skip-list-implementation

src/data-structures/skip-list/README.md

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+In computer science, a skip list is a probabilistic data structure that allows {\mathcal {O}} search complexity as well as {\mathcal {O}} insertion complexity within an ordered sequence of n elements.

src/data-structures/skip-list/SkipList.js

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+const DEFAULT_STACK_UP_PROBABILITY = 0.25;
+
+class ProperSkipList {
+  constructor(options) {
+    options = options || {};
+    this.stackUpProbability = options.stackUpProbability || DEFAULT_STACK_UP_PROBABILITY;
+    this.updateLength = options.updateLength !== false;
+    this.typePriorityMap = {
+      'undefined': 0,
+      'object': 1,
+      'number': 2,
+      'bigint': 2,
+      'string': 3
+    };
+    this.clear();
+  }
+
+  clear() {
+    let headNode = {
+      prev: null
+    };
+    let tailNode = {
+      next: null
+    };
+    this.head = {
+      isHead: true,
+      key: undefined,
+      value: undefined,
+      nodes: [headNode]
+    };
+    this.tail = {
+      isTail: true,
+      key: undefined,
+      value: undefined,
+      nodes: [tailNode]
+    };
+    headNode.next = tailNode;
+    tailNode.prev = headNode;
+    headNode.group = this.head;
+    tailNode.group = this.tail;
+    this.length = this.updateLength ? 0 : undefined;
+  }
+
+  upsert(key, value) {
+    let {matchingNode, prevNode, searchPath} = this._searchAndTrack(key);
+    if (matchingNode) {
+      let previousValue = matchingNode.group.value;
+      matchingNode.group.value = value;
+      return previousValue;
+    }
+
+    // Insert the entry.
+    let newNode = {
+      prev: prevNode,
+      next: prevNode.next
+    };
+    let newGroup = {
+      key,
+      value,
+      nodes: [newNode]
+    };
+    newNode.group = newGroup;
+    prevNode.next = newNode;
+    newNode.next.prev = newNode;
+
+    // Stack up the entry for fast search.
+    let layerIndex = 1;
+    while (Math.random() < this.stackUpProbability) {
+      let prevLayerNode = searchPath[layerIndex];
+      if (!prevLayerNode) {
+        let newHeadNode = {
+          prev: null,
+          group: this.head
+        };
+        let newTailNode = {
+          next: null,
+          group: this.tail
+        };
+        newHeadNode.next = newTailNode;
+        this.head.nodes.push(newHeadNode);
+        newTailNode.prev = newHeadNode;
+        this.tail.nodes.push(newTailNode);
+        prevLayerNode = newHeadNode;
+      }
+      let newNode = {
+        prev: prevLayerNode,
+        next: prevLayerNode.next,
+        group: newGroup
+      };
+      prevLayerNode.next = newNode;
+      newNode.next.prev = newNode;
+      newGroup.nodes.push(newNode);
+      layerIndex++;
+    }
+    if (this.updateLength) this.length++;
+
+    return undefined;
+  }
+
+  find(key) {
+    let {matchingNode} = this._search(key);
+    return matchingNode ? matchingNode.group.value : undefined;
+  }
+
+  has(key) {
+    return !!this.find(key);
+  }
+
+  _isAGreaterThanB(a, b) {
+    let typeA = typeof a;
+    let typeB = typeof b;
+    if (typeA === typeB) {
+      return a > b;
+    }
+    let typeAPriority = this.typePriorityMap[typeA];
+    let typeBPriority = this.typePriorityMap[typeB];
+    if (typeAPriority === typeBPriority) {
+      return a > b;
+    }
+    return typeAPriority > typeBPriority;
+  }
+
+  // The two search methods are similar but were separated for performance reasons.
+  _searchAndTrack(key) {
+    let layerCount = this.head.nodes.length;
+    let searchPath = new Array(layerCount);
+    let layerIndex = layerCount - 1;
+    let currentNode = this.head.nodes[layerIndex];
+    let prevNode = currentNode;
+
+    while (true) {
+      let currentNodeGroup = currentNode.group;
+      let currentKey = currentNodeGroup.key;
+      if (!currentNodeGroup.isTail) {
+        if (this._isAGreaterThanB(key, currentKey) || currentNodeGroup.isHead) {
+          prevNode = currentNode;
+          currentNode = currentNode.next;
+          continue;
+        }
+        if (key === currentKey) {
+          let matchingNode = currentNodeGroup.nodes[0];
+          searchPath[layerIndex] = matchingNode;
+          return {matchingNode, prevNode: matchingNode.prev, searchPath};
+        }
+      }
+      searchPath[layerIndex] = prevNode;
+      if (--layerIndex < 0) {
+        return {matchingNode: undefined, prevNode, searchPath};
+      }
+      currentNode = prevNode.group.nodes[layerIndex];
+    }
+  }
+
+  _search(key) {
+    let layerIndex = this.head.nodes.length - 1;
+    let currentNode = this.head.nodes[layerIndex];
+    let prevNode = currentNode;
+    while (true) {
+      let currentNodeGroup = currentNode.group;
+      let currentKey = currentNodeGroup.key;
+      if (!currentNodeGroup.isTail) {
+        if (this._isAGreaterThanB(key, currentKey) || currentNodeGroup.isHead) {
+          prevNode = currentNode;
+          currentNode = currentNode.next;
+          continue;
+        }
+        if (key === currentKey) {
+          let matchingNode = currentNodeGroup.nodes[0];
+          return {matchingNode, prevNode: matchingNode.prev};
+        }
+      }
+      if (--layerIndex < 0) {
+        return {matchingNode: undefined, prevNode};
+      }
+      currentNode = prevNode.group.nodes[layerIndex];
+    }
+  }
+
+  findEntriesFromMin() {
+    return this._createEntriesIteratorAsc(this.head.nodes[0].next);
+  }
+
+  findEntriesFromMax() {
+    return this._createEntriesIteratorDesc(this.tail.nodes[0].prev);
+  }
+
+  minEntry() {
+    let [key, value] = this.findEntriesFromMin().next().value;
+    return [key, value];
+  }
+
+  maxEntry() {
+    let [key, value] = this.findEntriesFromMax().next().value;
+    return [key, value];
+  }
+
+  minKey() {
+    return this.minEntry()[0];
+  }
+
+  maxKey() {
+    return this.maxEntry()[0];
+  }
+
+  minValue() {
+    return this.minEntry()[1];
+  }
+
+  maxValue() {
+    return this.maxEntry()[1];
+  }
+
+  _extractNode(matchingNode) {
+    let nodes = matchingNode.group.nodes;
+    for (let layerNode of nodes) {
+      let prevNode = layerNode.prev;
+      prevNode.next = layerNode.next;
+      prevNode.next.prev = prevNode;
+    }
+    if (this.updateLength) this.length--;
+    return matchingNode.group.value;
+  }
+
+  extract(key) {
+    let {matchingNode} = this._search(key);
+    if (matchingNode) {
+      return this._extractNode(matchingNode);
+    }
+    return undefined;
+  }
+
+  delete(key) {
+    return this.extract(key) !== undefined;
+  }
+
+  findEntries(fromKey) {
+    let {matchingNode, prevNode} = this._search(fromKey);
+    if (matchingNode) {
+      return {
+        matchingValue: matchingNode.group.value,
+        asc: this._createEntriesIteratorAsc(matchingNode),
+        desc: this._createEntriesIteratorDesc(matchingNode)
+      };
+    }
+    return {
+      matchingValue: undefined,
+      asc: this._createEntriesIteratorAsc(prevNode.next),
+      desc: this._createEntriesIteratorDesc(prevNode)
+    };
+  }
+
+  deleteRange(fromKey, toKey, deleteLeft, deleteRight) {
+    if (fromKey == null) {
+      fromKey = this.minKey();
+      deleteLeft = true;
+    }
+    if (toKey == null) {
+      toKey = this.maxKey();
+      deleteRight = true;
+    }
+    if (this._isAGreaterThanB(fromKey, toKey)) {
+      return;
+    }
+    let {prevNode: fromNode, searchPath: leftSearchPath, matchingNode: matchingLeftNode} = this._searchAndTrack(fromKey);
+    let {prevNode: toNode, searchPath: rightSearchPath, matchingNode: matchingRightNode} = this._searchAndTrack(toKey);
+    let leftNode = matchingLeftNode ? matchingLeftNode : fromNode;
+    let rightNode = matchingRightNode ? matchingRightNode : toNode.next;
+
+    if (leftNode === rightNode) {
+      if (deleteLeft) {
+        this._extractNode(leftNode);
+      }
+      return;
+    }
+
+    if (this.updateLength) {
+      let currentNode = leftNode;
+      while (currentNode && currentNode.next !== rightNode) {
+        this.length--;
+        currentNode = currentNode.next;
+      }
+    }
+
+    let leftGroupNodes = leftNode.group.nodes;
+    let rightGroupNodes = rightNode.group.nodes;
+    let layerCount = this.head.nodes.length;
+
+    for (let layerIndex = 0; layerIndex < layerCount; layerIndex++) {
+      let layerLeftNode = leftGroupNodes[layerIndex];
+      let layerRightNode = rightGroupNodes[layerIndex];
+
+      if (layerLeftNode && layerRightNode) {
+        layerLeftNode.next = layerRightNode;
+        layerRightNode.prev = layerLeftNode;
+        continue;
+      }
+      if (layerLeftNode) {
+        let layerRightmostNode = rightSearchPath[layerIndex];
+        if (!layerRightmostNode.group.isTail) {
+          layerRightmostNode = layerRightmostNode.next;
+        }
+        layerLeftNode.next = layerRightmostNode;
+        layerRightmostNode.prev = layerLeftNode;
+        continue;
+      }
+      if (layerRightNode) {
+        let layerLeftmostNode = leftSearchPath[layerIndex];
+        layerLeftmostNode.next = layerRightNode;
+        layerRightNode.prev = layerLeftmostNode;
+        continue;
+      }
+      // If neither left nor right nodes are present on the layer, connect based
+      // on search path to remove in-between entries.
+      let layerRightmostNode = rightSearchPath[layerIndex];
+      if (!layerRightmostNode.group.isTail) {
+        layerRightmostNode = layerRightmostNode.next;
+      }
+      let layerLeftmostNode = leftSearchPath[layerIndex];
+      layerLeftmostNode.next = layerRightmostNode;
+      layerRightmostNode.prev = layerLeftmostNode;
+    }
+    if (deleteLeft && matchingLeftNode) {
+      this._extractNode(matchingLeftNode);
+    }
+    if (deleteRight && matchingRightNode) {
+      this._extractNode(matchingRightNode);
+    }
+  }
+
+  _createEntriesIteratorAsc(currentNode) {
+    let i = 0;
+    return {
+      next: function () {
+        let currentGroup = currentNode.group;
+        if (currentGroup.isTail) {
+          return {
+            value: [currentNode.key, currentNode.value, i],
+            done: true
+          }
+        }
+        currentNode = currentNode.next;
+        return {
+          value: [currentGroup.key, currentGroup.value, i++],
+          done: currentGroup.isTail
+        };
+      },
+      [Symbol.iterator]: function () { return this; }
+    };
+  }
+
+  _createEntriesIteratorDesc(currentNode) {
+    let i = 0;
+    return {
+      next: function () {
+        let currentGroup = currentNode.group;
+        if (currentGroup.isHead) {
+          return {
+            value: [currentNode.key, currentNode.value, i],
+            done: true
+          }
+        }
+        currentNode = currentNode.prev;
+        return {
+          value: [currentGroup.key, currentGroup.value, i++],
+          done: currentGroup.isHead
+        };
+      },
+      [Symbol.iterator]: function () { return this; }
+    };
+  }
+}