二叉搜索树代码实现及测试

 

一、代码实现

#pragma once
namespace key
{
	template<class K>
	struct BSTreeNode
	{
		BSTreeNode<K>* _left;
		BSTreeNode<K>* _right;
		K _key;
		BSTreeNode(const K& key)
			:_left(nullptr)
			,_right(nullptr)
			,_key(key)
		{}
	};
	template<class K>
	class BSTree
	{
		typedef BSTreeNode <K> Node;
	public:
		BSTree()
			:_root(nullptr)
		{}
		~BSTree()
		{
			Destroy(_root);
		}
		BSTree(const BSTree<K>& t)
		{
			_root = Copy(t._root);
		}

		BSTree<K>& operator=(BSTree<K> t)
		{
			swap(_root, t._root);
			return *this;
		}
		//非递归
		bool Insert(const K& key)
		{
			if (_root == nullptr)
			{
				_root = new Node(key);
				return true;
			}
			Node* parent = nullptr;
			Node* cur = _root;
			while (cur)
			{
				//大了去右边
				if (key > cur->_key)
				{
					parent = cur;
					cur = cur->_right;
				}
				//小了去左边
				if (key < cur->_key)
				{
					parent = cur;
					cur = cur->_left;
				}
				else
				{
					return false;
				}
			}
			//找到后插入
			cur = new Node(key);
			if (key > parent->_key)
			{
				 parent->_right = cur  ;
			}
			else
			{
				parent->_left = cur;
			}
			return true;
		}
		bool Find(const K& key)
		{
			Node* cur = _root;
			while (cur)
			{
				//大了去右边
				if (key > cur->_key)
				{
					cur = cur->_right;
				}
				//小了去左边
				if (key < cur->_key)
				{
					cur = cur->_left;
				}
				else
				{
					return true;
				}
			}
			return false;
		}
		bool Erase(const K& key)
		{
			Node* parent = nullptr;
			Node* cur = _root;
			while (cur)
			{
				//大了去右边
				if (key > cur->_key)
				{
					parent = cur;
					cur = cur->_right;
				}
				//小了去左边
				if (key < cur->_key)
				{
					parent = cur;
					cur = cur->_left;
				}
				else
				{
					//左为空
					if (cur->_left == nullptr)
					{
						if (cur == _root)
						{
							_root = cur->_right;
						}
						else
						{
							if (cur == parent->_right)
							{
								parent->_right = cur->_right;
							}
							else
							{
								parent->_left = cur->_right;
							}
						}
					}
					//右为空
					else if (cur->_right == nullptr)
					{
						if (cur == _root)
						{
							_root = cur->_left;
						}
						else
						{
							if (cur == parent->_right)
							{
								parent->_right = cur->_left;
							}
							else
							{
								parent->_left = cur->_left;
							}
						}
					}
					//左右都不为空
					else
					{
					//找替代节点，可以是左边最大值，也可以是右边最小值
					//这里找左边最大值
					//父亲不能为空，下面会用到
					Node* parent = cur;
					Node* leftMax = cur->_left;
					while (leftMax->_right)
					{
						parent = leftMax;
						leftMax = leftMax->_right;
					}
					swap(cur->_key, leftMax->_key);
					//交换后不能直接erase，因为此时交换后可能就不符合搜索二叉树了，有可能大的值在左边，erase会跑到右边去找
					//因此需要手动删除，手动删除需要找到父节点
					if (parent->_left == leftMax)
					{
						parent->_left = leftMax->_left;
					}
					else
					{
						parent->_right = leftMax->_left;
					}
					cur = leftMax;
					}
					delete cur;
					return true;
				}
			}
			return false;
		}
		//递归
		bool EraseR(const K& key)
		{
			return _EraseR(_root, key);
		}
		bool InsertR(const K& key)
		{
			return _InsertR(_root, key);
		}
		bool FindR(const K& key)
		{
			return _FindR(_root, key);
		}

		void InOrder()
		{
			_InOrder(_root);
			cout << endl;
		}
		
	private:
		Node* _root;
		Node* Copy(Node* root)
		{
			if (root == nullptr)
				return nullptr;

			Node* copyroot = new Node(root->_key);
			copyroot->_left = Copy(root->_left);
			copyroot->_right = Copy(root->_right);
			return copyroot;
		}
		void Destroy(Node*& root)
		{
			if (root == nullptr)
				return;
			Destroy(root->_left);
			Destroy(root->_right);
			delete root;
			root = nullptr;
		}
		//递归
		bool _EraseR(Node*& root, const K& key)
		{
			if (root == nullptr)
				return false;
			if (key > root->_key)
			{
				return _EraseR(root->_right, key);
			}
			else if (key < root->_key)
			{
				return _EraseR(root->_left, key);
			}
			else
			{
				Node* del = root;
				//左为空
				if (root->_left == nullptr)
				{
					root = root->_right;
				}
				//右为空
				else if (root->_right == nullptr)
				{
					root = root->_left;
				}
				//左右都不为空
				else
				{
					//从左孩子结点重新当作树找最大值
					Node* leftMax = root->_left;
					while (leftMax->_right)
					{
						leftMax = leftMax->_right;
					}
					swap(root->_key, leftMax->_key);
					//从左子树递归删除
					return _EraseR(root->_left, key);
				}
				delete del;
				return true;
			}
		}
		bool _InsertR(Node*& root, const K& key)
		{
			if (root == nullptr)
			{
				root = new Node(key);
				return true;
			}
			if (key > root->_key)
			{
				return _InsertR(root->_right, key);
			}
			else if (key < root->_key)
			{
				return _InsertR(root->_left, key);
			}
			else
			{
				return false;
			}
		}
		bool _FindR(Node* root, const K& key)
		{
			if (root == nullptr)
			{
				return false;
			}
			if (key > root->_key)
			{
				return _InsertR(root->_right, key);
			}
			else if (key < root->_key)
			{
				return _InsertR(root->_left, key);
			}
			else
			{
				return true;
			}
		}
		void _InOrder(Node* root)
		{
			if (root == NULL)
			{
				return;
			}
			_InOrder(root->_left);
			cout << root->_key << " ";
			_InOrder(root->_right);

		}
	};
	void TestBSTree1()
	{
		int a[] = { 8, 3, 1, 10, 6, 4, 7, 14, 13 };
		BSTree<int> t;
		for (auto e : a)
		{
			t.InsertR(e);
		}

		t.InOrder();

		t.Erase(4);
		t.InOrder();

		t.EraseR(6);
		t.InOrder();

		t.EraseR(7);
		t.InOrder();

		t.EraseR(3);
		t.InOrder();

		for (auto e : a)
		{
			t.EraseR(e);
		}
		t.InOrder();
	}

	void TestBSTree2()
	{
		int a[] = { 8, 3, 1, 10, 6, 4, 7, 14, 13 };
		BSTree<int> t;
		for (auto e : a)
		{
			t.InsertR(e);
		}

		BSTree<int> t1(t);

		t.InOrder();
		t1.InOrder();
	}
}

namespace key_value
{
	template<class K, class V>
	struct BSTreeNode
	{
		BSTreeNode<K, V>* _left;
		BSTreeNode<K, V>* _right;
		K _key;
		V _value;

		BSTreeNode(const K& key, const V& value)
			:_left(nullptr)
			, _right(nullptr)
			, _key(key)
			, _value(value)
		{}
	};

	template<class K, class V>
	class BSTree
	{
		typedef BSTreeNode<K, V> Node;
	public:
		BSTree()
			:_root(nullptr)
		{}

		void InOrder()
		{
			_InOrder(_root);
			cout << endl;
		}

		Node* FindR(const K& key)
		{
			return _FindR(_root, key);
		}

		bool InsertR(const K& key, const V& value)
		{
			return _InsertR(_root, key, value);
		}

		bool EraseR(const K& key)
		{
			return _EraseR(_root, key);
		}

	private:
		bool _EraseR(Node*& root, const K& key)
		{
			if (root == nullptr)
				return false;

			if (root->_key < key)
			{
				return _EraseR(root->_right, key);
			}
			else if (root->_key > key)
			{
				return _EraseR(root->_left, key);
			}
			else
			{
				Node* del = root;

				// 1、左为空
				// 2、右为空
				// 3、左右都不为空
				if (root->_left == nullptr)
				{
					root = root->_right;
				}
				else if (root->_right == nullptr)
				{
					root = root->_left;
				}
				else
				{
					Node* leftMax = root->_left;
					while (leftMax->_right)
					{
						leftMax = leftMax->_right;
					}

					swap(root->_key, leftMax->_key);

					return _EraseR(root->_left, key);
				}

				delete del;
				return true;
			}
		}

		bool _InsertR(Node*& root, const K& key, const V& value)
		{
			if (root == nullptr)
			{
				root = new Node(key, value);
				return true;
			}

			if (root->_key < key)
			{
				return _InsertR(root->_right, key, value);
			}
			else if (root->_key > key)
			{
				return _InsertR(root->_left, key, value);
			}
			else
			{
				return false;
			}
		}

		Node* _FindR(Node* root, const K& key)
		{
			if (root == nullptr)
				return nullptr;

			if (root->_key < key)
			{
				return _FindR(root->_right, key);
			}
			else if (root->_key > key)
			{
				return _FindR(root->_left, key);
			}
			else
			{
				return root;
			}
		}

		void _InOrder(Node* root)
		{
			if (root == NULL)
			{
				return;
			}

			_InOrder(root->_left);
			cout << root->_key << ":" << root->_value << endl;
			_InOrder(root->_right);
		}
	private:
		Node* _root;
	};

	void TestBSTree1()
	{
		//BSTree<string, Date> carTree;
		//词典模拟
		BSTree<string, string> dict;
		dict.InsertR("insert", "插入");
		dict.InsertR("sort", "排序");
		dict.InsertR("right", "右边");
		dict.InsertR("date", "日期");

		string str;
		while (cin >> str)
		{
			BSTreeNode<string, string>* ret = dict.FindR(str);
			if (ret)
			{
				cout << ret->_value << endl;
			}
			else
			{
				cout << "无此单词" << endl;
			}
		}
	}

	void TestBSTree2()
	{
		// 统计水果出现的次数
		string arr[] = { "西瓜", "西瓜", "苹果", "西瓜", "苹果", "苹果", "西瓜", "苹果", "香蕉", "苹果", "香蕉" };
		BSTree<string, int> countTree;
		for (auto& str : arr)
		{
			auto ret = countTree.FindR(str);
			if (ret == nullptr)
			{
				countTree.InsertR(str, 1);
			}
			else
			{
				ret->_value++;
			}
		}

		countTree.InOrder();
	}
}

二、测试代码

#define _CRT_SECURE_NO_WARNINGS 1
#include<iostream>
using namespace std;
#include"BinarySearchTree.h"
int main()
{
	key::TestBSTree1();
	key::TestBSTree2();
	key_value::TestBSTree1();
	key_value::TestBSTree2();
	return 0;
}