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C# Algorithm for Combinations/Permutations of a defined range of integers

I am trying to generate a list of unique combinations/permutations of 3 allowable values for 20 different participants (each of the 20 participants can be assigned a value of either 1, 2, or 3).
An example of one combination would be an array on length 20 with all ones like such:
{ 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 }
...and everything possible all the way up to
{ 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3 }
where each value in the array can be 1, 2 or 3.
I am stuck on writing my GetAllCombinations() function and I looked at some articles on permutation, but everything I have found is just confusing me more. I am not even sure if permutation is what I need here
So far I have this:
public List<int[]> GetValidCombinations()
{
const int positions = 20;
int[] acceptableValues = new int[3] { 1, 2, 3 };
//DO I USE PERMUTATION HERE TO BUILD MY ARRAY LIST OF ALL POSSIBLE COMBINATIONS?
var allPossibleCombinations = GetAllCombinations(positions, acceptableValues);
List<int[]> validList = new List<int[]>();
foreach (var combination in allPossibleCombinations)
{
//omited for berevity but I would
//do some other validations here...
if (true)
{
validList.Add(combination);
}
}
return validList;
}
public List<int[]> GetAllCombinations(int positions, int[] acceptableValues)
{
//For now returning null because I
//don't know How the heck to do this...
return null;
}
I have looked at some examples of permutation and I tried to use something like this below, but it did not produce what I was looking for:
static IEnumerable<IEnumerable<T>>
GetPermutations<T>(IEnumerable<T> list, int length)
{
if (length == 1) return list.Select(t => new T[] { t });
return GetPermutations(list, length - 1)
.SelectMany(t => list.Where(o => !t.Contains(o)),
(t1, t2) => t1.Concat(new T[] { t2 }));
}
public void Test()
{
const int k = 20;
var n = new[] { 1, 2, 3 };
var combinations = GetPermutations(n, k);
//DOES NOT WORK FOR WHAT I NEED
}
Running Test() worked with k was 3 or less but returned nothing if k was greater then 3.

Try this:
public static List<int[]> GetAllCombinations(int position, int[] acceptableVaues)
{
List<int[]> result = new List<int[]>();
int[] parent = new int[] { };
result = AddAPosition(parent, acceptableVaues);
while(position > 1)
{
var tmpResult = new List<int[]>();
foreach(var _parent in result)
{
tmpResult.AddRange(AddAPosition(_parent, acceptableVaues));
}
position--;
result = tmpResult;
}
return result;
}
public static List<int[]> AddAPosition(int[] parent, int[] acceptableValues)
{
List<int[]> result = new List<int[]>();
for (int i = 0; i< acceptableValues.Length; i++)
{
var anArray = new int[parent.Length + 1];
for (int j = 0; j< parent.Length; j++)
{
anArray[j] = parent[j];
}
anArray[parent.Length] = acceptableValues[i];
result.Add(anArray);
}
return result;
}

Create a list of all permutation from different lists [duplicate]

This one should not be too hard but my mind seems to be having a stack overflow (huehue). I have a series of Lists and I want to find all permutations they can be ordered in. All of the lists have different lengths.
For example:
List 1: 1
List 2: 1, 2
All permutations would be:
1, 1
1, 2
In my case I don't switch the numbers around. (For example 2, 1)
What is the easiest way to write this?

I can't say if the following is the easiest way, but IMO it's the most efficient way. It's basically a generalized version of the my answer to the Looking at each combination in jagged array:
public static class Algorithms
{
public static IEnumerable<T[]> GenerateCombinations<T>(this IReadOnlyList<IReadOnlyList<T>> input)
{
var result = new T[input.Count];
var indices = new int[input.Count];
for (int pos = 0, index = 0; ;)
{
for (; pos < result.Length; pos++, index = 0)
{
indices[pos] = index;
result[pos] = input[pos][index];
}
yield return result;
do
{
if (pos == 0) yield break;
index = indices[--pos] + 1;
}
while (index >= input[pos].Count);
}
}
}
You can see the explanation in the linked answer (shortly it's emulating nested loops). Also since for performace reasons it yields the internal buffer w/o cloning it, you need to clone it if you want store the result for later processing.
Sample usage:
var list1 = new List<int> { 1 };
var list2 = new List<int> { 1, 2 };
var lists = new[] { list1, list2 };
// Non caching usage
foreach (var combination in lists.GenerateCombinations())
{
// do something with the combination
}
// Caching usage
var combinations = lists.GenerateCombinations().Select(c => c.ToList()).ToList();
UPDATE: The GenerateCombinations is a standard C# iterator method, and the implementation basically emulates N nested loops (where N is the input.Count) like this (in pseudo code):
for (int i0 = 0; i0 < input[0].Count; i0++)
for (int i1 = 0; i1 < input[1].Count; i1++)
for (int i2 = 0; i2 < input[2].Count; i2++)
...
for (int iN-1 = 0; iN-1 < input[N-1].Count; iN-1++)
yield { input[0][i0], input[1][i1], input[2][i2], ..., input[N-1][iN-1] }
or showing it differently:
for (indices[0] = 0; indices[0] < input[0].Count; indices[0]++)
{
result[0] = input[0][indices[0]];
for (indices[1] = 0; indices[1] < input[1].Count; indices[1]++)
{
result[1] = input[1][indices[1]];
// ...
for (indices[N-1] = 0; indices[N-1] < input[N-1].Count; indices[N-1]++)
{
result[N-1] = input[N-1][indices[N-1]];
yield return result;
}
}
}

Nested loops:
List<int> listA = (whatever), listB = (whatever);
var answers = new List<Tuple<int,int>>;
for(int a in listA)
for(int b in listB)
answers.add(Tuple.create(a,b));
// do whatever with answers

Try this:
Func<IEnumerable<string>, IEnumerable<string>> combine = null;
combine = xs =>
xs.Skip(1).Any()
? xs.First().SelectMany(x => combine(xs.Skip(1)), (x, y) => String.Format("{0}{1}", x, y))
: xs.First().Select(x => x.ToString());
var strings = new [] { "AB", "12", "$%" };
foreach (var x in combine(strings))
{
Console.WriteLine(x);
}
That gives me:
A1$
A1%
A2$
A2%
B1$
B1%
B2$
B2%

I made the following IEnumerable<IEnumerable<TValue>> class to solve this problem which allows use of generic IEnumerable's and whose enumerator returns all permutations of the values, one from each inner list. It can be conventiently used directly in a foreach loop.
It's a variant of Michael Liu's answer to IEnumerable and Recursion using yield return
I've modified it to return lists with the permutations instead of the single values.
using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
namespace Permutation
{
public class ListOfListsPermuter<TValue> : IEnumerable<IEnumerable<TValue>>
{
private int count;
private IEnumerable<TValue>[] listOfLists;
public ListOfListsPermuter(IEnumerable<IEnumerable<TValue>> listOfLists_)
{
if (object.ReferenceEquals(listOfLists_, null))
{
throw new ArgumentNullException(nameof(listOfLists_));
}
listOfLists =listOfLists_.ToArray();
count = listOfLists.Count();
for (int i = 0; i < count; i++)
{
if (object.ReferenceEquals(listOfLists[i], null))
{
throw new NullReferenceException(string.Format("{0}[{1}] is null.", nameof(listOfLists_), i));
}
}
}
// A variant of Michael Liu's answer in StackOverflow
// https://stackoverflow.com/questions/2055927/ienumerable-and-recursion-using-yield-return
public IEnumerator<IEnumerable<TValue>> GetEnumerator()
{
TValue[] currentList = new TValue[count];
int level = 0;
var enumerators = new Stack<IEnumerator<TValue>>();
IEnumerator<TValue> enumerator = listOfLists[level].GetEnumerator();
try
{
while (true)
{
if (enumerator.MoveNext())
{
currentList[level] = enumerator.Current;
level++;
if (level >= count)
{
level--;
yield return currentList;
}
else
{
enumerators.Push(enumerator);
enumerator = listOfLists[level].GetEnumerator();
}
}
else
{
if (level == 0)
{
yield break;
}
else
{
enumerator.Dispose();
enumerator = enumerators.Pop();
level--;
}
}
}
}
finally
{
// Clean up in case of an exception.
enumerator?.Dispose();
while (enumerators.Count > 0)
{
enumerator = enumerators.Pop();
enumerator.Dispose();
}
}
}
IEnumerator IEnumerable.GetEnumerator()
{
return GetEnumerator();
}
}
}
You can use it directly in a foreach like this:
public static void Main(string[] args)
{
var listOfLists = new List<List<string>>()
{
{ new List<string>() { "A", "B" } },
{ new List<string>() { "C", "D" } }
};
var permuter = new ListOfListsPermuter<string>(listOfLists);
foreach (IEnumerable<string> item in permuter)
{
Console.WriteLine("{ \"" + string.Join("\", \"", item) + "\" }");
}
}
The output:
{ "A", "C" }
{ "A", "D" }
{ "B", "C" }
{ "B", "D" }

Connect element in distinct array using recursion

if I have two array
A:[A,B]
B:[1,2,3]
how can I create a string List like [A_1, A_2, A_3, B_1, B_2, B_3]
the number of array is not regular, it's maybe have 3 more
A:[A,B]
B:[1,2,3]
C:[w,x,y,z]
D:[m,n]
E:[p,q,r]
can I use recursive to solve it?

So, we define a functions Mergethat takes lists of list of stings and merges them into the string enumerable you want
static void Main(string[] args)
{
var a = new[] { "A", "B" };
var b = new[] { "1", "2", "3" };
var c = new[] { "x", "y", "z", "w" };
var result = Merge(a, b, c);
foreach (var r in result)
{
Console.WriteLine(r);
}
}
public static IList<string> Merge(params IEnumerable<string>[] lists)
{
return Merge((IEnumerable<IEnumerable<string>>) lists);
}
public static IList<string> Merge(IEnumerable<IEnumerable<string>> lists)
{
var retval = new List<string>();
var first = lists.FirstOrDefault();
if (first != null)
{
var result = Merge(lists.Skip(1));
if (result.Count > 0)
{
foreach (var x in first)
{
retval.AddRange(result.Select(y => string.Format("{0}_{1}", x, y)));
}
}
else
{
retval.AddRange(first);
}
}
return retval;
}
we can also improve this, if you use Lists as inputs
public static IList<string> Merge(params IList<string>[] lists)
{
return Merge((IList<IList<string>>) lists);
}
public static IList<string> Merge(IList<IList<string>> lists, int offset = 0)
{
if (offset >= lists.Count)
return new List<string>();
var current = lists[offset];
if (offset + 1 == lists.Count) // last entry in lists
return current;
var retval = new List<string>();
var merged = Merge(lists, offset + 1);
foreach (var x in current)
{
retval.AddRange(merged.Select(y => string.Format("{0}_{1}", x, y)));
}
return retval;
}

This is simple iterating over n-ary dimension - no need for recursion for that, just array to store indexes.
static void Iterate(int[] iterators, ArrayList[] arrays) {
for (var j = iterators.Length - 1; j >= 0; j--) {
iterators[j]++;
if (iterators[j] == arrays[j].Count) {
if (j == 0) {
break;
}
iterators[j] = 0;
} else {
break;
}
}
}
static IList<string> Merge(ArrayList[] arrays) {
List<string> result = new List<string>();
int[] iterators = new int[arrays.Length];
while (iterators[0] != arrays[0].Count) {
var builder = new StringBuilder(20);
for(var index = 0; index < arrays.Length; index++) {
if (index > 0) {
builder.Append("_");
}
builder.Append(arrays[index][iterators[index]]);
}
result.Add(builder.ToString());
Iterate(iterators, arrays);
}
return result;
}
static void Main(string[] args) {
var list1 = new ArrayList();
var list2 = new ArrayList();
var list3 = new ArrayList();
list1.Add(1);
list1.Add(2);
list2.Add("a");
list2.Add("b");
list3.Add("x");
list3.Add("y");
list3.Add("z");
var result = Merge(new[] { list1, list2, list3 });
}

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace arrconn {
class Program {
static string[] conn(params Array[] arrs) {
if(arrs.Length == 0) return new string[0];
if(arrs.Length == 1) {
string[] result = new string[arrs[0].Length];
for(int i = 0; i < result.Length; i++)
result[i] = arrs[0].GetValue(i).ToString();
return result; }
else {
string[] result = new string[arrs[0].Length*arrs[1].Length];
for(int i = 0; i < arrs[0].Length; i++)
for(int j = 0; j < arrs[1].Length; j++)
result[i*arrs[1].Length+j] = string.Format("{0}_{1}", arrs[0].GetValue(i), arrs[1].GetValue(j));
if(arrs.Length == 2) return result;
Array[] next = new Array[arrs.Length-1];
next[0] = result; Array.Copy(arrs, 2, next, 1, next.Length-1);
return conn(next);
}
}
static void Main(string[] args) {
foreach(string s in conn(
new string[] { "A", "B" },
new int[] { 1, 2, 3 },
new string[] { "x" },
new string[] { "$", "%", "#" }))
Console.WriteLine(s);
Console.Read();
}
}
}

I guess your input are like this:
var A = ["A","B"];
var B = [1,2,3];
var C = ["x","y","z","w"];
And what you want to obtain is:
var result = ["A_1_x", "A_1_y",...
"A_2_x", "A_2_y",...
"A_3_x", "A_3_y",...
"B_1_x", "B_1_y",...
...
..., "B_3_z", "B_3_w"];
We'll be working with IEnumerable as it will simplify the work for us and give us access to the yield keyword.
First, let's take care of the case where we only concataining two collections:
IEnumerable<string> ConcatEnumerables(IEnumerable<object> first, IEnumerable<object> second)
{
foreach (var x in first)
{
foreach (var y in second)
{
yield return x.ToString() + "_" + y.ToString();
}
}
}
Then we can recursively takle any number of collections:
IEnumerable<string> ConcatEnumerablesRec(IEnumerable<IEnumerable<object>> enums)
{
//base cases
if(!enums.Any())
{
return Enumerable.Empty<string>();
}
if (enums.Count() == 1)
{
return enums.First().Select(o => o.ToString());
}
//recursively solve the problem
return ConcatEnumerables(enums.First(), ConcatEnumerablesRec(enums.Skip(1));
}
Now you just need to call ToArray on the result if you really need an array as your output.
string[] Concatenator(params object[][] parameters)
{
return ConcatEnumerablesRec(parameters).ToArray();
}

This should do the trick. Note that the input sequences do not have to be arrays - they can be any type that implements IEnumerable<>.
Also note that we have to case sequences of value types to sequences of <object> so that they are assignable to IEnumerable<object>.
Here's the compilable Console app demo code:
using System;
using System.Collections.Generic;
using System.Linq;
namespace Demo
{
internal static class Program
{
static void Main()
{
string[] a = {"A", "B", "C", "D"};
var b = Enumerable.Range(1, 3); // <-- See how it doesn't need to be an array.
char[] c = {'X', 'Y', 'Z'};
double[] d = {-0.1, -0.2};
var sequences = new [] { a, b.Cast<object>(), c.Cast<object>(), d.Cast<object>() };
Console.WriteLine(string.Join("\n", Combine("", sequences)));
}
public static IEnumerable<string> Combine(string prefix, IEnumerable<IEnumerable<object>> sequences)
{
foreach (var item in sequences.First())
{
string current = (prefix == "") ? item.ToString() : prefix + "_" + item;
var remaining = sequences.Skip(1);
if (!remaining.Any())
{
yield return current;
}
else
{
foreach (var s in Combine(current, remaining))
yield return s;
}
}
}
}
}

Use LINQ to group a sequence of numbers with no gaps

With this array int[]{ 1, 2, 3, 4, 7, 8, 11, 15,16,17,18 };
How can i convert to this string array "1-4","7-8","11","15-18"
Suggestions ? Linq ?

var array = new int[] { 1, 2, 3, 4, 7, 8, 11, 15, 16, 17, 18 };
var result = string.Join(",", array
.Distinct()
.OrderBy(x => x)
.GroupAdjacentBy((x, y) => x + 1 == y)
.Select(g => new int[] { g.First(), g.Last() }.Distinct())
.Select(g => string.Join("-", g)));
with
public static class LinqExtensions
{
public static IEnumerable<IEnumerable<T>> GroupAdjacentBy<T>(
this IEnumerable<T> source, Func<T, T, bool> predicate)
{
using (var e = source.GetEnumerator())
{
if (e.MoveNext())
{
var list = new List<T> { e.Current };
var pred = e.Current;
while (e.MoveNext())
{
if (predicate(pred, e.Current))
{
list.Add(e.Current);
}
else
{
yield return list;
list = new List<T> { e.Current };
}
pred = e.Current;
}
yield return list;
}
}
}
}

You don't need Linq; in fact, the easiest solution requires knowing about three positions in the array (your starting number, current number and the next number after the current), for which Enumerables are not well-suited.
Try this:
var start = 0;
var end = 0;
var write = false;
var builder = new StringBuilder();
for(var i=0; i<array.Length; i++)
{
//arranged this way to avoid ArrayOutOfBoundException
//if the next index doesn't exist or isn't one greater than the current,
//the current index is the end of our incremental range.
if(i+1 == array.Length || array[i+1] > array[i] + 1)
{
end = i;
write = true;
}
if(write)
{
if(end - start == 0) //one number
builder.Append(String.Format("{0}, ", array[start]);
else //multi-number range
builder.Append(String.Format("{0}-{1}, ", array[start], array[end]);
start = i+1;
end = i+1; //not really necessary but avoids any possible case of counting backwards
write = false;
}
}
You can rearrange this to reduce nesting of code, continue early in the loop logic, and remove a few vars; you'll gain a few millis of execution time. You'll also need to trim the last two characters (a trailing comma and space) off the end of the StringBuilder before getting the String out.

Here is a cut at it:
public static IEnumerable<string> ToRanges(this IEnumerable<int> values)
{
int? start = null, end = null;
foreach (var value in values.OrderBy(vv => vv))
{
if (!start.HasValue)
{
start = value;
}
else if (value == (end ?? start) + 1)
{
end = value;
}
else
{
yield return end.HasValue
? String.Format("{0}-{1}", start, end)
: String.Format("{0}", start);
start = value;
end = null;
}
}
if (start.HasValue)
{
yield return end.HasValue
? String.Format("{0}-{1}", start, end)
: String.Format("{0}", start);
}
}

What's the algorithm you want to implement? Figure out what you want to happen, then see if it could be made clearer with a LINQ translation. Here's something non-LINQ that could give you an idea.
int[] array = { 1, 2, 3, 4, 7, 8, 11, 15, 16, 17, 18};
List<string> ranges = new List<string>();
// code assumes array is not zero-length, is distinct, and is sorted.
// to do: handle scenario as appropriate if assumptions not valid
Action<int, int, List<string>> addToRanges = (first, last, list) =>
{
if (last == first)
list.Add(last.ToString());
else
list.Add(string.Format("{0}-{1}", first, last)); ;
};
int firstItem = array[0];
int lastItem = firstItem;
foreach (int item in array.Skip(1))
{
if (item > lastItem + 1)
{
addToRanges(firstItem, lastItem, ranges);
firstItem = lastItem = item;
}
else
{
lastItem = item;
}
}
addToRanges(firstItem, lastItem, ranges);
// return ranges or ranges.ToArray()

Checking for winner in TicTacToe?

What would be the best way to see (in a 2 player) game of Tic Tac Toe who won? Right now I'm using something similar to the following:
if (btnOne.Text == "X" && btnTwo.Text == "X" && btnThree.Text == "X")
{
MessageBox.Show("X has won!", "X won!");
return;
}
else
// I'm not going to write the rest but it's really just a bunch
// if statements.
So how do I get rid of the multiple if's?

Something alongs:
rowSum == 3 || columnSum == 3 || diagnolSum == 3
.. ?

If you store your buttons in a multidimenstional array, you can write some extension methods to get the rows, columns and diagonals.
public static class MultiDimensionalArrayExtensions
{
public static IEnumerable<T> Row<T>(this T[,] array, int row)
{
var columnLower = array.GetLowerBound(1);
var columnUpper = array.GetUpperBound(1);
for (int i = columnLower; i <= columnUpper; i++)
{
yield return array[row, i];
}
}
public static IEnumerable<T> Column<T>(this T[,] array, int column)
{
var rowLower = array.GetLowerBound(0);
var rowUpper = array.GetUpperBound(0);
for (int i = rowLower; i <= rowUpper; i++)
{
yield return array[i, column];
}
}
public static IEnumerable<T> Diagonal<T>(this T[,] array,
DiagonalDirection direction)
{
var rowLower = array.GetLowerBound(0);
var rowUpper = array.GetUpperBound(0);
var columnLower = array.GetLowerBound(1);
var columnUpper = array.GetUpperBound(1);
for (int row = rowLower, column = columnLower;
row <= rowUpper && column <= columnUpper;
row++, column++)
{
int realColumn = column;
if (direction == DiagonalDirection.DownLeft)
realColumn = columnUpper - columnLower - column;
yield return array[row, realColumn];
}
}
public enum DiagonalDirection
{
DownRight,
DownLeft
}
}
And if you use a TableLayoutPanel with 3 rows and 3 columns, you can easily create your buttons programmably and store it into a Button[3, 3] array.
Button[,] gameButtons = new Button[3, 3];
for (int row = 0; column <= 3; row++)
for (int column = 0; column <= 3; column++)
{
Button button = new Button();
// button...
gameLayoutPanel.Items.Add(button);
gameButtons[row, column] = button;
}
And to check for a winner:
string player = "X";
Func<Button, bool> playerWin = b => b.Value == player;
gameButtons.Row(0).All(playerWin) ||
// ...
gameButtons.Column(0).All(playerWin) ||
// ...
gameButtons.Diagonal(DiagonalDirection.DownRight).All(playerWin) ||
// ...

Another simple way out would be to save the winnable positions as a data in an array and use a loop to check all possible winning conditions instead of multiple ifs statements
// winnable positions
var winnables = new[] {
"012",
"345",
"678",
"036",
"147",
"258",
"048",
"246"
};
// extracted from btnOne Two Three....
var gameState = new[] { "X", "O", "X", "whatever" };
string winner = null;
// check each winnable positions
foreach (var position in winnables) {
var pos1 = int.Parse(position[0].ToString());
var pos2 = int.Parse(position[1].ToString());
var pos3 = int.Parse(position[2].ToString());
if (gameState[pos1] == gameState[pos2] &&
gameState[pos2] == gameState[pos3])
winner = gameState[pos1];
}
// do we have a winner?
if (!string.IsNullOrEmpty(winner))
/* we've got a winner */
Basically, don't use btnOne btnTwo btnThree, use a proper array of Buttons or an array that saves the game state in a more accessible format and it'll be easier to compute.

I tend to do things like this:
bool x_wins =
Enumerable
.Range(0, 3)
.SelectMany(i => new Func<int, string>[] { x => array[i, x], x => array[x, i] })
.Concat(new Func<int, string>[] { x => array[x, x], x => array[2 - x, x], })
.Where(f => String.Concat(Enumerable.Range(0, 3).Select(x => f(x))) == "XXX")
.Any();

I know you are no longer looking for an answer to this question. That said, someone might.
Using #fran-casadome's answer and #chakrit's answer, I would do something like this. Hard-coded possibilities seem appropriate. Linq let's up wrap the logic in fluent steps. A nice use.
private bool IsWinner(char player) => new[]
{
new[] { 0, 1, 2 },
new[] { 3, 4, 5 },
new[] { 6, 7, 8 },
new[] { 0, 3, 6 },
new[] { 1, 4, 7 },
new[] { 2, 5, 8 },
new[] { 0, 4, 8 },
new[] { 2, 4, 6 }
}.Any(indexes => indexes.All(index => _data[index] == player));
Here's the rest, for context.
private readonly char[] _data =
new[] { '1', '2', '3', '4', '5', '6', '7', '8', '9' };
public bool GameOver { get; private set; } = false;
public char? WinningPlayer { get; private set; } = null;
public char CurrentPlayer { get; private set; } = 'x';
public void Play(int position)
{
var index = Array.IndexOf(_data, position);
if (GameOver || index == -1)
{
return;
}
if (GameOver = IsWinner(_data[index] = CurrentPlayer))
{
WinningPlayer = CurrentPlayer;
}
else
{
CurrentPlayer = CurrentPlayer == 'x' ? 'o' : 'x';
}
}