Now I've always heard binary search trees are faster to build from randomly selected data than ordered data, simply because ordered data requires explicit rebalancing to keep the tree height at a minimum.
Recently I implemented an immutable treap, a special kind of binary search tree which uses randomization to keep itself relatively balanced. In contrast to what I expected, I found I can consistently build a treap about 2x faster and generally better balanced from ordered data than unordered data -- and I have no idea why.
Here's my treap implementation:
http://pastebin.com/VAfSJRwZ
And here's a test program:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
namespace ConsoleApplication1
{
class Program
{
static Random rnd = new Random();
const int ITERATION_COUNT = 20;
static void Main(string[] args)
{
List<double> rndTimes = new List<double>();
List<double> orderedTimes = new List<double>();
rndTimes.Add(TimeIt(50, RandomInsert));
rndTimes.Add(TimeIt(100, RandomInsert));
rndTimes.Add(TimeIt(200, RandomInsert));
rndTimes.Add(TimeIt(400, RandomInsert));
rndTimes.Add(TimeIt(800, RandomInsert));
rndTimes.Add(TimeIt(1000, RandomInsert));
rndTimes.Add(TimeIt(2000, RandomInsert));
rndTimes.Add(TimeIt(4000, RandomInsert));
rndTimes.Add(TimeIt(8000, RandomInsert));
rndTimes.Add(TimeIt(16000, RandomInsert));
rndTimes.Add(TimeIt(32000, RandomInsert));
rndTimes.Add(TimeIt(64000, RandomInsert));
rndTimes.Add(TimeIt(128000, RandomInsert));
string rndTimesAsString = string.Join("\n", rndTimes.Select(x => x.ToString()).ToArray());
orderedTimes.Add(TimeIt(50, OrderedInsert));
orderedTimes.Add(TimeIt(100, OrderedInsert));
orderedTimes.Add(TimeIt(200, OrderedInsert));
orderedTimes.Add(TimeIt(400, OrderedInsert));
orderedTimes.Add(TimeIt(800, OrderedInsert));
orderedTimes.Add(TimeIt(1000, OrderedInsert));
orderedTimes.Add(TimeIt(2000, OrderedInsert));
orderedTimes.Add(TimeIt(4000, OrderedInsert));
orderedTimes.Add(TimeIt(8000, OrderedInsert));
orderedTimes.Add(TimeIt(16000, OrderedInsert));
orderedTimes.Add(TimeIt(32000, OrderedInsert));
orderedTimes.Add(TimeIt(64000, OrderedInsert));
orderedTimes.Add(TimeIt(128000, OrderedInsert));
string orderedTimesAsString = string.Join("\n", orderedTimes.Select(x => x.ToString()).ToArray());
Console.WriteLine("Done");
}
static double TimeIt(int insertCount, Action<int> f)
{
Console.WriteLine("TimeIt({0}, {1})", insertCount, f.Method.Name);
List<double> times = new List<double>();
for (int i = 0; i < ITERATION_COUNT; i++)
{
Stopwatch sw = Stopwatch.StartNew();
f(insertCount);
sw.Stop();
times.Add(sw.Elapsed.TotalMilliseconds);
}
return times.Average();
}
static void RandomInsert(int insertCount)
{
Treap<double> tree = new Treap<double>((x, y) => x.CompareTo(y));
for (int i = 0; i < insertCount; i++)
{
tree = tree.Insert(rnd.NextDouble());
}
}
static void OrderedInsert(int insertCount)
{
Treap<double> tree = new Treap<double>((x, y) => x.CompareTo(y));
for(int i = 0; i < insertCount; i++)
{
tree = tree.Insert(i + rnd.NextDouble());
}
}
}
}
And here's a chart comparing random and ordered insertion times in milliseconds:
Insertions Random Ordered RandomTime / OrderedTime
50 1.031665 0.261585 3.94
100 0.544345 1.377155 0.4
200 1.268320 0.734570 1.73
400 2.765555 1.639150 1.69
800 6.089700 3.558350 1.71
1000 7.855150 4.704190 1.67
2000 17.852000 12.554065 1.42
4000 40.157340 22.474445 1.79
8000 88.375430 48.364265 1.83
16000 197.524000 109.082200 1.81
32000 459.277050 238.154405 1.93
64000 1055.508875 512.020310 2.06
128000 2481.694230 1107.980425 2.24
I don't see anything in the code which makes ordered input asymptotically faster than unordered input, so I'm at a loss to explain the difference.
Why is it so much faster to build a treap from ordered input than random input?
