二叉搜索树ADT_BSTree

二叉搜索树或是一颗空二叉树, 或是具有以下性质的二叉树:

1.若左子树不为空, 则左子树上所有结点的关键字值均小于根结点的关键字值.

2.若右子树不为空, 则右子树上所有结点的关键字值均大于根结点的关键字值.

3.左右子树也分别是二叉搜索树.

性质: 若以中序遍历一颗二叉搜索树, 将得到一个以关键字值递增排列的有序序列.

1.搜索实现: 若二叉树为空, 则搜索失败. 否则, 将x与根结点比较. 若x小于该结点的值, 则以同样的方法搜索左子树, 不必搜索右子树. 若x

大于该结点的值, 则以同样的方法搜索右子树, 而不必搜索左子树. 若x等于该结点的值, 则搜索成功终止.

search()为递归搜索, search1()为迭代搜索.

2.插入实现: 插入一个新元素时, 需要先搜索新元素的插入位置. 如果树种有重复元素, 返回Duplicate. 搜索达到空子树, 则表明树中不包

含重复元素. 此时构造一个新结点p存放新元素x, 连至结点q, 成为q的孩子, 则新结点p成为新二叉树的根.

3.删除实现: 删除一个元素时, 先搜索被删除结点p, 并记录p的双亲结点q. 若不存在被删除的元素, 返回NotPresent. 

(1)若p有两颗非空子树, 则搜索结点p的中序遍历次序下的直接后继结点, 设为s. 将s的值复制到p中. 

(2)若p只有一颗非空子树或p是叶子, 以结点p的唯一孩子c或空子树c = NULL取代p.

(3)若p为根结点, 删除后结点c成为新的根. 否则若p是其双亲确定左孩子, 则结点c也应成为q的左孩子, 最后释放结点p所占用的空间.

实现代码:

#include "iostream"#include "cstdio"#include "cstring"#include "algorithm"#include "cmath"#include "utility"#include "map"#include "set"#include "vector"using namespace std;typedef long long ll;const int MOD = 1e9 + 7;enum ResultCode{ Underflow, Overflow, Success, Duplicate, NotPresent }; // 赋值为0, 1, 2, 3, 4, 5template <class T>class DynamicSet{public:virtual ~DynamicSet() {}virtual ResultCode Search(T &x) const = 0;virtual ResultCode Insert(T &x) = 0;virtual ResultCode Remove(T &x) = 0;/* data */};template <class T>struct BTNode{BTNode() { lChild = rChild = NULL; }BTNode(const T &x) {element = x;lChild = rChild = NULL;}BTNode(const T &x, BTNode<T> *l, BTNode<T> *r) {element = x;lChild = l;rChild = r;}T element;BTNode<T> *lChild, *rChild;/* data */};template <class T>class BSTree : public DynamicSet<T>{public:explicit BSTree() { root = NULL; } // 只可显示转换virtual ~BSTree() { Clear(root); }ResultCode Search(T &x) const;ResultCode Search1(T &x) const;ResultCode Insert(T &x);ResultCode Remove(T &x);protected:BTNode<T> *root;private:void Clear(BTNode<T> *t);ResultCode Search(BTNode<T> *p, T &x) const;/* data */};template <class T>void BSTree<T>::Clear(BTNode<T> *t){if(t) {Clear(t -> lChild);Clear(t -> rChild);cout << "delete" << t -> element << "..." << endl;delete t;}}template< class T>ResultCode BSTree<T>::Search(T &x) const{return Search(root, x);}template <class T>ResultCode BSTree<T>::Search(BTNode<T> *p, T &x) const{if(!p) return NotPresent;if(x < p -> element) return Search(p -> lChild, x);if(x > p -> element) return Search(p -> rChild, x);x = p -> element;return Success;}template <class T>ResultCode BSTree<T>::Search1(T &x) const{BTNode<T> *p = root;while(p) {if(x < p -> element) p = p -> lChild;else if(x > p -> element) p = p -> rChild;else {x = p -> element;return Success;}}return NotPresent;}template <class T>ResultCode BSTree<T>::Insert(T &x){BTNode<T> *p = root, *q = NULL;while(p) {q = p;if(x < p -> element) p = p -> lChild;else if(x > p -> element) p = p -> rChild;else {x = p -> element;return Duplicate;}}p = new BTNode<T>(x);if(!root) root = p;else if(x < q -> element) q -> lChild = p;else q -> rChild = p;return Success;}template <class T>ResultCode BSTree<T>::Remove(T &x) {BTNode<T> *c, *s, *r, *p = root, *q = NULL;while(p && p -> element != x) {q = p;if(x < p -> element) p = p -> lChild;else p = p -> rChild;}if(!p) return NotPresent;x = p -> element;if(p -> lChild && p -> rChild) {s = p -> rChild;r = p;while(s -> lChild) {r = s;s = s -> lChild;}p -> element = s -> element;p = s;q = r;}if(p -> lChild) c = p -> lChild;else c = p -> rChild;if(p == root) root = c;else if(p == q -> lChild) q -> lChild = c;else q -> rChild = c;delete p;return Success;}int main(int argc, char const *argv[]){BSTree<int> bst;int x = 28; bst.Insert(x);x = 21; bst.Insert(x);x = 25; bst.Insert(x);x = 36; bst.Insert(x);x = 33; bst.Insert(x);x = 43; bst.Insert(x);return 0;}