I'm calculating intersection of 2 sets of sorted numbers in a time-critical part of my application. This calculation is the biggest bottleneck of the whole application so I need to speed it up.
I've tried a bunch of simple options and am currently using this:
foreach (var index in firstSet)
{
if (secondSet.BinarySearch(index) < 0)
continue;
//do stuff
}
Both firstSet and secondSet are of type List.
I've also tried using LINQ:
var intersection = firstSet.Where(t => secondSet.BinarySearch(t) >= 0).ToList();
and then looping through intersection.
But as both of these sets are sorted I feel there's a better way to do it. Note that I can't remove items from sets to make them smaller. Both sets usually consist of about 50 items each.
Please help me guys as I don't have a lot of time to get this thing done. Thanks.
NOTE: I'm doing this about 5.3 million times. So every microsecond counts.
If you have two sets which are both sorted, you can implement a faster intersection than anything provided out of the box with LINQ.
Basically, keep two IEnumerator<T> cursors open, one for each set. At any point, advance whichever has the smaller value. If they match at any point, advance them both, and so on until you reach the end of either iterator.
The nice thing about this is that you only need to iterate over each set once, and you can do it in O(1) memory.
Here's a sample implementation - untested, but it does compile :) It assumes that both of the incoming sequences are duplicate-free and sorted, both according to the comparer provided (pass in Comparer<T>.Default):
(There's more text at the end of the answer!)
static IEnumerable<T> IntersectSorted<T>(this IEnumerable<T> sequence1,
IEnumerable<T> sequence2,
IComparer<T> comparer)
{
using (var cursor1 = sequence1.GetEnumerator())
using (var cursor2 = sequence2.GetEnumerator())
{
if (!cursor1.MoveNext() || !cursor2.MoveNext())
{
yield break;
}
var value1 = cursor1.Current;
var value2 = cursor2.Current;
while (true)
{
int comparison = comparer.Compare(value1, value2);
if (comparison < 0)
{
if (!cursor1.MoveNext())
{
yield break;
}
value1 = cursor1.Current;
}
else if (comparison > 0)
{
if (!cursor2.MoveNext())
{
yield break;
}
value2 = cursor2.Current;
}
else
{
yield return value1;
if (!cursor1.MoveNext() || !cursor2.MoveNext())
{
yield break;
}
value1 = cursor1.Current;
value2 = cursor2.Current;
}
}
}
}
EDIT: As noted in comments, in some cases you may have one input which is much larger than the other, in which case you could potentially save a lot of time using a binary search for each element from the smaller set within the larger set. This requires random access to the larger set, however (it's just a prerequisite of binary search). You can even make it slightly better than a naive binary search by using the match from the previous result to give a lower bound to the binary search. So suppose you were looking for values 1000, 2000 and 3000 in a set with every integer from 0 to 19,999. In the first iteration, you'd need to look across the whole set - your starting lower/upper indexes would be 0 and 19,999 respectively. After you'd found a match at index 1000, however, the next step (where you're looking for 2000) can start with a lower index of 2000. As you progress, the range in which you need to search gradually narrows. Whether or not this is worth the extra implementation cost or not is a different matter, however.
Since both lists are sorted, you can arrive at the solution by iterating over them at most once (you may also get to skip part of one list, depending on the actual values they contain).
This solution keeps a "pointer" to the part of list we have not yet examined, and compares the first not-examined number of each list between them. If one is smaller than the other, the pointer to the list it belongs to is incremented to point to the next number. If they are equal, the number is added to the intersection result and both pointers are incremented.
var firstCount = firstSet.Count;
var secondCount = secondSet.Count;
int firstIndex = 0, secondIndex = 0;
var intersection = new List<int>();
while (firstIndex < firstCount && secondIndex < secondCount)
{
var comp = firstSet[firstIndex].CompareTo(secondSet[secondIndex]);
if (comp < 0) {
++firstIndex;
}
else if (comp > 0) {
++secondIndex;
}
else {
intersection.Add(firstSet[firstIndex]);
++firstIndex;
++secondIndex;
}
}
The above is a textbook C-style approach of solving this particular problem, and given the simplicity of the code I would be surprised to see a faster solution.
You're using a rather inefficient Linq method for this sort of task, you should opt for Intersect as a starting point.
var intersection = firstSet.Intersect(secondSet);
Try this. If you measure it for performance and still find it unwieldy, cry for further help (or perhaps follow Jon Skeet's approach).
I was using Jon's approach but needed to execute this intersect hundreds of thousands of times for a bulk operation on very large sets and needed more performance. The case I was running in to was heavily imbalanced sizes of the lists (eg 5 and 80,000) and wanted to avoid iterating the entire large list.
I found that detecting the imbalance and changing to an alternate algorithm gave me huge benifits over specific data sets:
public static IEnumerable<T> IntersectSorted<T>(this List<T> sequence1,
List<T> sequence2,
IComparer<T> comparer)
{
List<T> smallList = null;
List<T> largeList = null;
if (sequence1.Count() < Math.Log(sequence2.Count(), 2))
{
smallList = sequence1;
largeList = sequence2;
}
else if (sequence2.Count() < Math.Log(sequence1.Count(), 2))
{
smallList = sequence2;
largeList = sequence1;
}
if (smallList != null)
{
foreach (var item in smallList)
{
if (largeList.BinarySearch(item, comparer) >= 0)
{
yield return item;
}
}
}
else
{
//Use Jon's method
}
}
I am still unsure about the point at which you break even, need to do some more testing
try
firstSet.InterSect (secondSet).ToList ()
or
firstSet.Join(secondSet, o => o, id => id, (o, id) => o)
Related
I am perplexed by this issue. I believe I'm just missing an easy problem right in front of my face but I'm at the point where I need a second opinion to point out anything obvious that I'm missing. I minimized my code and simplified it so it only shows a small part of what it does. The full code is just many different calculations added on to what I have below.
for (int h = 2; h < 200; h++)
{
var List1 = CalculateSomething(testValues, h);
var masterLists = await AddToRsquaredList("Calculation1", h, actualValuesList, List1, masterLists.Item1, masterLists.Item2);
var List2 = CalculateSomething(testValues, h);
masterLists = await AddToRsquaredList("Calculation2", h, actualValuesList, List2, masterLists.Item1, masterLists.Item2);
var List3 = CalculateSomething(testValues, h);
masterLists = await AddToRsquaredList("Calculation3", h, actualValues, List3, masterLists.Item1, masterLists.Item2);
}
public static async Task<(List<RSquaredValues3>, List<ValueClass>)> AddToRsquaredList(string valueName, int days,
IEnumerable<double> estimatedValuesList, IEnumerable<double> actualValuesList,
List<RSquaredValues3> rSquaredList, List<ValueClass> valueClassList)
{
try
{
RSquaredValues3 rSquaredValue = new RSquaredValues3
{
ValueName = valueName,
Days = days,
RSquared = GoodnessOfFit.CoefficientOfDetermination(estimatedValuesList, actualValuesList),
StdError = GoodnessOfFit.PopulationStandardError(estimatedValuesList, actualValuesList)
};
int comboSize = 15;
double max = 0;
var query = await rSquaredList.OrderBy(i => i.StdError - i.RSquared).DistinctBy(i => i.ValueName).Take(comboSize).ToListAsync().ConfigureAwait(false);
if (query.Count > 0)
{
max = query.Last().StdError - query.Last().RSquared;
}
else
{
max = 10000000;
}
if ((rSquaredValue.StdError - rSquaredValue.RSquared < max || query.Count < comboSize) && rSquaredList.Contains(rSquaredValue) == false)
{
rSquaredList.Add(rSquaredValue);
valueClassList.Add(new ValueClass { ValueName = rSquaredValue.ValueName, ValueList = estimatedValuesList, Days = days });
}
}
catch (Exception ex)
{
ThrowExceptionInfo(ex);
}
return (rSquaredList, valueClassList);
}
There is clearly a significance to StdError - RSquared, so change RSquaredValues3 to expose that value (i.e. calculate it once, on construction, since the values do not change) rather than recalculating it in multiple places during the processing loop.
The value in this new property is the way that the list is being sorted. Rather than sorting the list over and over again, consider keeping the items in the list in that order in the first place. You can do this by ensuring that each time an item gets added, it is inserted in the right place in the list. This is called an insertion sort. (I have assumed that SortedList<TKey,TValue> is inappropriate due to duplicate 'key's.)
Similar improvements can be made to avoid the need for DistinctBy(i => i.ValueName). If you are only interested in distinct value names, then consider avoiding inserting the item if it is not providing an improvement.
Your List needs to grow during your processing - under the hood, the list doubles every time it grows, so the number of growths is O(log(n)). You can specify a suggested capacity in construction. If you specify the expected size large enough at the start, then the list will not need to do this during your processing.
The await of the ToListAsync is not adding any advantage to this code, as far as I can see.
The check for rSquaredList.Contains(rSquaredValue) == false looks like a redundant check, since this is a reference comparison of a newly instantiated item which cannot have been inserted in the list. So you can remove it to make it run faster.
With all that use of Task and await, you are not actually gaining anything at the moment, since you have a single thread handling it and are waiting for execution sequentially, so it appears to all be overhead. I am not sure if you can parallelize this workload but the main loop from 2 to 200 seems like a prime candidate for a Parallel.For() loop instead. You should also look into using a System.Collections.Concurrent.ConcurrentBag() for your master list if you implement parallelism to avoid deadlock issues.
Given a Deedle Series with time as the row index, I need to find the time at which the signal first satisfies a condition (in this case, stays below 0.005 for 50ms).
Currently I take a 50ms moving window and create a series from the start time and maximum value of each window, then get the first one whose max is < 0.005. It works well enough but can be very inefficient.
// Assume a timestep of 1ms
int numSteps = 50;
// Create a series from the first index and max of each window
var windowMaxes = mySeries.WindowInto(
numSteps,
s => new KeyValuePair<double, double>(s.FirstKey(), s.Max()));
var zeroes = windowMaxes.Where(kvp => kvp.Value <= 0.005);
// Set to -1 if the condition was never satisfied
var timeOfZero = zeroes.KeyCount > 0 ? zeroes.FirstKey() : -1D;
The problem is that it searches the entire series (which can get very large) even if the first window meets the condition.
Is there a simply way to do this but stop when the first window is found, instead of searching the entire Series?
Well I couldn't find a Deedly one-liner or any handy LINQ commands to do it, so I wrote the following extension method:
public static K FirstWindowWhere<K, V>(
this Series<K, V> series,
Func<V, bool> condition,
int windowSize)
{
int consecutiveTrues = 0;
foreach (var datum in series.Observations)
{
if (condition(datum.Value))
{
consecutiveTrues++;
}
else
{
consecutiveTrues = 0;
}
if (consecutiveTrues == windowSize)
{
return datum.Key;
}
}
return default(K);
}
To call with my above condition:
double zeroTime = mySeries.FirstWindowWhere(d => d <= 0.005, numSteps);
I tried a few different methods including a nice elegant one that used Series.Between instead of Series.GetObservations but it was noticeably slower. So this will do unless someone has a simpler/better solution.
Say I have a sorted list of 1000 or so unique decimals, arranged by value.
List<decimal> decList
How can I get a random x number of decimals from a list of unique decimals that total up to y?
private List<decimal> getWinningValues(int xNumberToGet, decimal yTotalValue)
{
}
Is there any way to avoid a long processing time on this? My idea so far is to take xNumberToGet random numbers from the pool. Something like (cool way to get random selection from a list)
foreach (decimal d in decList.OrderBy(x => randomInstance.Next())Take(xNumberToGet))
{
}
Then I might check the total of those, and if total is less, i might shift the numbers up (to the next available number) slowly. If the total is more, I might shift the numbers down. I'm still now sure how to implement or if there is a better design readily available. Any help would be much appreciated.
Ok, start with a little extension I got from this answer,
public static IEnumerable<IEnumerable<T>> Combinations<T>(
this IEnumerable<T> source,
int k)
{
if (k == 0)
{
return new[] { Enumerable.Empty<T>() };
}
return source.SelectMany((e, i) =>
source.Skip(i + 1).Combinations(k - 1)
.Select(c => (new[] { e }).Concat(c)));
}
this gives you a pretty efficient method to yield all the combinations with k members, without repetition, from a given IEnumerable. You could make good use of this in your implementation.
Bear in mind, if the IEnumerable and k are sufficiently large this could take some time, i.e. much longer than you have. So, I've modified your function to take a CancellationToken.
private static IEnumerable<decimal> GetWinningValues(
IEnumerable<decimal> allValues,
int numberToGet,
decimal targetValue,
CancellationToken canceller)
{
IList<decimal> currentBest = null;
var currentBestGap = decimal.MaxValue;
var locker = new object();
allValues.Combinations(numberToGet)
.AsParallel()
.WithCancellation(canceller)
.TakeWhile(c => currentBestGap != decimal.Zero)
.ForAll(c =>
{
var gap = Math.Abs(c.Sum() - targetValue);
if (gap < currentBestGap)
{
lock (locker)
{
currentBestGap = gap;
currentBest = c.ToList();
}
}
}
return currentBest;
}
I've an idea that you could sort the initial list and quit iterating the combinations at a certain point, when the sum must exceed the target. After some consideration, its not trivial to identify that point and, the cost of checking may exceed the benefit. This benefit would have to be balanced agaist some function of the target value and mean of the set.
I still think further optimization is possible but I also think that this work has already been done and I'd just need to look it up in the right place.
There are k such subsets of decList (k might be 0).
Assuming that you want to select each one with uniform probability 1/k, I think you basically need to do the following:
iterate over all the matching subsets
select one
Step 1 is potentially a big task, you can look into the various ways of solving the "subset sum problem" for a fixed subset size, and adapt them to generate each solution in turn.
Step 2 can be done either by making a list of all the solutions and choosing one or (if that might take too much memory) by using the clever streaming random selection algorithm.
If your data is likely to have lots of such subsets, then generating them all might be incredibly slow. In that case you might try to identify groups of them at a time. You'd have to know the size of the group without visiting its members one by one, then you can choose which group to use weighted by its size, then you've reduced the problem to selecting one of that group at random.
If you don't need to select with uniform probability then the problem might become easier. At the best case, if you don't care about the distribution at all then you can return the first subset-sum solution you find -- whether you'd call that "at random" is another matter...
I have a list of perhaps 100,000 strings in memory in my application. I need to find the top 20 strings that contain a certain keyword (case insensitive). That's easy to do, I just run the following LINQ.
from s in stringList
where s.ToLower().Contains(searchWord.ToLower())
select s
However, I have a distinct feeling that I could do this much faster and I need to find the way to that, because I need to look up in this list multiple times per second.
Finding substrings (not complete matches) is surprisingly hard. There is nothing built-in to help you with this. I suggest you look into Suffix Trees data structures which can be used to find substrings efficiently.
You can pull searchWord.ToLower() out to a local variable to save tons of string operations, btw. You can also pre-calculate the lower-case version of stringList. If you can't precompute, at least use s.IndexOf(searchWord, StringComparison.InvariantCultureIgnoreCase) != -1. This saves on expensive ToLower calls.
You can also slap an .AsParallel on the query.
Another option, although it would require a fair amount of memory, would be to precompute something like a suffix array (a list of positions within the strings, sorted by the strings to which they point).
http://en.wikipedia.org/wiki/Suffix_array
This would be most feasible if the list of strings you're searching against is relatively static. The entire list of string indexes could be stored in a single array of tuples(indexOfString, positionInString), upon which you would perform a binary search, using String.Compare(keyword, 0, target, targetPos, keyword.Length).
So if you had 100,000 strings of average 20 length, you would need 100,000 * 20 * 2*sizeof(int) of memory for the structure. You could cut that in half by packing both indexOfString and positionInString into a single 32 bit int, for example with positionInString in the lowest 12 bits, and the indexOfString in the remaining upper bits. You'd just have to do a little bit fiddling to get the two values back out. It's important to note that the structure contains no strings or substrings itself. The strings you're searching against exist only once.
This would basically give you a complete index, and allow finding any substring very quickly (binary search over the index the suffix array represents), with a minimum of actual string comparisons.
If memory is dear, a simple optimization of the original brute force algorithm would be to precompute a dictionary of unique chars, and assign ordinal numbers to represent each. Then precompute a bit array for each string with the bits set for each unique char contained within the string. Since your strings are relatively short, there should be a fair amount of variability of the resuting BitArrays (it wouldn't work well if your strings were very long). You then simply compute the BitArray or your search keyword, and only search for the keyword in those strings where keywordBits & targetBits == keywordBits. If your strings are preconverted to lower case, and are just the English alphabet, the BitArray would likely fit within a single int. So this would require a minimum of additional memory, be simple to implement, and would allow you to quickly filter out strings within which you will definitely not find the keyword. This might be a useful optimization since string searches are fast, but you have so many of them to do using the brute force search.
EDIT For those interested, here is a basic implementation of the initial solution I proposed. I ran tests using 100,000 randomly generated strings of lengths described by the OP. Although it took around 30 seconds to construct and sort the index, once made, the speed of searching for keywords 3000 times was 49,805 milliseconds for brute force, and 18 milliseconds using the indexed search, so a couple thousand times faster. If you rarely build the list, then my simple, but relatively slow method of initially building the suffix array should be sufficient. There are smarter ways to build it that are faster, but would require more coding than my basic implementation below.
// little test console app
static void Main(string[] args) {
var list = new SearchStringList(true);
list.Add("Now is the time");
list.Add("for all good men");
list.Add("Time now for something");
list.Add("something completely different");
while (true) {
string keyword = Console.ReadLine();
if (keyword.Length == 0) break;
foreach (var pos in list.FindAll(keyword)) {
Console.WriteLine(pos.ToString() + " =>" + list[pos.ListIndex]);
}
}
}
~~~~~~~~~~~~~~~~~~
// file for the class that implements a simple suffix array
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Collections;
namespace ConsoleApplication1 {
public class SearchStringList {
private List<string> strings = new List<string>();
private List<StringPosition> positions = new List<StringPosition>();
private bool dirty = false;
private readonly bool ignoreCase = true;
public SearchStringList(bool ignoreCase) {
this.ignoreCase = ignoreCase;
}
public void Add(string s) {
if (s.Length > 255) throw new ArgumentOutOfRangeException("string too big.");
this.strings.Add(s);
this.dirty = true;
for (byte i = 0; i < s.Length; i++) this.positions.Add(new StringPosition(strings.Count-1, i));
}
public string this[int index] { get { return this.strings[index]; } }
public void EnsureSorted() {
if (dirty) {
this.positions.Sort(Compare);
this.dirty = false;
}
}
public IEnumerable<StringPosition> FindAll(string keyword) {
var idx = IndexOf(keyword);
while ((idx >= 0) && (idx < this.positions.Count)
&& (Compare(keyword, this.positions[idx]) == 0)) {
yield return this.positions[idx];
idx++;
}
}
private int IndexOf(string keyword) {
EnsureSorted();
// binary search
// When the keyword appears multiple times, this should
// point to the first match in positions. The following
// positions could be examined for additional matches
int minP = 0;
int maxP = this.positions.Count - 1;
while (maxP > minP) {
int midP = minP + ((maxP - minP) / 2);
if (Compare(keyword, this.positions[midP]) > 0) {
minP = midP + 1;
} else {
maxP = midP;
}
}
if ((maxP == minP) && (Compare(keyword, this.positions[minP]) == 0)) {
return minP;
} else {
return -1;
}
}
private int Compare(StringPosition pos1, StringPosition pos2) {
int len = Math.Max(this.strings[pos1.ListIndex].Length - pos1.StringIndex, this.strings[pos2.ListIndex].Length - pos2.StringIndex);
return String.Compare(strings[pos1.ListIndex], pos1.StringIndex, this.strings[pos2.ListIndex], pos2.StringIndex, len, ignoreCase);
}
private int Compare(string keyword, StringPosition pos2) {
return String.Compare(keyword, 0, this.strings[pos2.ListIndex], pos2.StringIndex, keyword.Length, this.ignoreCase);
}
// Packs index of string, and position within string into a single int. This is
// set up for strings no greater than 255 bytes. If longer strings are desired,
// the code for the constructor, and extracting ListIndex and StringIndex would
// need to be modified accordingly, taking bits from ListIndex and using them
// for StringIndex.
public struct StringPosition {
public static StringPosition NotFound = new StringPosition(-1, 0);
private readonly int position;
public StringPosition(int listIndex, byte stringIndex) {
this.position = (listIndex < 0) ? -1 : this.position = (listIndex << 8) | stringIndex;
}
public int ListIndex { get { return (this.position >= 0) ? (this.position >> 8) : -1; } }
public byte StringIndex { get { return (byte) (this.position & 0xFF); } }
public override string ToString() {
return ListIndex.ToString() + ":" + StringIndex;
}
}
}
}
There's one approach that would be a lot faster. But it would mean looking for exact word matches, rather than using the Contains functionality.
Basically, if you have the memory for it you could create a Dictionary of words which also reference some sort of ID (or IDs) for the strings in which the word is found.
So the Dictionary might be of type <string, List<int>>. The benefit here of course is that you're consolidating a lot of words into a smaller collection. And, the Dictionary is very fast with lookups since it's built on a hash table.
Now if this isn't what you're looking for you might search for in-memory full-text searching libraries. SQL Server supports full-text searching using indexing to speed up the process beyond traditional wildcard searches. But a pure in-memory solution would surely be faster. This still may not give you the exact functionality of a wildcard search, however.
In that case what you need is a reverse index.
If you are keen to pay much you can use database specific full text search index, and tuning the indexing to index on every subset of words.
Alternatively, you can use a very successful open source project that can achieve the same thing.
You need to pre-index the string using tokenizer, and build the reverse index file. We have similar use case in Java where we have to have a very fast autocomplete in a big set of data.
You can take a look at Lucene.NET which is a port of Apache Lucene (in Java).
If you are willing to ditch LINQ, you can use NHibernate Search. (wink).
Another option is to implement the pre-indexing in memory, with preprocessing and bypass of scanning unneeded, take a look at the Knuth-Morris-Pratt algorithm.
Let's assume we have a large list of points List<Point> pointList (already stored in memory) where each Point contains X, Y, and Z coordinate.
Now, I would like to select for example N% of points with biggest Z-values of all points stored in pointList. Right now I'm doing it like that:
N = 0.05; // selecting only 5% of points
double cutoffValue = pointList
.OrderBy(p=> p.Z) // First bottleneck - creates sorted copy of all data
.ElementAt((int) pointList.Count * (1 - N)).Z;
List<Point> selectedPoints = pointList.Where(p => p.Z >= cutoffValue).ToList();
But I have here two memory usage bottlenecks: first during OrderBy (more important) and second during selecting the points (this is less important, because we usually want to select only small amount of points).
Is there any way of replacing OrderBy (or maybe other way of finding this cutoff point) with something that uses less memory?
The problem is quite important, because LINQ copies the whole dataset and for big files I'm processing it sometimes hits few hundreds of MBs.
Write a method that iterates through the list once and maintains a set of the M largest elements. Each step will only require O(log M) work to maintain the set, and you can have O(M) memory and O(N log M) running time.
public static IEnumerable<TSource> TakeLargest<TSource, TKey>
(this IEnumerable<TSource> items, Func<TSource, TKey> selector, int count)
{
var set = new SortedDictionary<TKey, List<TSource>>();
var resultCount = 0;
var first = default(KeyValuePair<TKey, List<TSource>>);
foreach (var item in items)
{
// If the key is already smaller than the smallest
// item in the set, we can ignore this item
var key = selector(item);
if (first.Value == null ||
resultCount < count ||
Comparer<TKey>.Default.Compare(key, first.Key) >= 0)
{
// Add next item to set
if (!set.ContainsKey(key))
{
set[key] = new List<TSource>();
}
set[key].Add(item);
if (first.Value == null)
{
first = set.First();
}
// Remove smallest item from set
resultCount++;
if (resultCount - first.Value.Count >= count)
{
set.Remove(first.Key);
resultCount -= first.Value.Count;
first = set.First();
}
}
}
return set.Values.SelectMany(values => values);
}
That will include more than count elements if there are ties, as your implementation does now.
You could sort the list in place, using List<T>.Sort, which uses the Quicksort algorithm. But of course, your original list would be sorted, which is perhaps not what you want...
pointList.Sort((a, b) => b.Z.CompareTo(a.Z));
var selectedPoints = pointList.Take((int)(pointList.Count * N)).ToList();
If you don't mind the original list being sorted, this is probably the best balance between memory usage and speed
You can use Indexed LINQ to put index on the data which you are processing. This can result in noticeable improvements in some cases.
If you combine the two there is a chance a little less work will be done:
List<Point> selectedPoints = pointList
.OrderByDescending(p=> p.Z) // First bottleneck - creates sorted copy of all data
.Take((int) pointList.Count * N);
But basically this kind of ranking requires sorting, your biggest cost.
A few more ideas:
if you use a class Point (instead of a struct Point) there will be much less copying.
you could write a custom sort that only bothers to move the top 5% up. Something like (don't laugh) BubbleSort.
If your list is in memory already, I would sort it in place instead of making a copy - unless you need it un-sorted again, that is, in which case you'll have to weigh having two copies in memory vs loading it again from storage):
pointList.Sort((x,y) => y.Z.CompareTo(x.Z)); //this should sort it in desc. order
Also, not sure how much it will help, but it looks like you're going through your list twice - once to find the cutoff value, and once again to select them. I assume you're doing that because you want to let all ties through, even if it means selecting more than 5% of the points. However, since they're already sorted, you can use that to your advantage and stop when you're finished.
double cutoffValue = pointlist[(int) pointList.Length * (1 - N)].Z;
List<point> selectedPoints = pointlist.TakeWhile(p => p.Z >= cutoffValue)
.ToList();
Unless your list is extremely large, it's much more likely to me that cpu time is your performance bottleneck. Yes, your OrderBy() might use a lot of memory, but it's generally memory that for the most part is otherwise sitting idle. The cpu time really is the bigger concern.
To improve cpu time, the most obvious thing here is to not use a list. Use an IEnumerable instead. You do this by simply not calling .ToList() at the end of your where query. This will allow the framework to combine everything into one iteration of the list that runs only as needed. It will also improve your memory use because it avoids loading the entire query into memory at once, and instead defers it to only load one item at a time as needed. Also, use .Take() rather than .ElementAt(). It's a lot more efficient.
double N = 0.05; // selecting only 5% of points
int count = (1-N) * pointList.Count;
var selectedPoints = pointList.OrderBy(p=>p.Z).Take(count);
That out of the way, there are three cases where memory use might actually be a problem:
Your collection really is so large as to fill up memory. For a simple Point structure on a modern system we're talking millions of items. This is really unlikely. On the off chance you have a system this large, your solution is to use a relational database, which can keep this items on disk relatively efficiently.
You have a moderate size collection, but there are external performance constraints, such as needing to share system resources with many other processes as you might find in an asp.net web site. In this case, the answer is either to 1) again put the points in a relational database or 2) offload the work to the client machines.
Your collection is just large enough to end up on the Large Object Heap, and the HashSet used in the OrderBy() call is also placed on the LOH. Now what happens is that the garbage collector will not properly compact memory after your OrderBy() call, and over time you get a lot of memory that is not used but still reserved by your program. In this case, the solution is, unfortunately, to break your collection up into multiple groups that are each individually small enough not to trigger use of the LOH.
Update:
Reading through your question again, I see you're reading very large files. In that case, the best performance can be obtained by writing your own code to parse the files. If the count of items is stored near the top of the file you can do much better, or even if you can estimate the number of records based on the size of the file (guess a little high to be sure, and then truncate any extras after finishing), you can then build your final collection as your read. This will greatly improve cpu performance and memory use.
I'd do it by implementing "half" a quicksort.
Consider your original set of points, P, where you are looking for the "top" N items by Z coordinate.
Choose a pivot x in P.
Partition P into L = {y in P | y < x} and U = {y in P | x <= y}.
If N = |U| then you're done.
If N < |U| then recurse with P := U.
Otherwise you need to add some items to U: recurse with N := N - |U|, P := L to add the remaining items.
If you choose your pivot wisely (e.g., median of, say, five random samples) then this will run in O(n log n) time.
Hmmmm, thinking some more, you may be able to avoid creating new sets altogether, since essentially you're just looking for an O(n log n) way of finding the Nth greatest item from the original set. Yes, I think this would work, so here's suggestion number 2:
Make a traversal of P, finding the least and greatest items, A and Z, respectively.
Let M be the mean of A and Z (remember, we're only considering Z coordinates here).
Count how many items there are in the range [M, Z], call this Q.
If Q < N then the Nth greatest item in P is somewhere in [A, M). Try M := (A + M)/2.
If N < Q then the Nth greatest item in P is somewhere in [M, Z]. Try M := (M + Z)/2.
Repeat until we find an M such that Q = N.
Now traverse P, removing all items greater than or equal to M.
That's definitely O(n log n) and creates no extra data structures (except for the result).
Howzat?
You might use something like this:
pointList.Sort(); // Use you own compare here if needed
// Skip OrderBy because the list is sorted (and not copied)
double cutoffValue = pointList.ElementAt((int) pointList.Length * (1 - N)).Z;
// Skip ToList to avoid another copy of the list
IEnumerable<Point> selectedPoints = pointList.Where(p => p.Z >= cutoffValue);
If you want a small percentage of points ordered by some criterion, you'll be better served using a Priority queue data structure; create a size-limited queue(with the size set to however many elements you want), and then just scan through the list inserting every element. After the scan, you can pull out your results in sorted order.
This has the benefit of being O(n log p) instead of O(n log n) where p is the number of points you want, and the extra storage cost is also dependent on your output size instead of the whole list.
int resultSize = pointList.Count * (1-N);
FixedSizedPriorityQueue<Point> q =
new FixedSizedPriorityQueue<Point>(resultSize, p => p.Z);
q.AddEach(pointList);
List<Point> selectedPoints = q.ToList();
Now all you have to do is implement a FixedSizedPriorityQueue that adds elements one at a time and discards the largest element when it is full.
You wrote, you are working with a DataSet. If so, you can use DataView to sort your data once and use them for all future accessing the rows.
Just tried with 50,000 rows and 100 times accessing 30% of them. My performance results are:
Sort With Linq: 5.3 seconds
Use DataViews: 0.01 seconds
Give it a try.
[TestClass]
public class UnitTest1 {
class MyTable : TypedTableBase<MyRow> {
public MyTable() {
Columns.Add("Col1", typeof(int));
Columns.Add("Col2", typeof(int));
}
protected override DataRow NewRowFromBuilder(DataRowBuilder builder) {
return new MyRow(builder);
}
}
class MyRow : DataRow {
public MyRow(DataRowBuilder builder) : base(builder) {
}
public int Col1 { get { return (int)this["Col1"]; } }
public int Col2 { get { return (int)this["Col2"]; } }
}
DataView _viewCol1Asc;
DataView _viewCol2Desc;
MyTable _table;
int _countToTake;
[TestMethod]
public void MyTestMethod() {
_table = new MyTable();
int count = 50000;
for (int i = 0; i < count; i++) {
_table.Rows.Add(i, i);
}
_countToTake = _table.Rows.Count / 30;
Console.WriteLine("SortWithLinq");
RunTest(SortWithLinq);
Console.WriteLine("Use DataViews");
RunTest(UseSoredDataViews);
}
private void RunTest(Action method) {
int iterations = 100;
Stopwatch watch = Stopwatch.StartNew();
for (int i = 0; i < iterations; i++) {
method();
}
watch.Stop();
Console.WriteLine(" {0}", watch.Elapsed);
}
private void UseSoredDataViews() {
if (_viewCol1Asc == null) {
_viewCol1Asc = new DataView(_table, null, "Col1 ASC", DataViewRowState.Unchanged);
_viewCol2Desc = new DataView(_table, null, "Col2 DESC", DataViewRowState.Unchanged);
}
var rows = _viewCol1Asc.Cast<DataRowView>().Take(_countToTake).Select(vr => (MyRow)vr.Row);
IterateRows(rows);
rows = _viewCol2Desc.Cast<DataRowView>().Take(_countToTake).Select(vr => (MyRow)vr.Row);
IterateRows(rows);
}
private void SortWithLinq() {
var rows = _table.OrderBy(row => row.Col1).Take(_countToTake);
IterateRows(rows);
rows = _table.OrderByDescending(row => row.Col2).Take(_countToTake);
IterateRows(rows);
}
private void IterateRows(IEnumerable<MyRow> rows) {
foreach (var row in rows)
if (row == null)
throw new Exception("????");
}
}