Last active
March 7, 2023 15:48
-
-
Save Sam-Belliveau/834ab56b1a5f6f3a0f09d07672bf6817 to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
/** | |
* Copyright 2023 Sam Belliveau | |
* | |
* Permission is hereby granted, free of charge, to any person obtaining a copy | |
* of this software and associated documentation files (the “Software”), to deal | |
* in the Software without restriction, including without limitation the rights | |
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | |
* copies of the Software, and to permit persons to whom the Software is | |
* furnished to do so, subject to the following conditions: | |
* | |
* The above copyright notice and this permission notice shall be included in | |
* all copies or substantial portions of the Software. | |
* | |
* THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | |
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | |
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | |
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | |
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | |
* SOFTWARE. | |
*/ | |
import java.util.Iterator; | |
import java.util.Optional; | |
/** | |
* A simple Radix Tree implemented in java that effectively acts as a map with a | |
* Long key. | |
* | |
* All functions are implemented using Optional to guarantee memory safety, an | |
* exception will never be thrown. | |
* | |
* For time complexities, n is the number of bits in the key, limited to 64. | |
* | |
* get(), set(), and remove() are all log(n). | |
* | |
* min(), next(), max(), and prev() are also all log(n) as empty trees are | |
* purged immediately when made empty, this allows us to efficiently scan | |
* through the tree for the next valid node in log(n) time. | |
* | |
* This means that iterating over the entire sorted tree is an k * log(n) | |
* where k is the number of elements in the array. | |
* | |
* Iterators may not function if removing elements that have not been iterated | |
* over yet. | |
* | |
* @author Sam B. (sam.belliveau@gmail.com) | |
*/ | |
public class RadixTree<T> implements Iterable<RadixTree.Pair<T>> { | |
/*** PAIR ***/ | |
public final static class Pair<V> { | |
private static <T> Optional<Pair<T>> of(final long key, | |
final Optional<T> value) { | |
return value.map(v -> new Pair<>(key, v)); | |
} | |
public final long key; | |
public final V value; | |
private Pair(final long key, final V value) { | |
this.key = key; | |
this.value = value; | |
} | |
} | |
/*** CONFIGURATION CONSTANTS ***/ | |
public static final int kBits = Long.BYTES * 8; | |
public static final long kMask = (-1L) ^ ((-1L) >>> 1); | |
/*** MEMBER VARIABLES ***/ | |
private Optional<T> mVal; | |
private Optional<RadixTree<T>> mL; | |
private Optional<RadixTree<T>> mH; | |
private int mSize; | |
/*** CONSTRUCTORS ***/ | |
private RadixTree() { | |
mVal = Optional.empty(); | |
mL = Optional.empty(); | |
mH = Optional.empty(); | |
mSize = 0; | |
} | |
/*** SIZE ***/ | |
// O(1) | |
public int size() { return mSize; } | |
// O(1) | |
public boolean isEmpty() { return size() == 0; } | |
/*** GETTERS / SETTERS ***/ | |
// O(1) | |
private Optional<RadixTree<T>> getChild(final long index) { | |
return ((index & kMask) == 0) ? mL : mH; | |
} | |
// O(1) | |
private Optional<RadixTree<T>> initChild(final long index) { | |
return ((index & kMask) == 0) | |
? (mL = mL.or(() -> Optional.of(new RadixTree<>()))) | |
: (mH = mH.or(() -> Optional.of(new RadixTree<>()))); | |
} | |
// O(log(n)) | |
public Optional<T> get(final long index) { | |
return mVal.filter(p -> index == 0) | |
.or(() -> getChild(index).flatMap(c -> c.get(index << 1))); | |
} | |
// O(log(n)) | |
public Optional<T> set(final long index, final T x) { | |
if (index == 0) { | |
final Optional<T> previous = mVal; | |
mVal = Optional.of(x); | |
return previous; | |
} | |
final var result = initChild(index).flatMap(c -> c.set(index << 1, x)); | |
if (result.isEmpty()) | |
++mSize; | |
return result; | |
} | |
// O(log(n)) | |
public Optional<T> remove(final long index) { | |
if (index == 0) { | |
final Optional<T> previous = mVal; | |
mVal = Optional.empty(); | |
return previous; | |
} | |
final var result = getChild(index).flatMap(c -> c.remove(index << 1)); | |
if (result.isPresent()) { | |
--mSize; | |
mL = mL.filter(t -> !t.isEmpty()); | |
mH = mH.filter(t -> !t.isEmpty()); | |
} | |
return result; | |
} | |
/*** SEARCH FORWARDS ***/ | |
// O(1) | |
private static <U> Pair<U> isL(final Pair<U> p) { | |
return new Pair<>(p.key >>> 1, p.value); | |
} | |
// O(1) | |
private static <U> Pair<U> isH(final Pair<U> p) { | |
return new Pair<>(p.key >>> 1 | kMask, p.value); | |
} | |
// O(log(n)) | |
public Optional<Pair<T>> min() { | |
return (Pair.of(0, mVal) | |
.or(() -> mL.flatMap(t -> t.min().map(p -> isL(p)))) | |
.or(() -> mH.flatMap(t -> t.min().map(p -> isH(p))))); | |
} | |
// O(log(n)) | |
public Optional<Pair<T>> next(final long index) { | |
return Pair.of(index, mVal).filter(p -> p.key == 0).or(() -> { | |
return ((index & kMask) != 0) | |
? mH.flatMap(t -> t.next(index << 1).map(p -> isH(p))) | |
: mL.flatMap(t -> t.next(index << 1).map(p -> isL(p))) | |
.or(() -> mH.flatMap(t -> t.min().map(p -> isH(p)))); | |
}); | |
} | |
/*** SEARCH BACKWARDS ***/ | |
// O(log(n)) | |
public Optional<Pair<T>> max() { | |
return (mH.flatMap(t -> t.min().map(p -> isH(p))) | |
.or(() -> mL.flatMap(t -> t.min()).map(p -> isL(p))) | |
.or(() -> Pair.of(0, mVal))); | |
} | |
// O(log(n)) | |
public Optional<Pair<T>> prev(final long index) { | |
return Pair.of(index, mVal).filter(p -> p.key != 0).or(() -> { | |
return ((index & kMask) == 0) | |
? mL.flatMap(t -> t.prev(index << 1).map(p -> isL(p))) | |
: mH.flatMap(t -> t.prev(index << 1).map(p -> isH(p))) | |
.or(() -> mL.flatMap(t -> t.max()).map(p -> isL(p))); | |
}); | |
} | |
/*** ITERATORS ***/ | |
public Iterator<Pair<T>> iterator() { | |
final var parent = this; | |
return new Iterator<Pair<T>>() { | |
Optional<Pair<T>> next = min(); | |
public void remove() { next.ifPresent(p -> parent.remove(p.key)); } | |
public boolean hasNext() { return next.isPresent(); } | |
public Pair<T> next() { | |
final Pair<T> r = next.get(); | |
next = parent.next(r.key + 1).filter(p -> r.key != -1); | |
return r; | |
} | |
}; | |
} | |
public Iterator<Pair<T>> reverseIterator() { | |
final var parent = this; | |
return new Iterator<Pair<T>>() { | |
Optional<Pair<T>> next = max(); | |
public void remove() { next.ifPresent(p -> parent.remove(p.key)); } | |
public boolean hasNext() { return next.isPresent(); } | |
public Pair<T> next() { | |
final Pair<T> r = next.get(); | |
next = parent.prev(r.key - 1).filter(p -> r.key != 0); | |
return r; | |
} | |
}; | |
} | |
/*** TESTS ***/ | |
public static void main(String... args) { | |
RadixTree<Integer> table = new RadixTree<>(); | |
table.set(6941, 100); | |
for (int a = 0; a < 10000; ++a) { | |
table.set(2 * (long)(Math.random() * Integer.MAX_VALUE), a); | |
} | |
for (Pair<Integer> l : table) { | |
System.out.println(l.key + ": " + l.value + | |
" | size: " + table.size()); | |
if (l.key % 2 == 0) { | |
table.remove(l.key); | |
} | |
} | |
System.out.println(); | |
for (Pair<Integer> l : table) { | |
System.out.println(l.key + ": " + l.value); | |
} | |
} | |
} |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment