Related
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 }
I need to optimize below code so it can execute faster, by means using more memory or parallel, currently it is taking 2 minutes to complete single record in Windows 10 64bit, 16GB RAM PC
data1 list array length = 1000
data2 list array length = 100000
data3 list array length = 100
for (int d1 = 0; d1 < data1.Count; d1++)
{
if (data1[d1].status == 'UNMATCHED')
{
for (int d2 = 0; d2 < data2.Count; d2++)
{
if (data2[d2].status == 'UNMATCHED')
{
vMatched = false;
for (int d3 = 0; d3 < data3.Count; d3++)
{
if (data3[d3].rule == "rule1")
{
if (data1[d1].value == data2[d2].value)
{
data1[d1].status = 'MATCHED';
data1[d2].status = 'MATCHED';
vMatched = true;
break;
}
}
else if (data3[d3].rule == "rule2")
{
...
}
else if (data3[d3].rule == "rule100")
{
...
}
}
if (vMatched)
break;
}
}
}
}
First of all, for any kind of performance oriented programming, avoid using strings, use more appropriate types, like enum or bools, instead. Another recommendation is to profile your code, so you know what parts actually take time.
In the given example there is only one rule presented, so the data3-loop could be eliminated by first checking if this rule exist and only then proceed with the matching.
This matching between items in data1 & data2 essentially pairs unmatched items with the same value. Whenever problems like this occur, the standard solution is some kind of search structure, like a dictionary, to get better than linear search time. For example
var data2Dictionary = data2.ToDictionary(d => Tuple.Create(d.value, d.status), d => d);
This should let you drastically decrease the time to find a item with a specific value and status. Keep in mind that the code above will throw in case multiple items share the same value & status, and that the dictionary key will not be updated if the item changes value or status.
You can avoid to start everytime the 2nd loop from 0. By keeping last index with "UNMATCHED" inside data2.
It should reduce the complexity.
In the worst case:
Now 1000 * 100000 * 100 iterations: 10000000000
New (1000+100000) * 100 iterations: 10100000
I've been trying to solve this interview problem which asks to shuffle a string so that no two adjacent letters are identical
For example,
ABCC -> ACBC
The approach I'm thinking of is to
1) Iterate over the input string and store the (letter, frequency)
pairs in some collection
2) Now build a result string by pulling the highest frequency (that is > 0) letter that we didn't just pull
3) Update (decrement) the frequency whenever we pull a letter
4) return the result string if all letters have zero frequency
5) return error if we're left with only one letter with frequency greater than 1
With this approach we can save the more precious (less frequent) letters for last. But for this to work, we need a collection that lets us efficiently query a key and at the same time efficiently sort it by values. Something like this would work except we need to keep the collection sorted after every letter retrieval.
I'm assuming Unicode characters.
Any ideas on what collection to use? Or an alternative approach?
You can sort the letters by frequency, split the sorted list in half, and construct the output by taking letters from the two halves in turn. This takes a single sort.
Example:
Initial string: ACABBACAB
Sort: AAAABBBCC
Split: AAAA+BBBCC
Combine: ABABABCAC
If the number of letters of highest frequency exceeds half the length of the string, the problem has no solution.
Why not use two Data Structures: One for sorting (Like a Heap) and one for key retrieval, like a Dictionary?
The accepted answer may produce a correct result, but is likely not the 'correct' answer to this interview brain teaser, nor the most efficient algorithm.
The simple answer is to take the premise of a basic sorting algorithm and alter the looping predicate to check for adjacency rather than magnitude. This ensures that the 'sorting' operation is the only step required, and (like all good sorting algorithms) does the least amount of work possible.
Below is a c# example akin to insertion sort for simplicity (though many sorting algorithm could be similarly adjusted):
string NonAdjacencySort(string stringInput)
{
var input = stringInput.ToCharArray();
for(var i = 0; i < input.Length; i++)
{
var j = i;
while(j > 0 && j < input.Length - 1 &&
(input[j+1] == input[j] || input[j-1] == input[j]))
{
var tmp = input[j];
input[j] = input[j-1];
input[j-1] = tmp;
j--;
}
if(input[1] == input[0])
{
var tmp = input[0];
input[0] = input[input.Length-1];
input[input.Length-1] = tmp;
}
}
return new string(input);
}
The major change to standard insertion sort is that the function has to both look ahead and behind, and therefore needs to wrap around to the last index.
A final point is that this type of algorithm fails gracefully, providing a result with the fewest consecutive characters (grouped at the front).
Since I somehow got convinced to expand an off-hand comment into a full algorithm, I'll write it out as an answer, which must be more readable than a series of uneditable comments.
The algorithm is pretty simple, actually. It's based on the observation that if we sort the string and then divide it into two equal-length halves, plus the middle character if the string has odd length, then corresponding positions in the two halves must differ from each other, unless there is no solution. That's easy to see: if the two characters are the same, then so are all the characters between them, which totals ⌈n/2⌉+1 characters. But a solution is only possible if there are no more than ⌈n/2⌉ instances of any single character.
So we can proceed as follows:
Sort the string.
If the string's length is odd, output the middle character.
Divide the string (minus its middle character if the length is odd) into two equal-length halves, and interleave the two halves.
At each point in the interleaving, since the pair of characters differ from each other (see above), at least one of them must differ from the last character output. So we first output that character and then the corresponding one from the other half.
The sample code below is in C++, since I don't have a C# environment handy to test with. It's also simplified in two ways, both of which would be easy enough to fix at the cost of obscuring the algorithm:
If at some point in the interleaving, the algorithm encounters a pair of identical characters, it should stop and report failure. But in the sample implementation below, which has an overly simple interface, there's no way to report failure. If there is no solution, the function below returns an incorrect solution.
The OP suggests that the algorithm should work with Unicode characters, but the complexity of correctly handling multibyte encodings didn't seem to add anything useful to explain the algorithm. So I just used single-byte characters. (In C# and certain implementations of C++, there is no character type wide enough to hold a Unicode code point, so astral plane characters must be represented with a surrogate pair.)
#include <algorithm>
#include <iostream>
#include <string>
// If possible, rearranges 'in' so that there are no two consecutive
// instances of the same character.
std::string rearrange(std::string in) {
// Sort the input. The function is call-by-value,
// so the argument itself isn't changed.
std::string out;
size_t len = in.size();
if (in.size()) {
out.reserve(len);
std::sort(in.begin(), in.end());
size_t mid = len / 2;
size_t tail = len - mid;
char prev = in[mid];
// For odd-length strings, start with the middle character.
if (len & 1) out.push_back(prev);
for (size_t head = 0; head < mid; ++head, ++tail)
// See explanatory text
if (in[tail] != prev) {
out.push_back(in[tail]);
out.push_back(prev = in[head]);
}
else {
out.push_back(in[head]);
out.push_back(prev = in[tail]);
}
}
}
return out;
}
you can do that by using a priority queue.
Please find the below explanation.
https://iq.opengenus.org/rearrange-string-no-same-adjacent-characters/
Here is a probabilistic approach. The algorithm is:
10) Select a random char from the input string.
20) Try to insert the selected char in a random position in the output string.
30) If it can't be inserted because of proximity with the same char, go to 10.
40) Remove the selected char from the input string and go to 10.
50) Continue until there are no more chars in the input string, or the failed attempts are too many.
public static string ShuffleNoSameAdjacent(string input, Random random = null)
{
if (input == null) return null;
if (random == null) random = new Random();
string output = "";
int maxAttempts = input.Length * input.Length * 2;
int attempts = 0;
while (input.Length > 0)
{
while (attempts < maxAttempts)
{
int inputPos = random.Next(0, input.Length);
var outputPos = random.Next(0, output.Length + 1);
var c = input[inputPos];
if (outputPos > 0 && output[outputPos - 1] == c)
{
attempts++; continue;
}
if (outputPos < output.Length && output[outputPos] == c)
{
attempts++; continue;
}
input = input.Remove(inputPos, 1);
output = output.Insert(outputPos, c.ToString());
break;
}
if (attempts >= maxAttempts) throw new InvalidOperationException(
$"Shuffle failed to complete after {attempts} attempts.");
}
return output;
}
Not suitable for strings longer than 1,000 chars!
Update: And here is a more complicated deterministic approach. The algorithm is:
Group the elements and sort the groups by length.
Create three empty piles of elements.
Insert each group to a separate pile, inserting always the largest group to the smallest pile, so that the piles differ in length as little as possible.
Check that there is no pile with more than half the total elements, in which case satisfying the condition of not having same adjacent elements is impossible.
Shuffle the piles.
Start yielding elements from the piles, selecting a different pile each time.
When the piles that are eligible for selection are more than one, select randomly, weighting by the size of each pile. Piles containing near half of the remaining elements should be much preferred. For example if the remaining elements are 100 and the two eligible piles have 49 and 40 elements respectively, then the first pile should be 10 times more preferable than the second (because 50 - 49 = 1 and 50 - 40 = 10).
public static IEnumerable<T> ShuffleNoSameAdjacent<T>(IEnumerable<T> source,
Random random = null, IEqualityComparer<T> comparer = null)
{
if (source == null) yield break;
if (random == null) random = new Random();
if (comparer == null) comparer = EqualityComparer<T>.Default;
var grouped = source
.GroupBy(i => i, comparer)
.OrderByDescending(g => g.Count());
var piles = Enumerable.Range(0, 3).Select(i => new Pile<T>()).ToArray();
foreach (var group in grouped)
{
GetSmallestPile().AddRange(group);
}
int totalCount = piles.Select(e => e.Count).Sum();
if (piles.Any(pile => pile.Count > (totalCount + 1) / 2))
{
throw new InvalidOperationException("Shuffle is impossible.");
}
piles.ForEach(pile => Shuffle(pile));
Pile<T> previouslySelectedPile = null;
while (totalCount > 0)
{
var selectedPile = GetRandomPile_WeightedByLength();
yield return selectedPile[selectedPile.Count - 1];
selectedPile.RemoveAt(selectedPile.Count - 1);
totalCount--;
previouslySelectedPile = selectedPile;
}
List<T> GetSmallestPile()
{
List<T> smallestPile = null;
int smallestCount = Int32.MaxValue;
foreach (var pile in piles)
{
if (pile.Count < smallestCount)
{
smallestPile = pile;
smallestCount = pile.Count;
}
}
return smallestPile;
}
void Shuffle(List<T> pile)
{
for (int i = 0; i < pile.Count; i++)
{
int j = random.Next(i, pile.Count);
if (i == j) continue;
var temp = pile[i];
pile[i] = pile[j];
pile[j] = temp;
}
}
Pile<T> GetRandomPile_WeightedByLength()
{
var eligiblePiles = piles
.Where(pile => pile.Count > 0 && pile != previouslySelectedPile)
.ToArray();
Debug.Assert(eligiblePiles.Length > 0, "No eligible pile.");
eligiblePiles.ForEach(pile =>
{
pile.Proximity = ((totalCount + 1) / 2) - pile.Count;
pile.Score = 1;
});
Debug.Assert(eligiblePiles.All(pile => pile.Proximity >= 0),
"A pile has negative proximity.");
foreach (var pile in eligiblePiles)
{
foreach (var otherPile in eligiblePiles)
{
if (otherPile == pile) continue;
pile.Score *= otherPile.Proximity;
}
}
var sumScore = eligiblePiles.Select(p => p.Score).Sum();
while (sumScore > Int32.MaxValue)
{
eligiblePiles.ForEach(pile => pile.Score /= 100);
sumScore = eligiblePiles.Select(p => p.Score).Sum();
}
if (sumScore == 0)
{
return eligiblePiles[random.Next(0, eligiblePiles.Length)];
}
var randomScore = random.Next(0, (int)sumScore);
int accumulatedScore = 0;
foreach (var pile in eligiblePiles)
{
accumulatedScore += (int)pile.Score;
if (randomScore < accumulatedScore) return pile;
}
Debug.Fail("Could not select a pile randomly by weight.");
return null;
}
}
private class Pile<T> : List<T>
{
public int Proximity { get; set; }
public long Score { get; set; }
}
This implementation can suffle millions of elements. I am not completely convinced that the quality of the suffling is as perfect as the previous probabilistic implementation, but should be close.
func shuffle(str:String)-> String{
var shuffleArray = [Character](str)
//Sorting
shuffleArray.sort()
var shuffle1 = [Character]()
var shuffle2 = [Character]()
var adjacentStr = ""
//Split
for i in 0..<shuffleArray.count{
if i > shuffleArray.count/2 {
shuffle2.append(shuffleArray[i])
}else{
shuffle1.append(shuffleArray[i])
}
}
let count = shuffle1.count > shuffle2.count ? shuffle1.count:shuffle2.count
//Merge with adjacent element
for i in 0..<count {
if i < shuffle1.count{
adjacentStr.append(shuffle1[i])
}
if i < shuffle2.count{
adjacentStr.append(shuffle2[i])
}
}
return adjacentStr
}
let s = shuffle(str: "AABC")
print(s)
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 })));
I am comparing two lists of data that were generated from a binary file. I have a good idea on why it's running slow, when there's a significant amount of records, it does un-needed redundant work.
For example, if a1 = a1, condition is true. Since 2a != 1a so why even bother checking it? I need to eliminate 1a from being checked again. If I don't, it will check the first record when it goes to check the 400,000th record. I thought about making the second for loop a foreach, but I can't remove 1a while iterating through the nested loop
The amount of items that can be in either 'for loop' can vary. I don't think a single for loop using 'i' will work since the match can be anywhere. I'm reading from a binary file
This is my current code. Program has been running for over an hour, and it's still going. I removed a lot of my iterating code for readability reasons.
for (int i = 0; i < origItemList.Count; i++)
{
int modFoundIndex = 0;
Boolean foundIt = false;
for (int g = 0; g < modItemList.Count; g++)
{
if ((origItemList[i].X == modItemList[g].X)
&& (origItemList[i].Y == modItemList[g].Y)
&& (origItemList[i].Z == modItemList[g].Z)
&& (origItemList[i].M == modItemList[g].M))
{
foundIt = true;
modFoundIndex = g;
break;
}
else
{
foundIt = false;
}
}
if (foundIt)
{
/*
* This is run assumming it finds an x,y,z,m
coordinate. It thenchecks the database file.
*
*/
//grab the rows where the coordinates match
DataRow origRow = origDbfFile.dataset.Tables[0].Rows[i];
DataRow modRow = modDbfFile.dataset.Tables[0].Rows[modFoundIndex];
//number matched indicates how many columns were matched
int numberMatched = 0;
//get the number of columns to match in order to detect all changes
int numOfColumnsToMatch = origDbfFile.datatable.Columns.Count;
List<String> mismatchedColumns = new List<String>();
//check each column name for a change
foreach (String columnName in columnNames)
{
//this grabs whatever value is in that field
String origRowValue = "" + origRow.Field<Object>(columnName);
String modRowValue = "" + modRow.Field<Object>(columnName);
//check if they are the same
if (origRowValue.Equals(modRowValue))
{
//if they aren the same, increase the number matched by one
numberMatched++;
//add the column to the list of columns that don't match
}
else
{
mismatchedColumns.Add(columnName);
}
}
/* In the event it matches 15/16 columns, show the change */
if (numberMatched != numOfColumnsToMatch)
{
//Grab the shapeFile in question
Item differentAttrShpFile = origItemList[i];
//start blue highlighting
result += "<div class='turnBlue'>";
//show where the change was made at
result += "Change Detected at<br/> point X: " +
differentAttrShpFile.X + ",<br/> point Y: " +
differentAttrShpFile.Y + ",<br/>";
result += "</div>"; //end turnblue div
foreach (String mismatchedColumn in mismatchedColumns)
{
//iterate changes here
}
}
}
}
You're coming at this in a totally wrong way. The loop you have is O(n^2), breaking when you find the match will on average cut the time in half for a hit, that's not enough. If you have a quarter million items in the list then this loop executes 62 billion times and even if the compiler optimizes out the extra array lookups you're still looking at at least a trillion instructions. You don't do O(n^2) for large n if you can possibly help it!
What you need to do is get rid of the O(n^2) aspect of this. My suggestion:
1) Define a hashing function that looks at the x, y, z & m and comes up with an integer value, my inclination would be to use one that's the wordsize of your target platform.
2) Iterate over both lists, compute hashes for everything.
3) Build an index to one of the tables, hash and the object. I suspect a dictionary is the best data structure here but a simple sorted array would also do.
4) Iterate over the list you didn't build the index over, compare the hashes to the entries in the index. If it's a hash that's an O(n) task, if it's a sorted array it's O(n log n).
5) When the hashes match do a full comparison to confirm the hit is real as you will get the occasional collision with a good 64-bit hash and you'll get a decent number of them if your hashes are 32-bit.
This is something similar to Loren said but below is in language of .NET :)
1. Override GetHashCode method to return sum of x,y,z and m. Override Equals method to check for this sum.
2. Iterate and create HashSet from modItemList (List) before loop.
3. In inner loop, first check if origItemList[i] exists in HashSet using YourModHashSet.Contains(MyObject) method.
4. If .Contains return you false, carry one, no match.
5. If .Contains return you true, iterate thru entire modItemList and apply your current logic of checking for x,y,z and m for entire list. Note that here you should use List as hash table might eat up many objects for which hash code is same.
Also, I would use Foreach instead of For because I've seen Foreach giving little better results (5 to 30% faster) in such case.
Update:
I created MyObject class like below:
public class MyObject
{
public int X, Y, Z, M;
public override int GetHashCode()
{
return X*10000 + Y*100 + Z*10 + M;
}
public override bool Equals(object obj)
{
return (obj.GetHashCode() == this.GetHashCode());
}
}
GetHashCode method is important here. We don't want many false positives. False positive occurs when Hash matches for some other combination of X, Y, Z and M. Best way to prevent false positive is to multiply each member such that each will impact one decimal place in HashCode. Note that you should consider not exceeding Int.Max value. If the expected value of X,Y,Z and M are small you should be good.
set2.Clear();
s1 = DateTime.Now;
MyObject matchingElement;
totalmatch = 0;
foreach (MyObject elem in list2)
set2.Add(elem);
foreach (MyObject t1 in list1)
{
if (set2.Contains(t1))
{
matchingElement = null;
foreach (MyObject t2 in list2)
{
if (t1.X == t2.X && t1.Y == t2.Y && t1.Z == t2.Z && t1.M == t2.M)
{
totalmatch++;
matchingElement = t2;
break;
}
}
//Do Something on matchingElement if not null
}
}
Console.WriteLine("set foreach with contains: " + (DateTime.Now - s1).TotalSeconds + "\t Total Match: " + totalmatch);
Above is sample code that I was trying to describe in my answer. This code should work super fast if matches are expected to be less.