June 2011

Skip lists are a data structure that can be used in place of balanced trees. Skip lists use probabilistic balancing rather than strictly enforced balancing and as a result the algorithms for insertion and deletion in skip lists are much simpler and significantly faster than equivalent algorithms for balanced trees. (Pugh)

My implementation was based on William Pugh’s original paper, which you can download here. Despite being called a list, the structure described in the paper has the interface of a dictionary, with each node containing a comparable key and a value. The full implementation, its unit tests, and Pugh’s original paper are available under the MIT license on GitHub.

SkipList.java

/*
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 * 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.AbstractMap;
import java.util.ArrayList;
import java.util.Collections;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.Objects;
import java.util.Random;
import java.util.Set;

/**
 * A probabilistically balanced {@link java.util.Map} ordered by key, as described in Pugh's
 * "Skip Lists: A Probabilistic Alternative to Balanced Trees". Keys must be non-null and mutually
 * comparable. Iteration order is ascending by key. Not thread-safe.
 */
public class SkipList<K extends Comparable<K>, V> extends AbstractMap<K, V> {
    private static final int MAX_LEVEL = 32;

    private final double p;
    private final Node<K, V> head;
    private final Node<K, V> tail;
    private final Random r;
    private int level;
    private int size;

    public SkipList(double p) {
        if (!(p > 0 && p < 1)) {
            throw new IllegalArgumentException("p must be in (0, 1)");
        }

        this.p = p;
        head = new Node<>(null, null);
        tail = new Node<>(null, null);
        r = new Random();
        clear();
    }

    public SkipList() {
        this(0.5);
    }

    @Override
    public void clear() {
        head.forward.clear();
        head.forward.add(tail);
        level = 1;
        size = 0;
    }

    @Override
    public boolean containsKey(Object key) {
        return findNode(key) != null;
    }

    @Override
    public boolean containsValue(Object value) {
        Node<K, V> cur = head.forward.get(0);
        while (cur != tail) {
            if (Objects.equals(cur.value, value)) {
                return true;
            }

            cur = cur.forward.get(0);
        }

        return false;
    }

    @Override
    public Set<Entry<K, V>> entrySet() {
        Set<Entry<K, V>> x = new LinkedHashSet<>(size);
        Node<K, V> cur = head.forward.get(0);
        while (cur != tail) {
            x.add(new SimpleImmutableEntry<>(cur.key, cur.value));
            cur = cur.forward.get(0);
        }

        return x;
    }

    @Override
    public V get(Object key) {
        Node<K, V> node = findNode(key);
        return node == null ? null : node.value;
    }

    @Override
    public V put(K key, V value) {
        Objects.requireNonNull(key);
        List<Node<K, V>> update = new ArrayList<>(Collections.nCopies(level, head));
        Node<K, V> cur = head;
        for (int i = level - 1; i >= 0; --i) {
            while (cur.forward.get(i) != tail && cur.forward.get(i).key.compareTo(key) < 0) {
                cur = cur.forward.get(i);
            }

            update.set(i, cur);
        }

        cur = cur.forward.get(0);
        if (cur != tail && cur.key.equals(key)) {
            V prev = cur.value;
            cur.value = value;
            return prev;
        }

        int newLevel = randomLevel();
        if (newLevel > level) {
            for (int i = level; i < newLevel; ++i) {
                update.add(head);
                head.forward.add(tail);
            }

            level = newLevel;
        }

        cur = new Node<>(key, value);
        for (int i = 0; i < newLevel; ++i) {
            Node<K, V> prev = update.get(i);
            cur.forward.add(prev.forward.get(i));
            prev.forward.set(i, cur);
        }

        ++size;
        return null;
    }

    @Override
    public V remove(Object key) {
        @SuppressWarnings("unchecked")
        K k = (K) Objects.requireNonNull(key);
        List<Node<K, V>> update = new ArrayList<>(Collections.nCopies(level, head));
        Node<K, V> cur = head;
        for (int i = level - 1; i >= 0; --i) {
            while (cur.forward.get(i) != tail && cur.forward.get(i).key.compareTo(k) < 0) {
                cur = cur.forward.get(i);
            }

            update.set(i, cur);
        }

        cur = cur.forward.get(0);
        if (cur == tail || !cur.key.equals(k)) {
            return null;
        }

        for (int i = 0; i < level; ++i) {
            Node<K, V> prev = update.get(i);
            if (prev.forward.get(i) != cur) {
                break;
            }

            prev.forward.set(i, cur.forward.get(i));
        }

        while (level > 1 && head.forward.get(level - 1) == tail) {
            head.forward.remove(level - 1);
            --level;
        }

        --size;
        return cur.value;
    }

    @Override
    public int size() {
        return size;
    }

    /** Finds the node for {@code key}, or {@code null} if absent. */
    private Node<K, V> findNode(Object key) {
        @SuppressWarnings("unchecked")
        K k = (K) Objects.requireNonNull(key);
        Node<K, V> cur = head;
        for (int i = level - 1; i >= 0; --i) {
            while (cur.forward.get(i) != tail && cur.forward.get(i).key.compareTo(k) < 0) {
                cur = cur.forward.get(i);
            }
        }

        cur = cur.forward.get(0);
        return cur != tail && cur.key.equals(k) ? cur : null;
    }

    private int randomLevel() {
        int lvl = 1;
        while (lvl < MAX_LEVEL && r.nextDouble() < p) {
            ++lvl;
        }

        return lvl;
    }

    private static class Node<K extends Comparable<K>, V> {
        private final K key;
        private final List<Node<K, V>> forward;
        private V value;

        Node(K key, V value) {
            this.key = key;
            this.value = value;
            forward = new ArrayList<>();
        }
    }
}