operations are cheap.) The point here is that understanding how this algorithm works is extremely instructive. Recursive programming on immutable structures is a powerful tool that many professional programmers do not have in their toolbox.

You can do it like this:
var data = Enumerable.Range(1, 7);
var r = from a in data
from b in data
from c in data
where a < b && b < c
select new {a, b, c};
foreach (var x in r) {
Console.WriteLine("{0} {1} {2}", x.a, x.b, x.c);
}
Demo.
Edit: Thanks Eric Lippert for simplifying the answer!

var ints = new int[] { 1, 2, 3, 4, 5, 6, 7 };
var permutations = ints.SelectMany(a => ints.Where(b => (b > a)).
SelectMany(b => ints.Where(c => (c > b)).
Select(c => new { a = a, b = b, c = c })));