JSPM

B+ tree

B+ trees are ordered collections of key-value pairs, sorted by key.

This is a fast B+ tree implementation, largely compatible with the standard Map, but with a much more diverse and powerful API. To use it, import BTree<K,V> from 'sorted-btree'.

Features

• Requires ES5 only (Symbol.iterator is not required but is used if defined.)
• Supports a custom comparator, which must be passed to the constructor.
• Supports O(1) fast cloning with subtree sharing. This works by marking the root node as "shared between instances". This makes the tree read-only with copy-on-edit behavior; both copies of the tree remain mutable.
• API similar to Map<K,V> with methods such as size(), clear(), foreach((k,v,tree)=>void), get(K), set(K,V), has(K), delete(K), plus iterator functions keys(), values() and entries().
• For efficiency, when a node fills up, items are shifted to siblings when possible to encourage nodes to stay near their capacity.
• Efficiently supports sets (keys without values). The collection does not allocate memory for values if the value undefined is associated with all keys in a given node.
• Includes neat stuff such as Range methods for batch operations
• Duplicate keys are not allowed (supporting duplicates properly is complex).
• Throws an exception if you try to use NaN as a key, but infinity is allowed.

Additional operations supported on this B+ tree:

• Set a value only if the key does not already exist: t.setIfNotPresent(k,v)
• Set a value only if the key already exists: t.changeIfPresent(k,v)
• Iterate in backward order: for (pair of t.entriesReversed()) {}
• Iterate from a particular first element: for (let p of t.entries(first)) {}
• Convert to an array: t.toArray(), t.keysArray(), t.valuesArray()
• Get pairs for a range of keys ([K,V][]): t.getRange(loK, hiK, includeHi)
• Delete a range of keys and their values: t.deleteRange(loK, hiK, includeHi)
• Scan all items: t.forEachPair((key, value, index) => {...})
• Scan a range of items: t.forRange(lowKey, highKey, includeHighFlag, (k,v) => {...})
• Count the number of keys in a range: c = t.forRange(loK, hiK, includeHi, undefined)
• Get smallest or largest key: t.minKey(), t.maxKey()
• Freeze to prevent modifications: t.freeze() (you can also t.unfreeze())
• Fast clone: t.clone()
• For more information, see full documentation in the source code.

Note: Confusingly, the ES6 Map.forEach(c) method calls c(value,key) instead of c(key,value), in contrast to other methods such as set() and entries() which put the key first. I can only assume that they reversed the order on the theory that users would usually want to examine values and ignore keys. BTree's forEach() therefore works the same way, but a second method .forEachPair((key,value)=>{...}) is provided which sends you the key first and the value second; this method is slightly faster because it is the "native" for-each method for this class.

The "scanning" methods (forEach, forRange, editRange, deleteRange) will normally return the number of elements that were scanned. However, the callback can return {break:R} to stop iterating early and return a value R from the scanning method.

B+ trees normally use memory more efficiently than hashtables (such as the standard Map), although in JavaScript this is not guaranteed because the B+ tree's memory efficiency depends on avoiding wasted space in the arrays for each node, and JavaScript provides no way to detect or control the capacity of an array's underlying memory area.

Custom comparator example

Given a set of {name: string, age: number} objects, you can create a tree sorted by name and then by age like this:

  // First constructor argument is an optional list of pairs ([K,V][])
  var tree = new BTree(undefined, (a, b) => {
    if (a.name > b.name)
      return 1; // Return a number >0 when a > b
    else if (a.name < b.name)
      return -1; // Return a number <0 when a < b
    else // names are equal (or incomparable)
      return a.age - b.age; // Return >0 when a.age > b.age
  });

  tree.set({name:"Bill", age:17}, "happy");
  tree.set({name:"Fran", age:40}, "busy & stressed");
  tree.set({name:"Bill", age:55}, "recently laid off");
  tree.forEachPair((k, v) => {
    console.log(`Name: ${k.name} Age: ${k.age} Status: ${v}`);
  });

editRange

You can scan a range of items and selectively delete or change some of them using t.editRange. For example, the following code adds an exclamation mark to each non-boring value and deletes key number 4:

var t = new BTree().setRange([[1,"fun"],[2,"yay"],[4,"whee"],[8,"zany"],[10,"boring"]);
t.editRange(t.minKey(), t.maxKey(), true, (k, v) => {
  if (k === 4) 
    return {delete: true};
  if (v !== "boring")
    return {value: v + '!'};
})

Endnote

♥ This package was made to help people learn TypeScript & React.

Are you a C# developer? You might like the similar data structures I made for C#: BDictionary, BList, etc. See http://core.loyc.net/collections/