go-qt

A Quadtree implemented in Go for the lecture Data Structures Data Management at the university of Fribourg, Switzerland.

Basic Usage

Before initializing the tree, one needs to decide a type for the item they want to store.

Say you want to only store vectors of dimension 3 with no associated values. Also, let the entries of the vectors be of type float32.

Then, you pass the type and a comparison function, which compares your item. Here, we're going to use the provided CompareOrdered() function, which can compare Integers and Floats and ~string. (See https://golang.org/x/exp/constraints for more information)

tree := NewQTree[[]float32](dim, CompareOrdered[float32])

To insert an item:

item := []float32{1.434, 21.222, 332.23432}
tree.NaiveInsert(item)

And search for an item:

found := tree.PointSearch([]float32{1.434, 21.222, 332.23432})
fmt.Println(found.item)

Please be aware that PointSearch() returns a *QNode[T] where T corresponds to []float32 in our case. The returned node has an property called .item to retrieve your stored item.

Range Search

const dim = 2
tree := NewQTree[[]int](dim, CompareOrdered[int])

//insert 5 items
var items [5][]int
items[0] = []int{-9, -9}
items[1] = []int{-9, -11}
items[2] = []int{-9, 2}
items[3] = []int{-10, -9}
items[4] = []int{12, -1}

for i := 0; i < 5; i++ {
	tree.NaiveInsert(items[i])
}

tl := []int{-10, 10}
tr := []int{10, 10}

bl := []int{-10, -10}
br := []int{10, -10}

bound := [][]int{tr, tl, bl, br}

for i, f := range tree.RangeSearch(bound) {
	fmt.Printf("[%d]: %v\n", i, f.item)
}

Custom Structs

One can also easily store any kind of struct. In this exmaple, we will show you how to use the tree as a KV Store.

First, let's define a simple Key-Value pair structure, where we will use a list of strings as keys and the corresponding value is a string, too.

type KVEntryString struct {
	key   *[]string
	value *string
}

Next, we need to specify a comparison function for our struct. On what properties do we want to compare it? Since strings are ordered, we can again rely on the provided CompareOrdered().

func compare_kv_str(a, b KVEntryString) (equal bool, quad int) {
	return CompareOrdered[string](*a.key, *b.key)
}

This is all we need. Now, we can insert elements as follows:

const dim = 3
tree := NewQTree[KVEntryString](dim, compareKvStr)

// First entry
keyFr := []string{"Switzerland", "Fribourg"} // key composite
valFr := "Hello Fribourg"
entryFr := KVEntryString{&keyFr, &valFr}
tree.NaiveInsert(entryFr)

// Second entry
keyBe := []string{"Switzerland", "Bern"} // key composite
valBe := "Hello Bern"
entryBe := KVEntryString{&keyBe, &valBe}
tree.NaiveInsert(entryBe)

If we want to fetch now the associated value, then we do the following:

//search for bern
emptyEntry := KVEntryString{&([]string{"Switzerland", "Bern"}), nil}
found := tree.PointSearch(emptyEntry)
if found != nil {
	AssertEqual(t, *found.item.value, valBe)
	t.Log(*found.item.value) // will print "Hello Bern"
} else {
	t.Errorf("Expected found = %T, Actual == %T", found, nil)
}

The comparison function

The comparison function is basically the heart of this data structure. We provide a CompareOrdered() function which compares Integers, Floats and ~string.

This is the built in comparison function. Your comparison function should behave, in regards to the return value, the same. This means, you should return a pair of (equal bool, quad int) where equal is true iff a and b are the same. It's good practice to return for quad a value like -1 $\notin [0,2^n] \subset \mathbb{N}$, in this case. However, if a and b are not the same, then equal should be false and your quad should be the integer from 0 to $2^n-1$ in which the item you're lookging for (b) lies in.

// CompareOrdered compares vectors with values that are part of the constraints.Ordered type, i.e. int, float, string.
func CompareOrdered[T constraints.Ordered](a, b []T) (equal bool, quad int) {
	if reflect.DeepEqual(a, b) {
		return true, -1
	}

	quad = 0
	for i := 0; i < len(a); i++ {
		if b[i] >= a[i] {
			quad += 0b1 << i
		}
	}

	return false, quad
}