NthItemUtils

A library for getting the nth smallest value, the nth largest value, etc. from a randomly accessible data structure like Span<T>,ReadOnlySpan<T>, IReadOnlyList<T>. Internally, it uses QuickSelect as well as C++ std::nth_element(), so the average performance is O(n).

The source code consists of only one file, so you can easily use it by copy and past.

source code

or nuget.

dotnet add package NthItemUtils

API

API is defined as an extension method of Span<T>, ReadOnlySpan<T>, and IReadOnlyList<T>. The range of n is between 0 and source.Length - 1. All return value types are struct ItemWithIndex<T>{ T Item; int index }.

NthSmallest<T>(this Span<T> source, int n)
NthSmallest<T>(this Span<T> source, int n, Comparer<T> comparer)

NthLargest<T>(this Span<T> source, int n)
NthLargest<T>(this Span<T> source, int n, Comparer<T> comparer)

MaxWithIndex<T>(this Span<T> source)
MaxWithIndex<T>(this Span<T> source, Comparer<T> comparer)

MinWithIndex<T>(this Span<T> source)
MinWithIndex<T>(this Span<T> source, Comparer<T> comparer)

Since QuickSelect is used internally, this is also published as an API.

public static class QuickSelect
{
    public static void Iota(Span<int> indices);
    
    public static void Execute<T>(ReadOnlySpan<T> source, Span<int> indices, int n);
    public static void Execute<T>(ReadOnlySpan<T> source, Span<int> indices, int n, Comparer<T> comparer);
    
    public static void Execute<T>(IReadOnlyList<T> source, Span<int> indices, int n);
    public static void Execute<T>(IReadOnlyList<T> source, Span<int> indices, int n, Comparer<T> comparer);
}

Example

Extension Method.

var random = new Random();
var randomSource = Enumerable.Range(0, 200).Select(_ => random.NextDouble() * 50).ToArray();

var order = randomSource.OrderBy(x => x).ToArray();

int n = random.Next(200);

Assert.IsTrue(order[n] == randomSource.AsSpan().NthSmallest(n).Item); // always true.

QuickSelect

ReadOnlySpan<int> source = new int[] { 4, 4, 8, 1, 2, 5, 4, 4, 4, 6, 7, 3 }.AsSpan();
var pool = ArrayPool<int>.Shared.Rent(source.Length);
var indices = pool.AsSpan(0, source.Length);

int n = 6;

QuickSelect.Iota(indices);
QuickSelect.Execute(source, indices, n);

var pivot = source[indices[n]];
for (int i = 0; i < n; i++)
{
    var result = Comparer<double>.Default.Compare(source[indices[i]], pivot);

    Assert.IsTrue(result <= 0); // always true.
}

for (int i = n + 1; i < source.Length; i++)
{
    var result = Comparer<double>.Default.Compare(source[indices[i]], pivot);

    Assert.IsTrue(0 <= result); // always true.
}

ArrayPool<int>.Shared.Return(pool);

Get items in some range

ReadOnlySpan<int> randomSource = Enumerable.Range(0, 100).Shuffle().ToArray().AsSpan();
var pool = ArrayPool<int>.Shared.Rent(randomSource.Length);
var indices = pool.AsSpan(0, randomSource.Length);

QuickSelect.Iota(indices);

//Get 50 <= item < 60
QuickSelect.Execute(randomSource, indices, 50);
QuickSelect.Execute(randomSource, indices[50..], 10);

for (int i = 0; i < 10; i++)
{
    Console.Write($"{randomSource[indices[50 + i]]}, ");
}
// output : 50, 56, 51, 57, 55, 54, 53, 52, 58, 59, 

ArrayPool<int>.Shared.Return(pool);