using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;namespace FirstSolver
{internal class Program{static void Main(string[] args){BinaryTreeNode<int> root1 = FullBinaryTree.CreateTree(1, 4);Console.WriteLine(FullBinaryTree.PrintTree(root1));Console.WriteLine();BinaryTreeNode<int> root2 = FullBinaryTree.CreateTree(101, 4);Console.WriteLine(FullBinaryTree.PrintTree(root2));Console.WriteLine();BinaryTreeNode<int> root3 = FullBinaryTree.CreateTree(201, 4);Console.WriteLine(FullBinaryTree.PrintTree(root3));Console.WriteLine();root1.ParentNode = root2;root2.ParentNode = root3;root3.ParentNode = root1;BinaryTreeNode<int> nodeA = FullBinaryTree.FindNode(root1, 5);BinaryTreeNode<int> nodeB = FullBinaryTree.FindNode(root1, 7);Console.WriteLine($"[A({nodeA.Value})]->[B({nodeB.Value})]");Stack<BinaryTreeNode<int>> path = FullBinaryTree.FindPath(nodeA, nodeB);Console.WriteLine(FullBinaryTree.PrintPath(path));Console.WriteLine(FullBinaryTree.PrintPath(FullBinaryTree.QuickFindPath(nodeA, nodeB)));Console.WriteLine();nodeB = FullBinaryTree.FindNode(root2, 107);Console.WriteLine($"[A({nodeA.Value})]->[B({nodeB.Value})]");path = FullBinaryTree.FindPath(nodeA, nodeB);Console.WriteLine(FullBinaryTree.PrintPath(path));Console.WriteLine(FullBinaryTree.PrintPath(FullBinaryTree.QuickFindPath(nodeA, nodeB)));Console.WriteLine();nodeB = FullBinaryTree.FindNode(root3, 207);Console.WriteLine($"[A({nodeA.Value})]->[B({nodeB.Value})]");path = FullBinaryTree.FindPath(nodeA, nodeB);Console.WriteLine(FullBinaryTree.PrintPath(path));Console.WriteLine(FullBinaryTree.PrintPath(FullBinaryTree.QuickFindPath(nodeA, nodeB)));Console.WriteLine();// 测试是否死循环nodeB = new BinaryTreeNode<int>(301);Console.WriteLine($"[A({nodeA.Value})]->[B({nodeB.Value})]");path = FullBinaryTree.FindPath(nodeA, nodeB);Console.WriteLine(FullBinaryTree.PrintPath(path));Console.WriteLine(FullBinaryTree.PrintPath(FullBinaryTree.QuickFindPath(nodeA, nodeB)));Console.WriteLine();Console.ReadKey();}}/// <summary>/// 满二叉树/// </summary>/// <typeparam name="T">数据类型</typeparam>public static class FullBinaryTree{/// <summary>/// 创建深度为depth的满二叉树/// </summary>/// <param name="intial">初始值</param>/// <param name="depth">深度</param>/// <returns>满二叉树头结点</returns>public static BinaryTreeNode<int> CreateTree(int intial, int depth){BinaryTreeNode<int> header = new BinaryTreeNode<int>(intial);CreateSub(header, intial, 2, depth);return header;}/// <summary>/// 创建子树/// </summary>/// <param name="node">父节点</param>/// <param name="initial">根节点初始值</param>/// <param name="level">层级</param>/// <param name="depth">深度</param>private static void CreateSub(BinaryTreeNode<int> node, int initial, int level, int depth){if (level > depth) return;int value = (node.Value << 1) - (initial - 1);BinaryTreeNode<int> leftChildNode = new BinaryTreeNode<int>(value);BinaryTreeNode<int> rightChildNode = new BinaryTreeNode<int>(value + 1);node.LeftChildNode = leftChildNode;node.RightChildNode = rightChildNode;leftChildNode.ParentNode = node;rightChildNode.ParentNode = node;CreateSub(leftChildNode, initial, level + 1, depth);CreateSub(rightChildNode, initial, level + 1, depth);}/// <summary>/// 打印二叉树/// </summary>/// <param name="header">节点</param>/// <returns>二叉树字符串</returns>public static string PrintTree(BinaryTreeNode<int> header){StringBuilder sb = new StringBuilder($"{header.Value}");if (header.LeftChildNode != null){sb.Append($"({header.LeftChildNode.Value},{header.RightChildNode.Value})");PrintTreeSub(header.LeftChildNode, sb);PrintTreeSub(header.RightChildNode, sb);}return sb.ToString();}private static void PrintTreeSub(BinaryTreeNode<int> node, StringBuilder sb){sb.Append($" {node.Value}");if (node.LeftChildNode != null){sb.Append($"({node.LeftChildNode.Value},{node.RightChildNode.Value})");PrintTreeSub(node.LeftChildNode, sb);PrintTreeSub(node.RightChildNode, sb);}}/// <summary>/// 查找指定值的节点/// </summary>/// <param name="node">二叉树</param>/// <param name="value">要匹配的值</param>/// <returns>找到的节点</returns>public static BinaryTreeNode<int> FindNode(BinaryTreeNode<int> node, int value){if (Equals(node.Value, value)) return node;if (node.LeftChildNode != null){return FindNode(node.LeftChildNode, value) ?? FindNode(node.RightChildNode, value);}return null;}/// <summary>/// 定位根节点/// </summary>/// <param name="node">初始节点</param>/// <returns>根节点</returns>public static BinaryTreeNode<int> GetRootNode(BinaryTreeNode<int> node){while (true){if (node.ParentNode == null) break;if (node.ParentNode.LeftChildNode != node && node.ParentNode.RightChildNode != node) break;node = node.ParentNode;}return node;}/// <summary>/// 寻找节点A到节点B的最短路径/// </summary>/// <param name="nodeA">节点A</param>/// <param name="nodeB">节点B</param>/// <returns>最短路径</returns>public static Stack<BinaryTreeNode<int>> FindPath(BinaryTreeNode<int> nodeA, BinaryTreeNode<int> nodeB){BinaryTreeNode<int> rootA = GetRootNode(nodeA);Stack<BinaryTreeNode<int>> path = new Stack<BinaryTreeNode<int>>();BinaryTreeNode<int> node = nodeA;path.Push(node);bool find = FindPathSub(node, nodeB, path);if (!find){while (!find){if (node.ParentNode == null) break;// 避免死循环if (node.ParentNode == rootA && (node != rootA.LeftChildNode && node != rootA.RightChildNode)) break;path.Push(node.ParentNode);int state = 0; // 进入另一颗二叉树if (node.ParentNode.LeftChildNode == node)state = 1;else if (node.ParentNode.RightChildNode == node)state = 2;if (state == 0 || state == 1){find = FindPathSub(node.ParentNode.RightChildNode, nodeB, path);if (find) break;}if (state == 0 || state == 2){find = FindPathSub(node.ParentNode.LeftChildNode, nodeB, path);if (find) break;}node = node.ParentNode;}}return find ? path : null;}private static bool FindPathSub(BinaryTreeNode<int> node, BinaryTreeNode<int> search, Stack<BinaryTreeNode<int>> path){path.Push(node);if (node == search) return true;if (node.LeftChildNode != null){if (FindPathSub(node.LeftChildNode, search, path)) return true;if (FindPathSub(node.RightChildNode, search, path)) return true;}path.Pop();return false;}/// <summary>/// 获取到根节点的路径/// </summary>/// <param name="node">起始节点</param>/// <returns>到根节点路径</returns>public static List<BinaryTreeNode<int>> GetRootNodePath(BinaryTreeNode<int> node){List<BinaryTreeNode<int>> path = new List<BinaryTreeNode<int>>();path.Add(node);while (true){if (node.ParentNode == null) break;if (node.ParentNode.LeftChildNode != node && node.ParentNode.RightChildNode != node) break;node = node.ParentNode;path.Add(node);}return path;}/// <summary>/// 快速寻找节点A到节点B的最短路径/// </summary>/// <param name="nodeA">节点A</param>/// <param name="nodeB">节点B</param>/// <returns>最短路径</returns>public static List<BinaryTreeNode<int>> QuickFindPath(BinaryTreeNode<int> nodeA, BinaryTreeNode<int> nodeB){List<BinaryTreeNode<int>> pathA = GetRootNodePath(nodeA);List<BinaryTreeNode<int>> pathB = GetRootNodePath(nodeB);BinaryTreeNode<int> rootA = pathA[pathA.Count - 1];BinaryTreeNode<int> rootB = pathB[pathB.Count - 1];if (rootA == rootB){int i = pathA.Count - 2;int j = pathB.Count - 2;for (; i >= 0 && j >= 0; i--, j--){if (pathA[i] != pathB[j]) break;}if (pathA.Count - 2 > i) pathA.RemoveRange(i + 2, pathA.Count - i - 2);pathB.RemoveRange(j + 1, pathB.Count - j - 1);pathB.Reverse();pathA.AddRange(pathB);return pathA;}else{BinaryTreeNode<int> node = rootA;while (node.ParentNode != null){node = node.ParentNode;if (node == rootB){pathB.Reverse();pathA.AddRange(pathB);return pathA;}else if (node == rootA){   // 避免死循环break;}pathA.Add(node);}return null;}            }/// <summary>/// 打印路径/// </summary>/// <param name="path">路径</param>/// <returns>路径字符串</returns>      public static string PrintPath(IEnumerable<BinaryTreeNode<int>> path){if (path == null) return "No Path!"; // 没有路径到达IEnumerable<BinaryTreeNode<int>> p = path;if (path is Stack<BinaryTreeNode<int>>){p = p.Reverse();}            StringBuilder sb = new StringBuilder();foreach (var item in p){sb.Append($"{item.Value}->");}sb.Remove(sb.Length - 2, 2);return sb.ToString();}}/// <summary>/// 节点定义/// </summary>/// <typeparam name="T">节点数据类型：要求值类型</typeparam>public class BinaryTreeNode<T> where T : struct{public T Value { get; set; }public BinaryTreeNode<T> ParentNode { get; set; }public BinaryTreeNode<T> LeftChildNode { get; set; }public BinaryTreeNode<T> RightChildNode { get; set; }public BinaryTreeNode() { Value = default; }public BinaryTreeNode(T value) { Value = value; }}
}