Develop Reference

Shortest list from a two dimensional array

This question is more about an algorithm than actual code, but example code would be appreciated.
Let's say I have a two-dimensional array such as this:
A B C D E
--------------
1 | 0 2 3 4 5
2 | 1 2 4 5 6
3 | 1 3 4 5 6
4 | 2 3 4 5 6
5 | 1 2 3 4 5
I am trying to find the shortest list that would include a value from each row. Currently, I am going row by row and column by column, adding each value to a SortedSet and then checking the length of the set against the shortest set found so far. For example:
Adding cells {1A, 2A, 3A, 4A, 5A} would add the values {0, 1, 1, 2, 1} which would result in a sorted set {0, 1, 2}. {1B, 2A, 3A, 4A, 5A} would add the values {2, 1, 1, 2, 1} which would result in a sorted set {1, 2}, which is shorter than the previous set.
Obviously, adding {1D, 2C, 3C, 4C, 5D} or {1E, 2D, 3D, 4D, 5E} would be the shortest sets, having only one item each, and I could use either one.
I don't have to include every number in the array. I just need to find the shortest set while including at least one number from every row.
Keep in mind that this is just an example array, and the arrays that I'm using are much, much larger. The smallest is 495x28. Brute force will take a VERY long time (28^495 passes). Is there a shortcut that someone knows, to find this in the least number of passes? I have C# code, but it's kind of long.
Edit:
Posting current code, as per request:
// Set an array of counters, Add enough to create largest initial array
int ListsCount = MatrixResults.Count();
int[] Counters = new int[ListsCount];
SortedSet<long> CurrentSet = new SortedSet<long>();
for (long X = 0; X < ListsCount; X++)
{
Counters[X] = 0;
CurrentSet.Add(X);
}
while (true)
{
// Compile sequence list from MatrixResults[]
SortedSet<long> ThisSet = new SortedSet<long>();
for (int X = 0; X < Count4; X ++)
{
ThisSet.Add(MatrixResults[X][Counters[X]]);
}
// if Sequence Length less than current low, set ThisSet as Current
if (ThisSet.Count() < CurrentSet.Count())
{
CurrentSet.Clear();
long[] TSI = ThisSet.ToArray();
for (int Y = 0; Y < ThisSet.Count(); Y ++)
{
CurrentSet.Add(TSI[Y]);
}
}
// Increment Counters
int Index = 0;
bool EndReached = false;
while (true)
{
Counters[Index]++;
if (Counters[Index] < MatrixResults[Index].Count()) break;
Counters[Index] = 0;
Index++;
if (Index >= ListsCount)
{
EndReached = true;
break;
}
Counters[Index]++;
}
// If all counters are fully incremented, then break
if (EndReached) break;
}

With all computations there is always a tradeoff, several factors are in play, like will You get paid for getting it perfect (in this case for me, no). This is a case of the best being the enemy of the good. How long can we spend on solving a problem and will it be sufficient to get close enough to fulfil the use case (imo) and when we can solve the problem without hand painting pixels in UHD resolution to get the idea of a key through, lets!
So, my choice is an approach which will get a covering set which is small and ehem... sometimes will be the smallest :) In essence because of the sequence in comparing would to be spot on be iterative between different strategies, comparing the length of the sets for different strategies - and for this evening of fun I chose to give one strategy which is I find defendable to be close to or equal the minimal set.
So this strategy is to observe the multi dimensional array as a sequence of lists that has a distinct value set each. Then if reducing the total amount of lists with the smallest in the remainder iteratively, weeding out any non used values in that smallest list when having reduced total set in each iteration we will get a path which is close enough to the ideal to be effective as it completes in milliseconds with this approach.
A critique of this approach up front is then that the direction you pass your minimal list in really would have to get iteratively varied to pick best, left to right, right to left, in position sequences X,Y,Z, ... because the amount of potential reducing is not equal. So to get close to the ideal iterations of sequences would have to be made for each iteration too until all combinations were covered, choosing the most reducing sequence. right - but I chose left to right, only!
Now I chose not to run compare execution against Your code, because of the way you instantiate your MatrixResults is an array of int arrays and not instantiated as a multidimension array, which your drawing is, so I went by Your drawing and then couldn't share data source with your code. No matter, you can make that conversion if you wish, onwards to generate sample data:
private int[,] CreateSampleArray(int xDimension, int yDimensions, Random rnd)
{
Debug.WriteLine($"Created sample array of dimensions ({xDimension}, {yDimensions})");
var array = new int[xDimension, yDimensions];
for (int x = 0; x < array.GetLength(0); x++)
{
for(int y = 0; y < array.GetLength(1); y++)
{
array[x, y] = rnd.Next(0, 4000);
}
}
return array;
}
The overall structure with some logging, I'm using xUnit to run the code in
[Fact]
public void SetCoverExperimentTest()
{
var rnd = new Random((int)DateTime.Now.Ticks);
var sw = Stopwatch.StartNew();
int[,] matrixResults = CreateSampleArray(rnd.Next(100, 500), rnd.Next(100, 500), rnd);
//So first requirement is that you must have one element per row, so lets get our unique rows
var listOfAll = new List<List<int>>();
List<int> listOfRow;
for (int y = 0; y < matrixResults.GetLength(1); y++)
{
listOfRow = new List<int>();
for (int x = 0; x < matrixResults.GetLength(0); x++)
{
listOfRow.Add(matrixResults[x, y]);
}
listOfAll.Add(listOfRow.Distinct().ToList());
}
var setFound = new HashSet<int>();
List<List<int>> allUniquelyRequired = GetDistinctSmallestList(listOfAll, setFound);
// This set now has all rows that are either distinctly different
// Or have a reordering of distinct values of that length value lists
// our HashSet has the unique value range
//Meaning any combination of sets with those values,
//grabbing any one for each set, prefering already chosen ones should give a covering total set
var leastSet = new LeastSetData
{
LeastSet = setFound,
MatrixResults = matrixResults,
};
List<Coordinate>? minSet = leastSet.GenerateResultsSet();
sw.Stop();
Debug.WriteLine($"Completed in {sw.Elapsed.TotalMilliseconds:0.00} ms");
Assert.NotNull(minSet);
//There is one for each row
Assert.False(minSet.Select(s => s.y).Distinct().Count() < minSet.Count());
//We took less than 25 milliseconds
var timespan = new TimeSpan(0, 0, 0, 0, 25);
Assert.True(sw.Elapsed < timespan);
//Outputting to debugger for the fun of it
var sb = new StringBuilder();
foreach (var coordinate in minSet)
{
sb.Append($"({coordinate.x}, {coordinate.y}) {matrixResults[coordinate.x, coordinate.y]},");
}
var debugLine = sb.ToString();
debugLine = debugLine.Substring(0, debugLine.Length - 1);
Debug.WriteLine("Resulting set: " + debugLine);
}
Now the more meaty iterative bits
private List<List<int>> GetDistinctSmallestList(List<List<int>> listOfAll, HashSet<int> setFound)
{
// Our smallest set must be a subset the distinct sum of all our smallest lists for value range,
// plus unknown
var listOfShortest = new List<List<int>>();
int shortest = int.MaxValue;
foreach (var list in listOfAll)
{
if (list.Count < shortest)
{
listOfShortest.Clear();
shortest = list.Count;
listOfShortest.Add(list);
}
else if (list.Count == shortest)
{
if (listOfShortest.Contains(list))
continue;
listOfShortest.Add(list);
}
}
var setFoundAddition = new HashSet<int>(setFound);
foreach (var list in listOfShortest)
{
foreach (var item in list)
{
if (setFound.Contains(item))
continue;
if (setFoundAddition.Contains(item))
continue;
setFoundAddition.Add(item);
}
}
//Now we can remove all rows with those found, we'll add the smallest later
var listOfAllRemainder = new List<List<int>>();
bool foundInList;
List<int> consumedWhenReducing = new List<int>();
foreach (var list in listOfAll)
{
foundInList = false;
foreach (int item in list)
{
if (setFound.Contains(item))
{
//Covered by data from last iteration(s)
foundInList = true;
break;
}
else if (setFoundAddition.Contains(item))
{
consumedWhenReducing.Add(item);
foundInList = true;
break;
}
}
if (!foundInList)
{
listOfAllRemainder.Add(list); //adding what lists did not have elements found
}
}
//Remove any from these smallestset lists that did not get consumed in the favour used pass before
if (consumedWhenReducing.Count == 0)
{
throw new Exception($"Shouldn't be possible to remove the row itself without using one of its values, please investigate");
}
var removeArray = setFoundAddition.Where(a => !consumedWhenReducing.Contains(a)).ToArray();
setFoundAddition.RemoveWhere(x => removeArray.Contains(x));
foreach (var value in setFoundAddition)
{
setFound.Add(value);
}
if (listOfAllRemainder.Count != 0)
{
//Do the whole thing again until there in no list left
listOfShortest.AddRange(GetDistinctSmallestList(listOfAllRemainder, setFound));
}
return listOfShortest; //Here we will ultimately have the sum of shortest lists per iteration
}
To conclude: I hope to have inspired You, at least I had fun coming up with a best approximate, and should you feel like completing the code, You're very welcome to grab what You like.
Obviously we should really track the sequence we go through the shortest lists, after all it is of significance if we start by reducing the total distinct lists by element at position 0 or 0+N and which one we reduce with after. I mean we must have one of those values but each time consuming each value has removed most of the total list all it really produces is a value range and the range consumption sequence matters to the later iterations - Because a position we didn't reach before there were no others left e.g. could have remove potentially more than some which were covered. You get the picture I'm sure.
And this is just one strategy, One may as well have chosen the largest distinct list even within the same framework and if You do not iteratively cover enough strategies, there is only brute force left.
Anyways you'd want an AI to act. Just like a human, not to contemplate the existence of universe before, after all we can reconsider pretty often with silicon brains as long as we can do so fast.
With any moving object at least, I'd much rather be 90% on target correcting every second while taking 14 ms to get there, than spend 2 seconds reaching 99% or the illusive 100% => meaning we should stop the vehicle before the concrete pillar or the pram or conversely buy the equity when it is a good time to do so, not figuring out that we should have stopped, when we are allready on the other side of the obstacle or that we should've bought 5 seconds ago, but by then the spot price already jumped again...
Thus the defense rests on the notion that it is opinionated if this solution is good enough or simply incomplete at best :D
I realize it's pretty random, but just to say that although this sketch is not entirely indisputably correct, it is easy to read and maintain and anyways the question is wrong B-] We will very rarely need the absolute minimal set and when we do the answer will be much longer :D
... woopsie, forgot the support classes
public struct Coordinate
{
public int x;
public int y;
public override string ToString()
{
return $"({x},{y})";
}
}
public struct CoordinateValue
{
public int Value { get; set; }
public Coordinate Coordinate { get; set; }
public override string ToString()
{
return string.Concat(Coordinate.ToString(), " ", Value.ToString());
}
}
public class LeastSetData
{
public HashSet<int> LeastSet { get; set; }
public int[,] MatrixResults { get; set; }
public List<Coordinate> GenerateResultsSet()
{
HashSet<int> chosenValueRange = new HashSet<int>();
var chosenSet = new List<Coordinate>();
for (int y = 0; y < MatrixResults.GetLength(1); y++)
{
var candidates = new List<CoordinateValue>();
for (int x = 0; x < MatrixResults.GetLength(0); x++)
{
if (LeastSet.Contains(MatrixResults[x, y]))
{
candidates.Add(new CoordinateValue
{
Value = MatrixResults[x, y],
Coordinate = new Coordinate { x = x, y = y }
}
);
continue;
}
}
if (candidates.Count == 0)
throw new Exception($"OMG Something's wrong! (this row did not have any of derived range [y: {y}])");
var done = false;
foreach (var c in candidates)
{
if (chosenValueRange.Contains(c.Value))
{
chosenSet.Add(c.Coordinate);
done = true;
break;
}
}
if (!done)
{
var firstCandidate = candidates.First();
chosenSet.Add(firstCandidate.Coordinate);
chosenValueRange.Add(firstCandidate.Value);
}
}
return chosenSet;
}
}

This problem is NP hard.
To show that, we have to take a known NP hard problem, and reduce it to this one. Let's do that with the Set Cover Problem.
We start with a universe U of things, and a collection S of sets that covers the universe. Assign each thing a row, and each set a number. This will fill different numbers of columns for each row. Fill in a rectangle by adding new numbers.
Now solve your problem.
For each new number in your solution that didn't come from a set in the original problem, we can replace it with another number in the same row that did come from a set.
And now we turn numbers back into sets and we have a solution to the Set Cover Problem.
The transformations from set cover to your problem and back again are both O(number_of_elements * number_of_sets) which is polynomial in the input. And therefore your problem is NP hard.
Conversely if you replace each number in the matrix with the set of rows covered, your problem turns into the Set Cover Problem. Using any existing solver for set cover then gives a reasonable approach for your problem as well.

The code is not particularly tidy or optimised, but illustrates the approach I think #btilly is suggesting in his answer (E&OE) using a bit of recursion (I was going for intuitive rather than ideal for scaling, so you may have to work an iterative equivalent).
From the rows with their values make a "values with the rows that they appear in" counterpart. Now pick a value, eliminate all rows in which it appears and solve again for the reduced set of rows. Repeat recursively, keeping only the shortest solutions.
I know this is not terribly readable (or well explained) and may come back to tidy up in the morning, so let me know if it does what you want (is worth a bit more of my time;-).
// Setup
var rowValues = new Dictionary<int, HashSet<int>>
{
[0] = new() { 0, 2, 3, 4, 5 },
[1] = new() { 1, 2, 4, 5, 6 },
[2] = new() { 1, 3, 4, 5, 6 },
[3] = new() { 2, 3, 4, 5, 6 },
[4] = new() { 1, 2, 3, 4, 5 }
};
Dictionary<int, HashSet<int>> ValueRows(Dictionary<int, HashSet<int>> rv)
{
var vr = new Dictionary<int, HashSet<int>>();
foreach (var row in rv.Keys)
{
foreach (var value in rv[row])
{
if (vr.ContainsKey(value))
{
if (!vr[value].Contains(row))
vr[value].Add(row);
}
else
{
vr.Add(value, new HashSet<int> { row });
}
}
}
return vr;
}
List<int> FindSolution(Dictionary<int, HashSet<int>> rAndV)
{
if (rAndV.Count == 0) return new List<int>();
var bestSolutionSoFar = new List<int>();
var vAndR = ValueRows(rAndV);
foreach (var v in vAndR.Keys)
{
var copyRemove = new Dictionary<int, HashSet<int>>(rAndV);
foreach (var r in vAndR[v])
copyRemove.Remove(r);
var solution = new List<int>{ v };
solution.AddRange(FindSolution(copyRemove));
if (bestSolutionSoFar.Count == 0 || solution.Count > 0 && solution.Count < bestSolutionSoFar.Count)
bestSolutionSoFar = solution;
}
return bestSolutionSoFar;
}
var solution = FindSolution(rowValues);
Console.WriteLine($"Optimal solution has values {{ {string.Join(',', solution)} }}");
output Optimal solution has values { 4 }

Sum a List, but only for values after a certain point

I'm writing a web page to keep the score for a card game. Getting the players score so far would be easy, but there is a twist. During any round the players score can be reset to zero at the start of the round. I don't want to change the score for any previous rounds, so I only want to get a sum of the rounds after (and including) the reset. A player could potentially have their score reset multiple times in a game, or not at all.
I can get the correct score by a multiple stage process of finding the last (if any) score reset, and summing all hands after that (or all hands in no resets) - see PlayerGame.GetPlayerScore.
I'm still trying to get my head around the more intricate ways of doing things with LINQ, and I was wondering if there was a way to do this using a single LINQ statement?
Minimal code:
class Program
{
static void Main(string[] args)
{
PlayerGame playerGame = new PlayerGame();
playerGame.PlayerHands = new List<PlayerHand>
{
new PlayerHand { Round = 1, Score = 10 },
new PlayerHand { Round = 2, Score = 20 },
new PlayerHand { Round = 3, Score = 30 },
new PlayerHand { Round = 4, Score = 40, Reset = true },
new PlayerHand { Round = 5, Score = 50 },
new PlayerHand { Round = 6, Score = 60 }
};
Console.WriteLine($"Players score was {playerGame.GetPlayerScore()}");
Console.ReadLine();
}
}
class PlayerHand
{
public int Round { get; set; }
public int Score { get; set; }
public bool Reset { get; set; } = false;
}
class PlayerGame
{
public List<PlayerHand> PlayerHands { get; set; }
public PlayerGame()
{
PlayerHands = new List<PlayerHand> { };
}
public int GetPlayerScore()
{
// Can all this be simplified to a single LINQ statement?
var ResetIndex = PlayerHands.OrderBy(t => t.Round).LastOrDefault(t => t.Reset == true);
if (ResetIndex != null)
{
return PlayerHands.Where(t => t.Round >= ResetIndex.Round).Sum(t => t.Score);
}
else
{
return PlayerHands.Sum(t => t.Score);
}
}
}
https://dotnetfiddle.net/s5rSqJ
As presented, the players score should be 150. I.e. the score gets reset at the start of Round 4, so the total score is the sum of Rounds 4, 5, and 6.

Summarizing a few points,
the number of rounds is finite (otherwise a really long game!). This observation is important when we talk about reversing below.
rounds are already sorted in ascending order (per the comments), so actual round number doesn't matter
if we sum backwards, we don't have to scan the whole list
So, we can come up with an implementation that is O(1) space (in-place, no allocations) and O(n) time (linear, less than the size of the list when there's a reset).
Using MoreLinq
var score = hands.ReverseInPlace().TakeUntil(x => x.Reset).Sum(x => x.Score);
Where ReverseInPlace() iterates in reverse order in place, and MoreEnumerable.TakeUntil() takes up to and including the round that has a true value for Reset or end of sequence.
ReverseInPlace would be an extension method (you could generalize to IEnumerable<> if you wanted).
public static class ListExtensions
{
public static IEnumerable<T> ReverseInPlace<T>(this IList<T> source)
{
// add guard checks here, then do...
for (int i=source.Length-1; i != -1; --i)
yield return source[i];
}
}
Not using MoreLinq
You could create a TakeInReverseUntil:
public static IEnumerable<T> TakeInReverseUntil<T>(this IList<T> source, Func<T, bool> predicate)
{
// add guard checks here, then do...
for (int i=source.Length-1; i != -1; --i)
{
yield return source[i];
if (predicate(source[i]) yield break;
}
}
giving you the simplified call
var score = hands.TakeInReverseUntil(x => x.Reset).Sum(x => x.Score);
NOTE: Enumerable.Reverse() allocates a buffer, so is O(n) space, and is why I rolled my own ReverseInPlace instead for this answer.

The best way I can see here is to simply change your check for the last reset round a bit and combine both statements:
public int GetPlayerScore()
{
// selects the highest Round if Reset == true or 1 by default
var lastResetRound = PlayerHands.Max(hand => hand.Reset ? hand.Round : 1);
return PlayerHands.Where(t => t.Round >= lastResetRound.Round).Sum(t => t.Score);
// or all toghether like this:
return PlayerHands.Where(t => t.Round >= PlayerHands.Max(hand => hand.Reset ? hand.Round : 1)).Sum(t => t.Score);
}

If you used MoreLinq's TakeUntil() then you could do something like:
PlayerHands
.OrderByDescending(x => x.Round)
.TakeUntil(x => x.Reset)
.Sum(x => x.Score);
Edit: formatting & simplified bool conditional per #PrasadTelkikar

I like the morelinq TakeUntil most which others have shown, missing it in the standard library.
I've tried to do it without creating new extension methods(cheating) and without morelinq. Following works, but is not as readable and also requires an ordered list(which is the case acc. to your comments).
return PlayerHands
.TakeLast(PlayerHands.Count + 1 - (PlayerHands.FindLast(x => x.Reset)?.Round ?? 1))
.Sum(x => x.Score);
Maybe someone finds a way to simplify the count-calculation.

Why I cannot generate more than 6551 random numbers

I have the following code in C#, inside the Main method of a Simple Console Application.
I have debuged and, after List.Count = 6551 it seems the random values repeat themselves.
List<int> list = new List<int>(9999);
bool waiting = true;
Random random = new Random(DateTime.Today.Milliseconds);
do
{
int units = random.Next(0, 9);
int tens = random.Next(0, 9);
int hundreds = random.Next(0, 9);
int thousands = random.Next(0, 9);
int result = int.Parse(String.Format("{0}{1}{2}{3}", units, tens, hundreds, thousands));
if(list.Contains(result))
{
continue;
}
else
{
list.Add(result);
}
if(list.Count == 9999)
{
waiting = false;
}
}while(waiting);
Console.WriteLine("Finished"):
Console.ReadKey();

Your digts range from 0 to (and excluding!) 9, which makes eight choices per digit (0-8) and thus 6561 combinations (9*9*9*9).
Also, beware that your algorithm is extremely inefficient. Eventually, your list will be very crowded and then, the algorithm will spend most of the time checking whether a given random number is already contained in your result list.
If your goal is to shuffle indices, you can reach that more eficiently by keeping a list of indices you haven't inserted already.

The answer has already be given by Georg, but concerning your efficiency problem: if what you want is a shuffled list of integer, you can do it with an extension method on the list.
var shuffled = Enumerable.Range(0, 10000).Shuffle();
Look here for more info An extension method on IEnumerable needed for shuffling

Avoiding 'System.OutOfMemoryException' while iterating over a IEnumerable<IEnumerable<object>>

I have the following code to get the cheapest List of objects which satisfy the requiredNumbers criteria. This list of objects can have a length varying from 1 to maxLength, i.e. there can be a combination of 1 to maxLength of objects with repitition allowed. Right now, this this iterates over the whole list of combinations (IEnumerable of IEnumerable of OBJECT) fine till maxLength = 9 and breaks after that with a "System.OutOfMemoryException" at
t1.Concat(new OBJECT[] { t2 }
I tried another approach to solve this (mentioned in the code comments), but that seems to have its own demons. What I understand right now is , I'll have to somehow know the least priced combination of objects without iterating over the whole List of combination, which I can't seem to find feasible.
Could someone suggest any changes that let the maxLength be higher(much higher ideally), without hindering the performance. Any help is much appreciated. Please let me know if I am not clear.
private static int leastPrice = int.MaxValue;
private IEnumerable<IEnumerable<OBJECT>> CombinationOfObjects(IEnumerable<OBJECT> objects, int length)
{
if (length == 1)
return objects.Select(t => new OBJECT[] { t });
return CombinationOfObjects(objects, length - 1).SelectMany(t => objects, (t1, t2) => t1.Concat(new OBJECT[] { t2 }));
}
//Gets the least priced Valid combination out of all possible
public IEnumerable<OBJECT> GetValidCombination(IEnumerable<OBJECT> list, int maxLength, int[] matArray)
{
IEnumerable<IEnumerable<OBJECT>> tempList = null;
List<IEnumerable<OBJECT>> validList = new List<IEnumerable<OBJECT>>();
for (int i = 1; i <= maxLength; i++)
{
tempList = CombinationOfObjects(list, i);
tempList = from alist in tempList
orderby alist.Sum(x => x.Price)
select alist;
foreach (var lst in tempList)
{
//This check will not be required if the least priced value is returned as soon as found
int price = lst.Sum(c => c.Price);
if (price < leastPrice)
{
if (CheckMaterialSum(lst, matArray))
{
validList.Add(lst);
leastPrice = price;
break;
//return lst;
//returning lst as soon as valid combo is found is fastest
//Con being it also returns the least priced least item containing combo
//i.e. even if a 4 item combo is cheaper than the 2 item combo satisfying the need,
//it'll never even check for the 4 item combo
}
}
}
}
//This whole thing would go too if lst was returned earlier
foreach (IEnumerable<OBJECT> combination in validList)
{
int priceTotal = combination.Sum(combo => combo.Price);
if (priceTotal == leastPrice)
{
return combination;
}
}
return new List<OBJECT>();
}
//Checks if the given combination satisfies the requirement
private bool CheckMaterialSum(IEnumerable<OBJECT> combination, int[] matArray)
{
int[] sumMatProp = new int[matArray.Count()];
for (int i = 0; i < matArray.Count(); i++)
{
sumMatProp[i] = combination.Sum(combo => combo.Numbers[i]);
}
bool isCombinationValid = matArray.Zip(sumMatProp, (requirement, c) => c >= requirement).All(comboValid => comboValid);
return isCombinationValid;
}
static void Main(string[] args)
{
List<OBJECT> testList = new List<OBJECT>();
OBJECT object1 = new OBJECT();
object1.Name = "object1";
object1.Price = 2000;
object1.Numbers = new int[] { 2, 3, 4 };
testList.Add(object1);
OBJECT object2 = new OBJECT();
object2.Name = "object2";
object2.Price = 1900;
object2.Numbers = new int[] { 3, 2, 4 };
testList.Add(object1);
OBJECT object3 = new OBJECT();
object3.Name = "object3";
object3.Price = 1600;
object3.Numbers = new int[] { 4, 3, 2 };
testList.Add(object1);
int requiredNumbers = new int[]{10,10,10};
int maxLength = 9;//This is the max length possible, OutOf Mememory exception after this
IEnumerable<OBJECT> resultCombination = GetValidCombination(testList, maxLength, requiredNumbers);
}
EDIT
Requirement:
I have a number of objects having several properties, namely, Price, Name , and Materials. Now, I need to find such a combination of these objects that the sum of all materials in a combination satisfies the user input qty of materials. Also, the combination needs to be of least price possible.
There is a constraint of maxLength and it sets the maximum total number of objects that can be in a combination, i.e. for a maxLength = 8, the combination may contain anywhere from 1 to 8 objects.
Approaches tried:
1.
-I find all combinations of objects possible (valid + invalid)
-Iterate over them to find the least priced combination. This goes out of memory while iterating.
2.
-I find all combinations possible (valid + invalid)
-Apply a validity check (i.e if it fulfills the user requirement)
-Add only valid combinations in a List of List
-Iterate over this valid List of lists to find the cheapest list and return that. Also goes out of memory
3.
-I find combinations in increasing order of objects (i.e. first all combinations having 1 object, then 2 then so on...)
-Sort the combinations according to price
-Apply validity check and return the first valid combination
-Now this works fine performance wise, but does not always return the cheapest possible combination.
If I could somehow get the optimal solution without iterating over the whole list , that would solve it. But, all of the things that I've tried either have to iterate over all combinations or simply do not result in the optimal solution.
Any help regarding even some other approach that I can't seem to think of is most welcome.

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 })));