كيفية الحصول على عنصر من شجرة ثنائية بواسطة الفهرس في فترة زمنية معقولة؟

public class UNode { UNode parent; int key; int countLefter; int add; UNode left; UNode right; public UNode() { } public UNode(UNode parent, int key, int countLefter, int add, UNode left, UNode right) { this.parent = parent; this.key = key; this.countLefter = countLefter; this.add = add; this.left = left; this.right = right; } public void push() { countLefter += add; if (left != null) left.add += add; if (right != null) right.add += add; add = 0; } @Override public String toString() { return "Node{" + "key=" + key + ", countLefter=" + countLefter + '}'; } } 

 import java.util.LinkedList; public class UTree { private UNode root; private int size; public UTree() { } public int size() { return size; } public int get(int index) { return get(index, root); } public boolean add(int key) { if (root == null) { root = new UNode(null, key, 0, 0, null, null); size++; return true; } boolean res = add(key, root); if (res) size++; return res; } public boolean remove(int key) { if (root == null) return false; if (key == this.root.key) { root.push(); removeRoot(); size--; return true; } boolean res = remove(key, root); if (res) size--; return res; } private int get(int index, UNode root) { root.push(); if (index == root.countLefter) return root.key; if (index < root.countLefter) return get(index, root.left); return get(index, root.right); } private boolean add(int key, UNode root) { if (key == root.key) return false; root.push(); if (key < root.key) if (root.left != null) { boolean res = add(key, root.left); if (res) { root.countLefter++; if (root.right != null) root.right.add++; } return res; } else { root.left = new UNode(root, key, root.countLefter, 0, null, null); root.countLefter++; if (root.right != null) root.right.add++; return true; } if (root.right != null) return add(key, root.right); else { root.right = new UNode(root, key, root.countLefter + 1, 0, null, null); return true; } } public boolean removeByIndex(int index) { if(this.root == null) return false; root.push(); if (index == this.root.countLefter) { removeRoot(); return true; } boolean res = removeByIndex(index, root); if (res) size--; return res; } private boolean removeByIndex(int index, UNode root) { if (root == null) return false; root.push(); if (index == root.countLefter) return removeNode(root); if (index < root.countLefter) { boolean res = removeByIndex(index, root.left); if (res) { root.countLefter--; if (root.right != null) root.right.add--; } return res; } else return removeByIndex(index, root.right); } private boolean removeNode(UNode root) { if (root.left == root.right) { if (root.parent.left == root) root.parent.left = null; else root.parent.right = null; return true; } if (root.left == null) { if (root.parent.left == root) { root.parent.left = root.right; root.right.add--; } else { root.parent.right = root.right; root.right.add--; } root.right.parent = root.parent; return true; } if (root.right == null) { if (root.parent.left == root) root.parent.left = root.left; else root.parent.right = root.left; root.left.parent = root.parent; return true; } UNode right = getRight(root.left); cut(right); root.key = right.key; root.countLefter--; root.right.add--; return true; } private boolean remove(int key, UNode root) { if (root == null) return false; root.push(); if (key == root.key) return removeNode(root); if (key < root.key) { boolean res = remove(key, root.left); if (res) { root.countLefter--; if (root.right != null) root.right.add--; } return res; } else return remove(key, root.right); } private void removeRoot() { if (root.left == root.right) { root = null; return; } if (root.left == null) { root = root.right; root.add--; return; } if (root.right == null) { root = root.left; return; } UNode right = getRight(root.left); cut(right); root.key = right.key; root.countLefter--; root.right.add--; } private static void cut(UNode node) { if (node.parent.left == node) node.parent.left = node.left; else node.parent.right = node.left; if (node.left != null) node.left.parent = node.parent; } private UNode getRight(UNode root) { root.push(); if (root.right == null) return root; return getRight(root.right); } public void printTree() { printTree(root); } private void printTree(UNode root) { if (root == null) return; root.push(); printTree(root.left); System.out.println(root); printTree(root.right); } public LinkedList<UNode> getAll(){ LinkedList<UNode> res = new LinkedList<>(); getAll(root, res); return res; } private void getAll(UNode root, LinkedList<UNode> res){ if (root == null) return; root.push(); getAll(root.left, res); res.add(root); getAll(root.right, res); } }