用c++实现了一个BinarySearchTree的模板类
其他都很简单，重点说一下删除结点的方法。
如果结点是一片叶子，那么可以立即被删除；如果结点只有一个左儿子或一个右儿子，则左儿子或右儿子代替结点位置即可；
复杂的情况是有两个儿子，可以用被删除节点A的左子树的最右节点或者A的右子树的最左节点作为替代A的节点，并修改相应的最左或最右节点的父节点的指针。下面采用的是用右子树的最小数据（即右子树的最左结点）代替该结点的数据并递归地删除那个结点。
void BinarySearchTree<Comparable>::Remove(const Comparable &x, BinaryNode *&t) const { if (t == NULL) return; if (x < t->element) Remove(x, t->left); else if (x > t->element) Remove(x, t->right); else if (t->left != NULL && t->right != NULL)//两个儿子的结点 { t->element = FindMin(t->right)->element; Remove(t->element, t->right); } else { BinaryNode *oldNode = t; t = (t->left != NULL) ? t->left : t->right; delete oldNode; } }
全部代码：
BinarySearchTree.h
1 #include <iostream> 2 using namespace std; 3 4 #pragma once 5 6 template <typename Comparable> 7 class BinarySearchTree 8 { 9 public: 10 BinarySearchTree(); 11 BinarySearchTree(const BinarySearchTree &rhs); 12 ~BinarySearchTree(); 13 14 const Comparable &FindMin() const; 15 const Comparable &FindMax() const; 16 bool Contains(const Comparable &x) const; 17 bool IsEmpty() const; 18 void PrintTree() const; 19 20 void MakeEmpty(); 21 void Insert(const Comparable &x); 22 void Remove(const Comparable &x); 23 24 const BinarySearchTree & operator=(const BinarySearchTree &rhs); 25 26 private: 27 struct BinaryNode 28 { 29 Comparable element; 30 BinaryNode *left; 31 BinaryNode *right; 32 33 BinaryNode(const Comparable &theElement, BinaryNode *lt, BinaryNode *rt) 34 :element(theElement), left(lt), right(rt){} 35 }; 36 BinaryNode *root; 37 void Insert(const Comparable &x, BinaryNode *&t) const; 38 void Remove(const Comparable &x, BinaryNode *&t) const; 39 BinaryNode * FindMin(BinaryNode *t) const; 40 BinaryNode * FindMax(BinaryNode *t) const; 41 bool Contains(const Comparable &x, BinaryNode *t) const; 42 void MakeEmpty(BinaryNode *&t); 43 void PrintTree(BinaryNode *t) const; 44 BinaryNode * Clone(BinaryNode *t) const; 45 }; 46 47 48 49 template <typename Comparable> 50 void BinarySearchTree<Comparable>::PrintTree() const 51 { 52 PrintTree(root); 53 } 54 55 template <typename Comparable> 56 void BinarySearchTree<Comparable>::MakeEmpty(BinaryNode *&t) 57 { 58 if (t != NULL) 59 { 60 MakeEmpty(t->left); 61 MakeEmpty(t->right); 62 delete t; 63 } 64 t = NULL; 65 } 66 67 template <typename Comparable> 68 BinarySearchTree<Comparable>::BinarySearchTree() 69 { 70 } 71 72 template <typename Comparable> 73 BinarySearchTree<Comparable>::~BinarySearchTree() 74 { 75 MakeEmpty(root); 76 } 77 78 template <typename Comparable> 79 BinarySearchTree<Comparable>::BinarySearchTree(const BinarySearchTree &rhs) 80 { 81 82 } 83 84 template <typename Comparable> 85 bool BinarySearchTree<Comparable>::Contains(const Comparable &x) const 86 { 87 return Contains(x, root); 88 } 89 90 91 template <typename Comparable> 92 void BinarySearchTree<Comparable>::Insert(const Comparable &x) 93 { 94 return Insert(x, root); 95 } 96 97 template <typename Comparable> 98 void BinarySearchTree<Comparable>::Remove(const Comparable &x) 99 { 100 return Remove(x, root); 101 } 102 103 template <typename Comparable> 104 const Comparable & BinarySearchTree<Comparable>::FindMax() const 105 { 106 return FindMax(root)->element; 107 } 108 109 template <typename Comparable> 110 const Comparable & BinarySearchTree<Comparable>::FindMin() const 111 { 112 return FindMin(root)->element; 113 } 114 115 template <typename Comparable> 116 void BinarySearchTree<Comparable>::PrintTree(BinaryNode *t) const 117 { 118 if (t != NULL) 119 { 120 PrintTree(t->left); 121 std::cout << t->element << ' '; 122 PrintTree(t->right); 123 } 124 } 125 126 template <typename Comparable> 127 bool BinarySearchTree<Comparable>::Contains(const Comparable &x, BinaryNode *t) const 128 { 129 if (t == NULL) 130 return false; 131 else if (x < t->element) 132 return Contains(x, t->left); 133 else if (x > t->element) 134 return Contains(x, t->right); 135 else 136 return true;//匹配到 137 } 138 139 140 template <typename Comparable> 141 void BinarySearchTree<Comparable>::Insert(const Comparable &x, BinaryNode *&t) const 142 { 143 if (t == NULL) 144 t = new BinaryNode(x, NULL, NULL); 145 else if (x < t->element) 146 Insert(x, t->left); 147 else if (x > t->element) 148 Insert(x, t->right); 149 else 150 return;//重复，不插入 151 152 } 153 154 template <typename Comparable> 155 typename BinarySearchTree<Comparable>::BinaryNode * BinarySearchTree<Comparable>::FindMax(BinaryNode *t) const 156 { 157 if (t == NULL) 158 return NULL; 159 else if (t->right == NULL) 160 return t; 161 else 162 return FindMax(t->right); 163 } 164 165 template <typename Comparable> 166 typename BinarySearchTree<Comparable>::BinaryNode * BinarySearchTree<Comparable>::FindMin(BinaryNode *t) const 167 { 168 if (t == NULL) 169 return NULL; 170 else if (t->left == NULL) 171 return t; 172 else 173 return FindMin(t->left); 174 } 175 176 template <typename Comparable> 177 void BinarySearchTree<Comparable>::Remove(const Comparable &x, BinaryNode *&t) const 178 { 179 if (t == NULL) 180 return; 181 if (x < t->element) 182 Remove(x, t->left); 183 else if (x > t->element) 184 Remove(x, t->right); 185 else if (t->left != NULL && t->right != NULL)//两个儿子的结点 186 { 187 t->element = FindMin(t->right)->element; 188 Remove(t->element, t->right); 189 } 190 else 191 { 192 BinaryNode *oldNode = t; 193 t = (t->left != NULL) ? t->left : t->right; 194 delete oldNode; 195 } 196 } 197 198 199 template <typename Comparable> 200 const BinarySearchTree<Comparable> & BinarySearchTree<Comparable>::operator=(const BinarySearchTree<Comparable> &rhs) 201 { 202 if (this != &rhs) 203 { 204 MakeEmpty(); 205 root = Clone(rhs.root); 206 } 207 return *this; 208 } 209 210 211 template <typename Comparable> 212 typename BinarySearchTree<Comparable>::BinaryNode * BinarySearchTree<Comparable>::Clone(BinaryNode *t) const 213 { 214 if (t == NULL) 215 return NULL; 216 return new BinaryNode(t->element, Clone(t->left), Clone(t->right)); 217 }
BinarySearchTree.cpp
#include "BinarySearchTree.h" int main() { int value; int tmp; BinarySearchTree<int> tree; cout << "请输入整数建立二叉树(-1结束)：" << endl; while (cin >> value) { if (value == -1) break; tree.Insert(value); } cout << "二叉树中序遍历如下："; tree.PrintTree(); cout << "\n最大值：" << tree.FindMax() << endl; cout << "最小值：" << tree.FindMin() << endl; cout << "请输入要查找的值:"; cin >> tmp; if (tree.Contains(tmp)) cout << "查找到结点" << endl; else cout << "未找到结点" << endl; cout << "请输入要查找的值:"; cin >> tmp; if (tree.Contains(tmp)) cout << "查找到结点"; else cout << "未找到结点"; cout << "请输入要删除的值："; cin >> tmp; tree.Remove(tmp); cout << "已删除，删除后的二叉树为："; tree.PrintTree(); }
测试结果：
