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A thread-safe, persistent Treap (tree + heap) for ordered key-value mapping and priority sorting.

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# Treap

Tread-safe, persistent treaps in pure Go.

![tests](https://github.com/lthibault/treap/workflows/tests/badge.svg?branch=master)
[![Godoc Reference](https://img.shields.io/badge/godoc-reference-blue.svg?style=flat-square)](https://godoc.org/github.com/lthibault/treap)
[![Go Report Card](https://goreportcard.com/badge/github.com/SentimensRG/ctx?style=flat-square)](https://goreportcard.com/report/github.com/lthibault/treap)

## Installation

```bash
go get github.com/lthibault/treap
```

Treap is tested using go 1.14 and later, but is likely to work with earlier versions.

## Why Treaps?

Most developers are familiar with maps and heaps.

- Maps provide keyed lookups.  Some even sort entries by key.
- Heaps provide priority-ordering, with fast inserts and pops.

But what if you need **both?**  And what if it needs to be both **thread-safe**, _and_
non-blocking?

Enter the _Immutable Treap_.

Immutable treaps are persistent datastructures that provide:

- Keyed lookups (like maps)
- Priority ordering, pops and weighted inserts (like heaps)
- Wait-free concurrency through immutability
- Memory-efficiency through structural sharing
- O(log n) time complexity for all operations

When used in conjunction with `atomic.CompareAndSwapPointer`, it is possible to read
from a treap without ever blocking -- even in the presence of concurrent writers!  Your
typical CAS-loop will look like this:

```go
type Foo struct {
    ptr unsafe.Pointer  // a *treap.Node
}

func (f *Foo) AddItem(key string, value, weight int) {
    for {
        old := (*treap.Node)(atomic.LoadPointer(&f.ptr))
        new, _ := handle.Upsert(old, key, value, weight)

// attempt CAS
        if atomic.CompareAndSwapPointer(&f.ptr,
            unsafe.Pointer(old),
            unsafe.Pointer(new),
        ) {
            break  // value successfully set; we're done
        }
    }
}
```

In addition, this package features zero external dependencies and extensive test
coverage.

## Usage

The treap data-structure is purely functional and immutable.  Methods like `Insert` and
`Delete` return a **new** treap containing the desired modifications.

A fully-runnable version of the following example can be found in `example_test.go`.

```go
package main

import (
    "fmt"

"github.com/lthibault/treap"
)

// Treap operations are performed by a lightweight handle.  Usually, you'll create a
// single global handle and share it between goroutines.  Handle's methods are thread-
// safe.
//
// A handle is defined by it's comparison functions (type `treap.Comparator`).
var handle = treap.Handle{
    // CompareKeys is used to store and receive mapped entries.  The comparator must be
    // compatible with the Go type used for keys.  In this example, we'll use strings as
    // keys.
    CompareKeys: treap.StringComparator,

// CompareWeights is used to maintain priority-ordering of mapped entries, providing
    // us with fast `Pop`, `Insert` and `SetWeight` operations.  You'll usually want
    // to use a `treap.IntComparator` for weights, but you can use any comparison
    // function you require.  Try it with `treap.TimeComparator`!
    //
    // Note that treaps are min-heaps by default, so `Pop` will always return the item
    // with the _smallest_ weight.  You can easily switch to a max-heap by using
    // `treap.MaxTreap`, if required.
    CompareWeights: treap.IntComparator,
}

func main() {
    // We define an empty root node.  Don't worry -- there's no initialization required!
    var root *treap.Node

// We're going to insert each of these boxers into the treap, and observe how the
    // treap treap provides us with a combination of map and heap semantics.
    for _, boxer := range []struct{
        FirstName, LastName string
        Weight int
    }{{
        FirstName: "Cassius",
        LastName: "Clay",
        Weight: 210,
    }, {
        FirstName: "Joe",
        LastName: "Frazier",
        Weight: 215,
    }, {
        FirstName: "Marcel",
        LastName: "Cerdan",
        Weight: 154,
    }, {
        FirstName: "Jake",
        LastName: "LaMotta",
        Weight: 160,
    }}{
        // Again, the treap is a purely-functional, persistent data structure.  `Insert`
        // returns a _new_ heap, which replaces `root` on each iteration.
        //
        // When used in conjunction with `atomic.CompareAndSwapPointer`, it is possible
        // to read from a treap without ever blocking -- even in the presence of
        // concurrent writers!
        root, _ = handle.Insert(root, boxer.FirstName, boxer.LastName, boxer.Weight)
    }

// Now that we've populated the treap, we can query it like an ordinary map.
    lastn, _ := handle.Get(root, "Cassius")
    fmt.Printf("Cassius %s\n", lastn)  // prints:  "Cassius Clay"

// Treaps also behave like binary heaps.  Let's start by peeking at the first value
    // in the resulting priority queue.  Remember:  this is a min-heap by default.
    fmt.Printf("%s %s, %d lbs\n", root.Key, root.Value, root.Weight)

// Woah, that was easy!  Now let's Pop that first value off of the heap.
    // Remember:  this is an immutable data-structure, so `Pop` doesn't actually mutate
    // any state!
    lastn, _ = handle.Pop(root)
    fmt.Printf("Marcel %s\n", lastn)  // prints:  "Marcel Cerdan"

// Jake LaMotta moved up to the heavyweight class late in his career.  Let's made an
    // adjustment to his weight.
    root, _ = handle.SetWeight(root, "Jake", 205)

// Let's list our boxers in ascending order of weight.  You may have noticed
    // there's no `PopNode` method on `treap.Handler`.  This is not a mistake!  A `Pop`
    // is just a merge on the root node's subtrees.  Check it out:
    for n := root; n != nil; {
        fmt.Printf("%s %s: %d\n", n.Key, n.Value, n.Weight)
        n = handle.Merge(n.Left, n.Right)
    }

// Lastly, we can iterate through the treap in key-order (smallest to largest).
    // To do this, we use an iterator.  Contrary to treaps, iterators are stateful and
    // mutable!  As such, they are NOT thread-safe.  However, multiple concurrent
    // iterators can traverse the same treap safely.
    for iterator := handle.Iter(root); iterator.Node != nil; iterator.Next(); {
        fmt.Printf("%s %s: %d\n", iterator.Key, iterator.Value, iterator.Weight)
    }
}
```

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