二叉搜索树的性质:
- 每个节点都有一个作为搜索依据的关键码(key),所有节点的关键码互不相同。
- 左子树上所有节点的关键码(key)都小于根节点的关键码(key)。
- 右子树上所有节点的关键码(key)都大于根节点的关键码(key)。
- 左右子树都是二叉搜索树。
//BSTree.h #pragma once template<class K,class V> struct BSTreeNode { BSTreeNode(const K& key,const V& value) :_key(key),_value(value),_left(NULL),_right(NULL) {} K _key; V _value; BSTreeNode<K,V>* _left; BSTreeNode<K,V>* _right; }; template<class K,class V> class BSTree { typedef BSTreeNode<K,V> Node; public: BSTree() :_root(NULL) {} bool Insert(const K& key,const V& value) { if(_root == NULL) { _root = new Node(key,value); } Node* cur = _root; Node* parent = NULL; while(cur) { if(cur->_key < key) { parent = cur; cur = cur->_right; } else if(cur->_key > key) { parent = cur; cur = cur->_left; } else return false; } cur = new Node(key,value); if(parent->_key < key) { parent->_right = cur; } else { parent->_left = cur; } return true; } Node* Find(const K& key) { Node* cur = _root; while(cur) { if(cur->_key < key) cur = cur->_right; else if(cur->_key > key) cur = cur->_left; else { cout<<cur->_key<<":"<<cur->_value<<endl; return cur; } } return NULL; } bool Remove(const K& key) { if(_root == NULL) { return false; } Node* cur = _root; Node* parent = NULL; //找到要删除的节点 while(cur) { if(cur->_key > key) { parent = cur; cur = cur->_left; } else if(cur->_key < key) { parent = cur; cur = cur->_right; } else { break; } } Node* del = NULL; //1.要删除节点的左孩子或者右孩子为空 if(cur->_left == NULL) { del = cur; if(parent->_left == cur) { parent->_left = cur->_right; } else { parent->_right = cur->_right; } delete del; } //删除节点的右孩子为空 else if(cur->_right == NULL) { del = cur; if(parent->_left == cur) { parent->_left = cur->_left; } else { parent->_right = cur->_left; } delete del; } // //找以该节点为根节点的左边(最大的)最右的孩子代替它,然后删除 else //要删除节点的左右孩子都不为空 { parent = cur; //找以该节点为根节点的右边(最小的)最左的孩子代替它,然后删除 Node* subLeft = cur->_right; while(subLeft->_left) { parent = subLeft; subLeft = subLeft->_left; } cur->_key = subLeft->_key; cur->_value = subLeft->_value; if(parent->_left == subLeft) parent->_left = subLeft->_right; else parent->_right = subLeft->_right; delete subLeft; } return false; } //递归插入 bool InsertR(const K& key,const V& value) { return _InsertR(_root,key,value); } //递归删除 bool RemoveR(const K& key) { return _RemoveR(_root,key); } //递归查找 Node* FindR(const K& key) { return _FindR(_root,key); } void InOrder() { _InOrder(_root); cout<<endl; } protected: bool _InsertR(Node*& root,const K& key,const V& value) { if(root == NULL) { root = new Node(key,value); return true; } if(root->_key > key) { return _InsertR(root->_left,value); } else if(root->_key < key) { return _InsertR(root->_right,value); } else { return false; } } //递归的删除一个节点 bool _RemoveR(Node*& root,const K& key) { if(root == NULL) { return false; } if(root->_key < key) { _RemoveR(root->_right,key); } else if(root->_key > key) { _RemoveR(root->_left,key); } else { Node* del = root; if(root->_left == NULL) { root = root->_right; } else if(root->_right == NULL) { root = root->_left; } else { Node* subLeft = root->_right; while(subLeft->_left) { subLeft = subLeft->_left; } swap(root->_key,subLeft->_key); swap(root->_value,subLeft->_value); return _RemoveR(root->_right,key); } delete del; } return true; } Node* _FindR(Node*& root,const K& key) { if(_root == NULL) { return NULL; } if(root->_key > key) { _FindR(root->_left,key); } else if(root->_key < key) { _FindR(root->_right,key); } else { cout<<root->_key<<":"<<root->_value<<endl; return root; } return NULL; } void _InOrder(Node* root) { if(root == NULL) { return; } _InOrder(root->_left); cout<<root->_key<<" "; _InOrder(root->_right); } protected: Node* _root; }; //测试迭代 void TestTree() { BSTree<int,int> bst; int a[] = {5,3,7,1,4,6,8,2,9}; for(size_t i = 0; i < sizeof(a)/sizeof(a[0]); i++) { bst.Insert(a[i],i); } bst.InOrder(); BSTreeNode<int,int>* ret = bst.Find(6); bst.Remove(9); bst.InOrder(); bst.Remove(7); bst.InOrder(); bst.Remove(5); bst.InOrder(); bst.Remove(3); bst.InOrder(); } //测试递归 void TestTreeR() { BSTree<int,int> bst1; int a1[] = {5,9}; for(size_t i = 0; i < sizeof(a1)/sizeof(a1[0]); i++) { bst1.InsertR(a1[i],i); } bst1.InOrder(); BSTreeNode<int,int>* ret1 = bst1.FindR(6); bst1.RemoveR(9); bst1.InOrder(); bst1.RemoveR(5); bst1.InOrder(); bst1.RemoveR(3); bst1.InOrder(); bst1.RemoveR(7); bst1.InOrder(); bst1.RemoveR(8); bst1.InOrder(); bst1.RemoveR(2); bst1.InOrder(); bst1.RemoveR(6); bst1.InOrder(); }
//Test.cpp #include<iostream> using namespace std; #include"BSTree.h" int main() { //TestTree(); TestTreeR(); getchar(); return 0; }