Binary Search Tree

insert(value)
  Pre: value has passed custom type checks for type T
  Post: value has been placed in the correct location in the tree
  if root = ø
    root ← node(value)
  else
    insertNode(root, value)
  end if
end insert

insertNode(current, value)
  Pre: current is the node to start from
  Post: value has been placed in the correct location in the tree
  if value < current.value
    if current.left = ø
      current.left ← node(value)
    else
      InsertNode(current.left, value)
    end if
  else
    if current.right = ø
      current.right ← node(value)
    else
      InsertNode(current.right, value)
    end if
  end if
end insertNode

contains(root, value)
  Pre: root is the root node of the tree, value is what we would like to locate
  Post: value is either located or not
  if root = ø
    return false
  end if
  if root.value = value
    return true
  else if value < root.value
    return contains(root.left, value)
  else
    return contains(root.right, value)
  end if
end contains

remove(value)
  Pre: value is the value of the node to remove, root is the node of the BST
      count is the number of items in the BST
  Post: node with value is removed if found in which case yields true, otherwise false
  nodeToRemove ← findNode(value)
  if nodeToRemove = ø
    return false
  end if
  parent ← findParent(value)
  if count = 1
    root ← ø
  else if nodeToRemove.left = ø and nodeToRemove.right = ø
    if nodeToRemove.value < parent.value
      parent.left ←  nodeToRemove.right
    else
      parent.right ← nodeToRemove.right
    end if
  else if nodeToRemove.left != ø and nodeToRemove.right != ø
    next ← nodeToRemove.right
    while next.left != ø
      next ← next.left
    end while
    if next != nodeToRemove.right
      remove(next.value)
      nodeToRemove.value ← next.value
    else
      nodeToRemove.value ← next.value
      nodeToRemove.right ← nodeToRemove.right.right
    end if
  else
    if nodeToRemove.left = ø
      next ← nodeToRemove.right
    else
      next ← nodeToRemove.left
    end if
    if root = nodeToRemove
      root = next
    else if parent.left = nodeToRemove
      parent.left = next
    else if parent.right = nodeToRemove
      parent.right = next
    end if
  end if
  count ← count - 1
  return true
end remove

findParent(value, root)
  Pre: value is the value of the node we want to find the parent of
       root is the root node of the BST and is != ø
  Post: a reference to the prent node of value if found; otherwise ø
  if value = root.value
    return ø
  end if
  if value < root.value
    if root.left = ø
      return ø
    else if root.left.value = value
      return root
    else
      return findParent(value, root.left)
    end if
  else
    if root.right = ø
      return ø
    else if root.right.value = value
      return root
    else
      return findParent(value, root.right)
    end if
  end if
end findParent

findNode(root, value)
  Pre: value is the value of the node we want to find the parent of
       root is the root node of the BST
  Post: a reference to the node of value if found; otherwise ø
  if root = ø
    return ø
  end if
  if root.value = value
    return root
  else if value < root.value
    return findNode(root.left, value)
  else
    return findNode(root.right, value)
  end if
end findNode

findMin(root)
  Pre: root is the root node of the BST
    root = ø
  Post: the smallest value in the BST is located
  if root.left = ø
    return root.value
  end if
  findMin(root.left)
end findMin

findMax(root)
  Pre: root is the root node of the BST
    root = ø
  Post: the largest value in the BST is located
  if root.right = ø
    return root.value
  end if
  findMax(root.right)
end findMax

inorder(root)
  Pre: root is the root node of the BST
  Post: the nodes in the BST have been visited in inorder
  if root != ø
    inorder(root.left)
    yield root.value
    inorder(root.right)
  end if
end inorder

preorder(root)
  Pre: root is the root node of the BST
  Post: the nodes in the BST have been visited in preorder
  if root != ø
    yield root.value
    preorder(root.left)
    preorder(root.right)
  end if
end preorder

postorder(root)
  Pre: root is the root node of the BST
  Post: the nodes in the BST have been visited in postorder
  if root != ø
    postorder(root.left)
    postorder(root.right)
    yield root.value
  end if
end postorder

import BinarySearchTreeNode from './BinarySearchTreeNode';

export default class BinarySearchTree {
  /**
   * @param {function} [nodeValueCompareFunction]
   */
  constructor(nodeValueCompareFunction) {
    this.root = new BinarySearchTreeNode(null, nodeValueCompareFunction);

    // Steal node comparator from the root.
    this.nodeComparator = this.root.nodeComparator;
  }

  /**
   * @param {*} value
   * @return {BinarySearchTreeNode}
   */
  insert(value) {
    return this.root.insert(value);
  }

  /**
   * @param {*} value
   * @return {boolean}
   */
  contains(value) {
    return this.root.contains(value);
  }

  /**
   * @param {*} value
   * @return {boolean}
   */
  remove(value) {
    return this.root.remove(value);
  }

  /**
   * @return {string}
   */
  toString() {
    return this.root.toString();
  }
}

import BinaryTreeNode from '../BinaryTreeNode';
import Comparator from '../../../utils/comparator/Comparator';

export default class BinarySearchTreeNode extends BinaryTreeNode {
  /**
   * @param {*} [value] - node value.
   * @param {function} [compareFunction] - comparator function for node values.
   */
  constructor(value = null, compareFunction = undefined) {
    super(value);

    // This comparator is used to compare node values with each other.
    this.compareFunction = compareFunction;
    this.nodeValueComparator = new Comparator(compareFunction);
  }

  /**
   * @param {*} value
   * @return {BinarySearchTreeNode}
   */
  insert(value) {
    if (this.nodeValueComparator.equal(this.value, null)) {
      this.value = value;

      return this;
    }

    if (this.nodeValueComparator.lessThan(value, this.value)) {
      // Insert to the left.
      if (this.left) {
        return this.left.insert(value);
      }

      const newNode = new BinarySearchTreeNode(value, this.compareFunction);
      this.setLeft(newNode);

      return newNode;
    }

    if (this.nodeValueComparator.greaterThan(value, this.value)) {
      // Insert to the right.
      if (this.right) {
        return this.right.insert(value);
      }

      const newNode = new BinarySearchTreeNode(value, this.compareFunction);
      this.setRight(newNode);

      return newNode;
    }

    return this;
  }

  /**
   * @param {*} value
   * @return {BinarySearchTreeNode}
   */
  find(value) {
    // Check the root.
    if (this.nodeValueComparator.equal(this.value, value)) {
      return this;
    }

    if (this.nodeValueComparator.lessThan(value, this.value) && this.left) {
      // Check left nodes.
      return this.left.find(value);
    }

    if (this.nodeValueComparator.greaterThan(value, this.value) && this.right) {
      // Check right nodes.
      return this.right.find(value);
    }

    return null;
  }

  /**
   * @param {*} value
   * @return {boolean}
   */
  contains(value) {
    return !!this.find(value);
  }

  /**
   * @param {*} value
   * @return {boolean}
   */
  remove(value) {
    const nodeToRemove = this.find(value);

    if (!nodeToRemove) {
      throw new Error('Item not found in the tree');
    }

    const { parent } = nodeToRemove;

    if (!nodeToRemove.left && !nodeToRemove.right) {
      // Node is a leaf and thus has no children.
      if (parent) {
        // Node has a parent. Just remove the pointer to this node from the parent.
        parent.removeChild(nodeToRemove);
      } else {
        // Node has no parent. Just erase current node value.
        nodeToRemove.setValue(undefined);
      }
    } else if (nodeToRemove.left && nodeToRemove.right) {
      // Node has two children.
      // Find the next biggest value (minimum value in the right branch)
      // and replace current value node with that next biggest value.
      const nextBiggerNode = nodeToRemove.right.findMin();
      if (!this.nodeComparator.equal(nextBiggerNode, nodeToRemove.right)) {
        this.remove(nextBiggerNode.value);
        nodeToRemove.setValue(nextBiggerNode.value);
      } else {
        // In case if next right value is the next bigger one and it doesn't have left child
        // then just replace node that is going to be deleted with the right node.
        nodeToRemove.setValue(nodeToRemove.right.value);
        nodeToRemove.setRight(nodeToRemove.right.right);
      }
    } else {
      // Node has only one child.
      // Make this child to be a direct child of current node's parent.
      /** @var BinarySearchTreeNode */
      const childNode = nodeToRemove.left || nodeToRemove.right;

      if (parent) {
        parent.replaceChild(nodeToRemove, childNode);
      } else {
        BinaryTreeNode.copyNode(childNode, nodeToRemove);
      }
    }

    // Clear the parent of removed node.
    nodeToRemove.parent = null;

    return true;
  }

  /**
   * @return {BinarySearchTreeNode}
   */
  findMin() {
    if (!this.left) {
      return this;
    }

    return this.left.findMin();
  }
}