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C# sort List<int> recursively

there's an exercise i need to do, given a List i need to sort the content using ONLY recursive methods (no while, do while, for, foreach).
So... i'm struggling (for over 2 hours now) and i dont know how to even begin.
The function must be
List<int> SortHighestToLowest (List<int> list) {
}
I THINK i should check if the previous number is greater than the actual number and so on but what if the last number is greater than the first number on the list?, that's why im having a headache.
I appreciate your help, thanks a lot.
[EDIT]
I delivered the exercise but then teacher said i shouldn't use external variables like i did here:
List<int> _tempList2 = new List<int>();
int _actualListIndex = 0;
int _actualMaxNumber = 0;
int _actualMaxNumberIndex = 0;
List<int> SortHighestToLowest(List<int> list)
{
if (list.Count == 0)
return _tempList2;
if (_actualListIndex == 0)
_actualMaxNumber = list[0];
if (_actualListIndex < list.Count -1)
{
_actualListIndex++;
if (list[_actualListIndex] > _actualMaxNumber)
{
_actualMaxNumberIndex = _actualListIndex;
_actualMaxNumber = list[_actualListIndex];
}
return SortHighestToLowest(list);
}
_tempList2.Add(_actualMaxNumber);
list.RemoveAt(_actualMaxNumberIndex);
_actualListIndex = 0;
_actualMaxNumberIndex = 0;
return SortHighestToLowest(list);
}
Exercise is done and i approved (thanks to other exercises as well) but i was wondering if there's a way of doing this without external variables and without using System.Linq like String.Empty's response (im just curious, the community helped me to solve my issue and im thankful).

I am taking your instructions to the letter here.
Only recursive methods
No while, do while, for, foreach
Signature must be List<int> SortHighestToLowest(List<int> list)
Now, I do assume you may use at least the built-in properties and methods of the List<T> type. If not, you would have a hard time even reading the elements of your list.
That said, any calls to Sort or OrderBy methods would be beyond the point here, since they would render any recursive method useless.
I also assume it is okay to use other lists in the process, since you didn't mention anything in regards to that.
With all that in mind, I came to this piece below, making use of Max and Remove methods from List<T> class, and a new list of integers for each recursive call:
public static List<int> SortHighestToLowest(List<int> list)
{
// recursivity breaker
if (list.Count <= 1)
return list;
// remove highest item
var max = list.Max();
list.Remove(max);
// append highest item to recursive call for the remainder of the list
return new List<int>(SortHighestToLowest(list)) { max };
}

For solving this problem, try to solve smaller subsets. Consider the following list
[1,5,3,2]
Let's take the last element out of list, and consider the rest as sorted which will be [1,3,5] and 2. Now the problem reduces to another problem of inserting this 2 in its correct position. If we can insert it in correct position then the array becomes sorted. This can be applied recursively.
For every recursive problem there should be a base condition w.r.t the hypothesis we make. For the first problem the base condition is array with single element. A single element array is always sorted.
For the second insert problem the base condition will be an empty array or the last element in array is less than the element to be inserted. In both cases the element is inserted at the end.
Algorithm
---------
Sort(list)
if(list.count==1)
return
temp = last element of list
temp_list = list with last element removed
Sort(temp_list)
Insert(temp_list, temp)
Insert(list, temp)
if(list.count ==0 || list[n-1] <= temp)
list.insert(temp)
return
insert_temp = last element of list
insert_temp_list = list with last element removed
Insert(insert_temo_list, insert_temp)
For Insert after base condition its calling recursively till it find the correct position for the last element which is removed.

Determine if array contains all zeroes

I create the following array like this:
array<UInt16>^ temp = gcnew array<UInt16>(1000);
How do I determine if this entire array has been filled with zero or not.
I think I may be able to use TrueForAll(T) but I'm not sure.

var allElementsAreZero = temp.All(o => o == 0);
Simple as that.
It'll return when it finds one that doesn't satisfy the condition, so may not necessarily iterate through your whole collection:
"The enumeration of source is stopped as soon as the result can be determined."
https://msdn.microsoft.com/en-us/library/bb548541(v=vs.110).aspx

This should work properly (here I used LINQ):
IEnumerable<int> values = new List<int>(); // Or use any array type instead of List.
... Add your values here ...
var allAreZero = !values.Any(v => v != 0);
P.S. the array class inherits IEnumerable.
And here is a solution with foreach:
var isAllZero = true;
foreach (var value in values)
{
if (value != 0)
{
isAllZero = false;
break;
}
}
UPDATE
The really difference between TrueForAll, and my LINQ code is: LINQ code uses the fluent (or maybe also query) syntax, where TrueForAll is just a normal function where you send the array as a parameter.

initialize a counter from 0 then use for loop to interate through the array and increment the counter whenever it finds 0, and at the end compare the counter with size of array if its equal, it has all zeros

Reading the C++/CLI specification, it has been filled with
0s because you created it with a "new-expression" and the default value of the element type is 0.
24.2 CLI array creation
CLI array instances are created by new-expressions containing gcnew (§15.4.6) or …
Elements of CLI arrays created by new-expressions are always initialized to their default value.

get next available integer using LINQ

Say I have a list of integers:
List<int> myInts = new List<int>() {1,2,3,5,8,13,21};
I would like to get the next available integer, ordered by increasing integer. Not the last or highest one, but in this case the next integer that is not in this list. In this case the number is 4.
Is there a LINQ statement that would give me this? As in:
var nextAvailable = myInts.SomeCoolLinqMethod();
Edit: Crap. I said the answer should be 2 but I meant 4. I apologize for that!
For example: Imagine that you are responsible for handing out process IDs. You want to get the list of current process IDs, and issue a next one, but the next one should not just be the highest value plus one. Rather, it should be the next one available from an ordered list of process IDs. You could get the next available starting with the highest, it does not really matter.

I see a lot of answers that write a custom extension method, but it is possible to solve this problem with the standard linq extension methods and the static Enumerable class:
List<int> myInts = new List<int>() {1,2,3,5,8,13,21};
// This will set firstAvailable to 4.
int firstAvailable = Enumerable.Range(1, Int32.MaxValue).Except(myInts).First();

The answer provided by #Kevin has a undesirable performance profile. The logic will access the source sequence numerous times: once for the .Count call, once for the .FirstOrDefault call, and once for each .Contains call. If the IEnumerable<int> instance is a deferred sequence, such as the result of a .Select call, this will cause at least 2 calculations of the sequence, along with once for each number. Even if you pass a list to the method, it will potentially go through the entire list for each checked number. Imagine running it on the sequence { 1, 1000000 } and you can see how it would not perform well.
LINQ strives to iterate source sequences no more than once. This is possible in general and can have a big impact on the performance of your code. Below is an extension method which will iterate the sequence exactly once. It does so by looking for the difference between each successive pair, then adds 1 to the first lower number which is more than 1 away from the next number:
public static int? FirstMissing(this IEnumerable<int> numbers)
{
int? priorNumber = null;
foreach(var number in numbers.OrderBy(n => n))
{
var difference = number - priorNumber;
if(difference != null && difference > 1)
{
return priorNumber + 1;
}
priorNumber = number;
}
return priorNumber == null ? (int?) null : priorNumber + 1;
}
Since this extension method can be called on any arbitrary sequence of integers, we make sure to order them before we iterate. We then calculate the difference between the current number and the prior number. If this is the first number in the list, priorNumber will be null and thus difference will be null. If this is not the first number in the list, we check to see if the difference from the prior number is exactly 1. If not, we know there is a gap and we can add 1 to the prior number.
You can adjust the return statement to handle sequences with 0 or 1 items as you see fit; I chose to return null for empty sequences and n + 1 for the sequence { n }.

This will be fairly efficient:
static int Next(this IEnumerable<int> source)
{
int? last = null;
foreach (var next in source.OrderBy(_ => _))
{
if (last.HasValue && last.Value + 1 != next)
{
return last.Value + 1;
}
last = next;
}
return last.HasValue ? last.Value + 1 : Int32.MaxValue;
}

public static class IntExtensions
{
public static int? SomeCoolLinqMethod(this IEnumerable<int> ints)
{
int counter = ints.Count() > 0 ? ints.First() : -1;
while (counter < int.MaxValue)
{
if (!ints.Contains(++counter)) return counter;
}
return null;
}
}
Usage:
var nextAvailable = myInts.SomeCoolLinqMethod();

Ok, here is the solution that I came up with that works for me.
var nextAvailableInteger = Enumerable.Range(myInts.Min(),myInts.Max()).FirstOrDefault( r=> !myInts.Contains(r));
If anyone has a more elegant solution I would be happy to accept that one. But for now, this is what I'm putting in my code and moving on.
Edit: this is what I implemented after Kevin's suggestion to add an extension method. And that was the real answer - that no single LINQ extension would do so it makes more sense to add my own. That is really what I was looking for.
public static int NextAvailableInteger(this IEnumerable<int> ints)
{
return NextAvailableInteger(ints, 1); // by default we use one
}
public static int NextAvailableInteger(this IEnumerable<int> ints, int defaultValue)
{
if (ints == null || ints.Count() == 0) return defaultValue;
var ordered = ints.OrderBy(v => v);
int counter = ints.Min();
int max = ints.Max();
while (counter < max)
{
if (!ordered.Contains(++counter)) return counter;
}
return (++counter);
}

Not sure if this qualifies as a cool Linq method, but using the left outer join idea from This SO Answer
var thelist = new List<int> {1,2,3,4,5,100,101};
var nextAvailable = (from curr in thelist
join next in thelist
on curr + 1 equals next into g
from newlist in g.DefaultIfEmpty()
where !g.Any ()
orderby curr
select curr + 1).First();
This puts the processing on the sql server side if you're using Linq to Sql, and allows you to not have to pull the ID lists from the server to memory.

var nextAvailable = myInts.Prepend(0).TakeWhile((x,i) => x == i).Last() + 1;
It is 7 years later, but there are better ways of doing this than the selected answer or the answer with the most votes.
The list is already in order, and based on the example 0 doesn't count. We can just prepend 0 and check if each item matches it's index. TakeWhile will stop evaluating once it hits a number that doesn't match, or at the end of the list.
The answer is the last item that matches, plus 1.
TakeWhile is more efficient than enumerating all the possible numbers then excluding the existing numbers using Except, because we TakeWhile will only go through the list until it finds the first available number, and the resulting Enumerable collection is at most n.
The answer using Except generates an entire enumerable of answers that are not needed just to grab the first one. Linq can do some optimization with First(), but it still much slower and more memory intensive than TakeWhile.

issue while getting values from Dictionary<int, List<int>>

I am having a dictionary which was defined as follows
Dictionary<int, List<int>> dict1 = new Dictionary<int, List<int>>();
I will have a list element where i can store the values which will come from database
List<int> lstdbTaskID = new List<int>();
assume this holds
100 105 110 200
respectively.
I will have my dictionary with values stored as follows. Assume that i have 2 keys 10,20 respectively, and for this key values i will have my values as for 10 i will have 100,105 and 110 and for 20 i will have 200.
I would like to compare these values with the list available lstdbTaskID
I tried this
foreach (int strlst in lstdbTaskID)
{
if (dict1.ContainsValue(lstdbTaskID[strlst]))
}
But i am getting errors as follows
The best overloaded method match for 'System.Collections.Generic.Dictionary>.ContainsValue(System.Collections.Generic.List)' has some invalid arguments`
and
Cannot convert from 'int' to 'System.Collections.Generic.List'`
can any help me on this?

Your code is wrong at because you are trying to compare int value with List of int.
Your dictionary is:
Dictionary of int to List of int.
and you have another structure as
List of int
so when you do:
// Compiler fails here because you are trying to check whether dictionary contains
// the given integer value. Dictionary in this case has a list of integers as its `Value`
// in its `<Key,Value>` pair.
dict1.ContainsValue(lstdbTaskID[strlst])
Use linq statement:
foreach (int strlst in lstdbTaskID)
{
if (dict1.Any(pair => pair.Value.Contains(strlst)))
{
// do something
}
}
Edit: If you want this without linq, do the linq task by self.
foreach (int strlst in lstdbTaskID)
{
foreach (int key in dict1.Keys)
{
if (dict1[key].Contains(strlst))
{
// do something
}
}
}

Look at the type of the value you're storing in your dictionary - it's a List<int>, not an int. So it makes no sense to ask whether the dictionary contains a value of 5, say.
However, it does make sense to ask if the dictionary contains any value (list) which itself contains 5.
For example:
foreach (int strlst in lstdbTaskID)
{
if (dict1.Values.Any(list => list.Contains(strlst))
{
...
}
}
However, that's really not a very efficient way of representing it. It's not clear what the best of representing it is though, without knowing what you're going to do with the results. You may just want a HashSet<int> containing all the values from all the lists, for example - but if you want to get back to the keys whose values contained a particular ID, that's a different matter.
EDIT: In .NET 2.0 land, you could use:
foreach (int strlst in lstdbTaskID)
{
foreach (List<int> list in dict1.Values)
{
if (list.Contains(strlst))
}
}
... but you're really not using the dictionary as a dictionary in either case here...

I am having slight problems understanding your question fully, however, my answer should push you in the right direction. Seeing as you do not have access to Linq (as you are using .Net 2.0):
static bool IsContained(IEnumerable<int> lstdbTaskID, Dictionary<int, HashSet<int>> dict1)
{
foreach (int strlst in lstdbTaskID)
foreach (HashSet<int> value in dict1.Values)
if (value != null && value.Contains(strlst))
return true;
return false;
}
You should use a HashSet<int> as it is far faster for looking up values (and is supported in .Net 2.0); however, you should not use HashSet<int> (and instead use List<int>) if:
The list needs to store duplicates.
- or - The order of the values is important.

Well, dict1 is a dictionary of dictionaries, not ints. So dict1.ContainsValue takes a dictionary as a parameter - you're checking whether it contains a given dictionary or not. But you're giving it an int.
Try this:
if (dict1.Any(x => x.Value.ContainsValue(strlst))) // ...

Examining two string arrays for equivalence

Is there a better way to examine whether two string arrays have the same contents than this?
string[] first = new string[]{"cat","and","mouse"};
string[] second = new string[]{"cat","and","mouse"};
bool contentsEqual = true;
if(first.Length == second.Length){
foreach (string s in first)
{
contentsEqual &= second.Contains(s);
}
}
else{
contentsEqual = false;
}
Console.WriteLine(contentsEqual.ToString());// true

Enumerable.SequenceEquals if they're supposed to be in the same order.

You should consider using the intersect method. It will give you all the matching values and then you can just compare the count of the resulting array with one the arrays that were compared.
http://msdn.microsoft.com/en-us/library/system.linq.enumerable.intersect.aspx

This is O(n^2). If the arrays have the same length, sort them, then compare elements in the same position. This is O(n log n).
Or you can use a hash set or dictionary: insert each word in the first array, then see if every word in the second array is in the set or dictionary. This is O(n) on average.

Nothing wrong with the logic of the method, but the fact that you're testing Contains for each item in the first sequence means the algorithm runs in O(n^2) time in general. You can also make one or two other smaller optimisations and improvements
I would implement such a function as follows. Define an extension method as such (example in .NET 4.0).
public static bool SequenceEquals<T>(this IEnumerable<T> seq1, IEnumerable<T> seq2)
{
foreach (var pair in Enumerable.Zip(seq1, seq2)
{
if (!pair.Item1.Equals(pair.Item2))
return;
}
return false;
}

You could try Enumerable.Intersect: http://msdn.microsoft.com/en-us/library/bb460136.aspx
The result of the operation is every element that is common to both arrays. If the length of the result is equal to the length of both arrays, then the two arrays contain the same items.
Enumerable.Union: http://msdn.microsoft.com/en-us/library/bb341731.aspx would work too; just check that the result of the Union operation has length of zero (meaning there are no elements that are unique to only one array);
Although I'm not exactly sure how the functions handle duplicates.