Is the sorting algorithm used by .NET's `Array.Sort()` method a stable algorithm?

Adding to Rasmus Faber's answer…

Sorting in LINQ, via Enumerable.OrderBy and Enumerable.ThenBy, is a stable sort implementation, which can be used as an alternative to Array.Sort. From Enumerable.OrderBy documentation over at MSDN:

This method performs a stable sort; that is, if the keys of two elements are equal, the order of the elements is preserved. In contrast, an unstable sort does not preserve the order of elements that have the same key.

Also, any unstable sort implementation, like that of Array.Sort, can be stabilized by using the position of the elements in the source sequence or array as an additional key to serve as a tie-breaker. Below is one such implementation, as a generic extension method on any single-dimensional array and which turns Array.Sort into a stable sort:

using System;
using System.Collections.Generic;

public static class ArrayExtensions {

    public static void StableSort<T>(this T[] values, Comparison<T> comparison) {
        var keys = new KeyValuePair<int, T>[values.Length];
        for (var i = 0; i < values.Length; i++)
            keys[i] = new KeyValuePair<int, T>(i, values[i]);
        Array.Sort(keys, values, new StabilizingComparer<T>(comparison));
    }

    private sealed class StabilizingComparer<T> : IComparer<KeyValuePair<int, T>> 
    {
        private readonly Comparison<T> _comparison;

        public StabilizingComparer(Comparison<T> comparison) {
            _comparison = comparison;
        }

        public int Compare(KeyValuePair<int, T> x, 
                           KeyValuePair<int, T> y) {
            var result = _comparison(x.Value, y.Value);
            return result != 0 ? result : x.Key.CompareTo(y.Key);
        }
    }
}

Below is a sample program using StableSort from above:

static class Program 
{
    static void Main() 
    {
        var unsorted = new[] {
            new Person { BirthYear = 1948, Name = "Cat Stevens" },
            new Person { BirthYear = 1955, Name = "Kevin Costner" },
            new Person { BirthYear = 1952, Name = "Vladimir Putin" },
            new Person { BirthYear = 1955, Name = "Bill Gates" },
            new Person { BirthYear = 1948, Name = "Kathy Bates" },
            new Person { BirthYear = 1956, Name = "David Copperfield" },
            new Person { BirthYear = 1948, Name = "Jean Reno" },
        };

        Array.ForEach(unsorted, Console.WriteLine);

        Console.WriteLine();
        var unstable = (Person[]) unsorted.Clone();
        Array.Sort(unstable, (x, y) => x.BirthYear.CompareTo(y.BirthYear));
        Array.ForEach(unstable, Console.WriteLine);

        Console.WriteLine();
        var stable = (Person[]) unsorted.Clone();
        stable.StableSort((x, y) => x.BirthYear.CompareTo(y.BirthYear));
        Array.ForEach(stable, Console.WriteLine);
    }
}

sealed class Person 
{
    public int BirthYear { get; set; }
    public string Name { get; set; }

    public override string ToString() {
        return string.Format(
            "{{ BirthYear = {0}, Name = {1} }}", 
            BirthYear, Name);
    }
}

Below is the output from the sample program above (running on a machine with Windows Vista SP1 and .NET Framework 3.5 SP1 installed):

{ BirthYear = 1948, Name = Cat Stevens }
{ BirthYear = 1955, Name = Kevin Costner }
{ BirthYear = 1952, Name = Vladimir Putin }
{ BirthYear = 1955, Name = Bill Gates }
{ BirthYear = 1948, Name = Kathy Bates }
{ BirthYear = 1956, Name = David Copperfield }
{ BirthYear = 1948, Name = Jean Reno }

{ BirthYear = 1948, Name = Jean Reno }
{ BirthYear = 1948, Name = Kathy Bates }
{ BirthYear = 1948, Name = Cat Stevens }
{ BirthYear = 1952, Name = Vladimir Putin }
{ BirthYear = 1955, Name = Bill Gates }
{ BirthYear = 1955, Name = Kevin Costner }
{ BirthYear = 1956, Name = David Copperfield }

{ BirthYear = 1948, Name = Cat Stevens }
{ BirthYear = 1948, Name = Kathy Bates }
{ BirthYear = 1948, Name = Jean Reno }
{ BirthYear = 1952, Name = Vladimir Putin }
{ BirthYear = 1955, Name = Kevin Costner }
{ BirthYear = 1955, Name = Bill Gates }
{ BirthYear = 1956, Name = David Copperfield }

As other answers have stated, Array.Sort isn't stable. However, the LINQ OrderBy methods (and OrderByDescending etc) are stable, which can be very useful.

No, it isn't:

This method uses the QuickSort algorithm. This implementation performs an unstable sort