treap

Overview ¶

Package treap implements a persistent treap (tree/heap combination).

https://en.wikipedia.org/wiki/Treap

A treap is a binary search tree for storing ordered distinct values (duplicates not allowed). In addition, each node actually a random priority field which is stored in heap order (i.e. all children have lower priority than the parent)

This provides the basis for efficient immutable ordered Set operations. See the ordered map example for how this can be used as an ordered map

Much of this is based on "Fast Set Operations Using Treaps" by Guy E Blelloch and Margaret Reid-Miller: https://www.cs.cmu.edu/~scandal/papers/treaps-spaa98.pdf

Benchmark ¶

The most interesting benchmark is the performance of insert where a single random key is inserted into a 5k sized map. As the example shows, the treap structure does well here as opposed to a regular persistent map (which involves full copying). This benchmark does not take into account the fact that the regular maps are not sorted unlike treaps.

The intersection benchmark compares the case where two 10k sets with 5k in common being interesected. The regular persistent array is about 30% faster but this is still respectable showing for treaps.

$ go test --bench=. -benchmem
goos: darwin
goarch: amd64
pkg: github.com/perdata/treap
BenchmarkInsert-4                   	 1000000	      2347 ns/op	    1719 B/op	      36 allocs/op
BenchmarkInsertRegularMap-4         	    2000	    890745 ns/op	  336311 B/op	       8 allocs/op
BenchmarkIntersection-4             	     500	   3125772 ns/op	 1719838 B/op	   35836 allocs/op
BenchmarkIntersectionRegularMap-4   	     500	   2436519 ns/op	  718142 B/op	     123 allocs/op
BenchmarkUnion-4                    	    1000	   1451047 ns/op	  939846 B/op	   19580 allocs/op
BenchmarkDiff-4                     	     500	   3280823 ns/op	 1742080 B/op	   36298 allocs/op
PASS

package main

import (
	"fmt"
	"github.com/perdata/treap"
	"math/rand"
)

type pair struct {
	key, value interface{}
}

type comparer func(kv1, kv2 pair) int

func (c comparer) Compare(v1, v2 interface{}) int {
	return c(v1.(pair), v2.(pair))
}

type Map struct {
	*treap.Node
	treap.Comparer
}

func NewMap(keyCompare treap.Comparer) Map {
	c := comparer(func(v1, v2 pair) int {
		return keyCompare.Compare(v1.key, v2.key)
	})
	return Map{nil, c}
}

func (m Map) Get(key interface{}) (interface{}, bool) {
	n := m.Find(pair{key, nil}, m.Comparer)
	if n == nil {
		return nil, false
	}
	return n.Value.(pair).value, true
}

func (m Map) Set(key, value interface{}) Map {
	node := &treap.Node{pair{key, value}, rand.Intn(1000000), nil, nil}
	n := m.Node.Union(node, m.Comparer, true)
	return Map{n, m.Comparer}
}

func (m Map) Delete(key interface{}) Map {
	n := m.Node.Delete(pair{key, nil}, m.Comparer)
	return Map{n, m.Comparer}
}

func (m Map) ForEach(fn func(key, value interface{})) {
	m.Node.ForEach(func(v interface{}) {
		p := v.(pair)
		fn(p.key, p.value)
	})
}

func (m Map) Count() int {
	result := 0
	m.Node.ForEach(func(_ interface{}) {
		result++
	})
	return result
}

func main() {
	rand.Seed(42)

	m := NewMap(IntComparer{})
	fmt.Println("Count:", m.Count())

	m = m.Set(52, "hello")
	m = m.Set(53, "world")
	m = m.Set(52, "Hello")

	m.ForEach(func(k, v interface{}) {
		fmt.Println("[", k, "] =", v)
	})
	fmt.Println("Count:", m.Count())

	old := m.Set(500, 500)
	m = m.Delete(53)

	fmt.Println(m.Get(53))
	fmt.Println(old.Get(53))
	fmt.Println(old.Get(52))
	fmt.Println(old.Get(500))

}

Output:

Count: 0
[ 52 ] = Hello
[ 53 ] = world
Count: 2
<nil> false
world true
Hello true
500 true