Develop Reference

Consuming a number into descending groups

I always struggle with these types of algorithms. I have a scenario where I have a cubic value for freight and need to split this value into cartons of different sizes, there are 3 sizes available in this instance, 0.12m3, 0.09m3 and 0.05m3. A few examples;
Assume total m3 is 0.16m3, I need to consume this value into the appropriate cartons.
I will have 1 carton of 0.12m3, this leave 0.04m3 to consume. This fits into the 0.05m3 so therefore I will have 1 carton of 0.05m, consumption is now complete. Final answer is 1 x 0.12m3 and 1 x 0.05m3.
Assume total m3 is 0.32m3, I would end up with 2 x 0.12m3 and 1 x 0.09m3.
I would prefer something either in c# or SQL that would easily return to me the results.
Many thanks for any help.
Cheers

I wrote an algorithm that may be a little messy but I do think it works. Your problem statement isn't 100% unambiguous, so this solution is assuming you want to pick containers so that you minimize the remaining space, when started filling from the largest container.
// List of cartons
var cartons = new List<double>
{
0.12,
0.09,
0.05
};
// Amount of stuff that you want to put into cartons
var stuff = 0.32;
var distribution = new Dictionary<double, int>();
// For this algorithm, I want to sort by descending first.
cartons = cartons.OrderByDescending(x => x).ToList();
foreach (var carton in cartons)
{
var count = 0;
while (stuff >= 0)
{
if (stuff >= carton)
{
// If the amount of stuff bigger than the carton size, we use carton size, then update stuff
count++;
stuff = stuff - carton;
distribution.CreateNewOrUpdateExisting(carton, 1);
}
else
{
// Otherwise, among remaining cartons we pick the ones that will have empty space if the remaining stuff is put in
var partial = cartons.Where(x => x - stuff >= 0 && x != carton);
if (partial != null && partial.Count() > 0)
{
var min = partial.Min();
if (min > 0)
{
distribution.CreateNewOrUpdateExisting(min, 1);
stuff = stuff - min;
}
}
else
{
break;
}
}
}
There' an accompanying extension method, which either adds an item to a dictionary, or if the Key exists, then increments the Value.
public static class DictionaryExtensions
{
public static void CreateNewOrUpdateExisting(this IDictionary<double, int> map, double key, int value)
{
if (map.ContainsKey(key))
{
map[key]++;
}
else
{
map.Add(key, value);
}
}
}
EDIT
Found a bug in the case where initial stuff is smaller than the largest container, so code updated to fix it.
NOTE
This may still not be a 100% foolproof algorithm as I haven't tested extensively. But it should give you an idea on how to proceed.
EDIT EDIT
Changing the condition to while (stuff > 0) should fix the bug mentioned in the comments.

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 })));

Reading out dice

We need to make some small program for school that rolls 5 dices and see if you get a three of a kind with it, if so, increase points etc.
The problem isnt to reading out the dice, I have the knowledge to get it done, but I want it to be a little efficient, not a ugly piece of code that takes up half a page. I have found ways to filter out the the duplicates in an array, but not the other way around. It rolls with 5 dices, so its an array with 5 numbers, is there like a built in function or a nice, efficient way of returning the number that has been rolled three times or return null if none of the number are rolled three times?
Hope anyone can push me in the right direction. :)

You can do it easily and succinctly with LINQ:
var diceRolls = new[] {1, 3, 3, 3, 4};
var winningRolls = diceRolls.GroupBy(die => die).Select(groupedRoll => new {DiceNumber = groupedRoll.Key, Count = groupedRoll.Count()}).Where(x => x.Count >= 3).ToList();
What this is doing is grouping the rolls by the roll number ("Key") and the count of occurrences of that roll. Then, it's selecting any rolls that have a count greater than or equal to 3. The result will be a List containing your winning rolls.

One approach is to store a 6-element array containing the count of how many dice have that face. Loop through the 5 dice and increment the appropriate face's total count.
var rolls = new List<Roll>();
// run as many rolls as you want. e.g.:
rolls.Add(new Roll(5));
var threeOfAKindRolls = rolls.Where(r => r.HasThreeOfAKind());
public class Roll
{
public Roll( int diceCount )
{
// Do your random generation here for the number of dice
DiceResults = new int[0]; // your results.
ResultCounts = new int[6]; // assuming 6 sided die
foreach (var diceResult in DiceResults)
{
ResultCounts[diceResult]++;
}
}
public int[] DiceResults { get; private set; }
public int[] ResultCounts { get; private set; }
public bool HasThreeOfAKind()
{
return ResultCounts.Any(count => count >= 3);
}
}
This code can be shortened somewhat if you don't need the result counts to perform other tests on the results:
public Roll( int diceCount )
{
// Do your random generation here for the number of dice
DiceResults = new int[0]; // your results.
}
public bool HasThreeOfAKind()
{
ResultCounts = new int[6]; // assuming 6 sided die
foreach (var diceResult in DiceResults)
{
// Increment and shortcut if the previous value was 2
if( (ResultCounts[diceResult]++) == 2) return true;
}
return false;
}

Given what you are describing your answer as looking like it sounds like you're trying to do a massive comparison. That's the wrong approach.
Pretend it's 20 dice rather than 5, a good answer will work just as well in a larger case.

I would use something like the following:
public int? WinningRoll(IEnumerable<int> rolls)
{
int threshold = rolls.Count() / 2;
var topRollGroup = rolls.GroupBy(r => r)
.SingleOrDefault(rg => rg.Count() > threshold);
if (topRollGroup != null)
return topRollGroup.Key;
return null;
}
This will work with any number of rolls, not just 5, so if you had 10 rolls, if 6 of them were the same value, that value would be returned. If there is no winning roll, null is returned.

C# Look up dictionary

I'm currently trying to create a program that estimates location based on signal strength. The signal strength value is an int and then i need a lookup dictionary with ranges.
So I would have something like:
Signal Strenth Position
0-9 1
10-19 2
20-29 3
and then I would want to look up what position a signal strength relates to, for example 15 would relate to position 2.
I know I can just have a load of if statements but is there a good way to do this using some sort of lookup dictionary?

If you have arbitrary but consecutive ranges you can use an array of the upper bounds and perform a binary search to get the position:
// Definition of ranges
int[] ranges = new int[] { 9, 19, 29 };
// Lookup
int position = Array.BinarySearch(ranges, 15);
if (position < 0)
position = ~position;
// Definition of range names
string[] names = new string[] { "home", "street", "city", "far away" };
Console.WriteLine("Position is: {0}", names[position]);
Array.BinarySearch returns the index of the item in the array if it exists (array must be sorted obviously) or the bitwise inverted index where the item should be inserted to keep the array sorted.

What about :
int position = signalStrength / 10 + 1;
Kindness,
Dan

When you want to use Dictionary, you need at least some special key type to deal with the ranges. KeyType can be abstract and two derived types KeyTypeRange(int int) and KEyTypeSearch( int). Some special comparison logic must be implemented to compare an KeyTypeSearch with an KeyTypeRange.
SortedDictionary<KeyType,int> lookup = new Dictionary<int,int>();
lookup.Add( new KeyTypeRange(1,10),1);
lookup.Add( new KeyTypeRange(11,20),2);
lookup.Add( new KeyTypeRange(21,30),3);
lookup.TryGetValue( new KeyTypeSearch(15) );
It shows a possible solution to use different esearch keys and key values in dictionaries. But this seems to be Overkill for this problem. This problem is solved best by the BinarySearch solution.

Good is a function of purpose. All of the above solutions work well presuming that any given range is a small number of integers. Otherwise you may want to use whatever the real world math function is to determine your group. For instance, for the example given, your answer function would be x % 10 + 1; That'll run much faster than a dictionary.

You could do a Dictionary, where the first int is the signal strength and the second int is the position. You would need to add an entry for every value in the range (so, one for signal strength 0, position 1, signal strength 1, position 1, etc.), but it would be a very quick, single line lookup.
Something like:
Dictionary<int, int> values;
values = new Dictionary<int, int>();
values[0] = 1;
values[1] = 1;
...
values[29] = 3;
and then, to access it:
Console.WriteLine(values[27].ToString());

For future expansion i would do 2 dictionaries.
Just in case those rates change
so a
dictionary<string,dictionary<int,int>>
or just use custom classes
the string would be static strings like low med, high, then you can change the ranges in your foreach initilixing the initial values

One solution would be to use a simple list, where each position in the list represents a different position that you're scanning for. In code, it might look something like this (assuming that all position numbers are sequential):
** Note: I have not actually run this code to make sure it works as-is... you might also need to implement an IEqualityComparer on Range in order for the IndexOf operation to return the proper position:
public class Controller
{
List m_positions = new List();
public void LoadPositions()
{
m_positions.Add(new Range(0, 9));
m_positions.Add(new Range(10, 19));
m_positions.Add(new Range(20, 29));
}
public int GetPosition (int signal)
{
Range range = m_positions.Single(a => IsBetween(signal, a.Min, a.Max));
return m_positions.IndexOf(range);
}
private static bool IsBetween (int target, int min, int max)
{
return min = target;
}
}
It's probably pretty self-explanatory, but to avoid any confusion, here's what the Range class might look like:
public class Range
{
public Range(int min, int max)
{
this.Min = min;
this.Max = max;
}
public int Min
{
get;
private set;
}
public int Max
{
get;
private set;
}
}

if there is a direct correlation between signal range and the position then use what #agileguy suggested.
If you have positions distributed non linearly across the signal strength then one way would be:
class SignalStrengthPositionMapper
{
private static readonly int[] signalStrength = { Int32.MinValue, 0, 5, 11, 15, 20, 27, 35 };
public static int GetPosition(int strength)
{
return StrengthSearch(0, signalStrength.Length, strength);
}
// modified binary search
private static int StrengthSearch(int start, int end, int strength)
{
int mid = 0;
while (start <= end)
{
mid = (start + end) / 2;
if (strength >= signalStrength[mid]) // lower bound check
{
start = mid + 1;
if (strength < signalStrength[start]) // upper bound check
return mid;
}
else if (strength < signalStrength[mid]) // upper bound check
{
end = mid - 1;
if (strength >= signalStrength[end]) // lower bound check
return mid;
}
}
return 0;
}
}

Try using generics:
Dictionary<int,int> lookup = new Dictionary<int,int>();
lookup.Add(0,1);
lookup.Add(1,1);
lookup.Add(2,1);
lookup.Add(3,1);
...
lookup.Add(9,1);
lookup.Add(10,2);
lookup.Add(11,2);
etc
Then, lookup[22] would return value of 3. I suggest using a set of loops to create your 'ranges'. With this method, you're guaranteed O(1) access time.