二叉搜索树BST的C++实现

BST

包含的功能：插入，删除，查找，查找某一结点的后续和前驱，中序遍历和前序遍历

这里，用于实验的二叉树:

//二叉搜索树BST#include <iostream> #include <vector>using namespace std;class TreeNode{public:int key;TreeNode* left;TreeNode* right;TreeNode* p;//指向父节点 public:TreeNode();TreeNode(int val);};TreeNode::TreeNode(){key=0;left=right=p=NULL;}TreeNode::TreeNode(int val){key=val;left=right=p=NULL;}void inorder_tree_walk(TreeNode* x){if(x!=NULL){inorder_tree_walk(x->left);cout<<x->key<<" ";inorder_tree_walk(x->right);}else return;}void preorder_tree_walk(TreeNode*x){if(x){cout<<x->key<<" ";preorder_tree_walk(x->left);preorder_tree_walk(x->right);}} TreeNode* tree_search(TreeNode* x, int k){if(x==NULL||k==x->key)return x;if(k<x->key)return tree_search(x->left,k);else return tree_search(x->right,k);}TreeNode* tree_minmum(TreeNode* x){while(x->left!=NULL)x=x->left;return x;}TreeNode* tree_maxmum(TreeNode* x){while(x->right!=NULL)x=x->right;return x;}TreeNode* tree_successor(TreeNode* x)//大于x.key的最小关键字的节点为后继 {if(x->right) return tree_minmum(x->right);TreeNode* y=x->p;while(y&& x==y->right){x=y;y=y->p;}return y;} TreeNode* tree_predecessor(TreeNode* x)//小于x.key的最大关键字的节点为前驱 {if(x->left) return tree_maxmum(x->left);TreeNode* y=x->p;while(y&& x==y->left){x=y;y=y->p;}return y;} //c插入void tree_insert(TreeNode* T, TreeNode* z) //T是现在的BST的树根{TreeNode * y,*x=T;while(x){y=x;if(z->key<x->key)x=x->left;else x=x->right; }  z->p=y; if(!y) T=z;//T是颗空树 else if(z->key<y->key) y->left=z; else y->right=z;// return T; } //删除节点void transplant(TreeNode* T, TreeNode* u,TreeNode* v)//用一颗子树代v替另一个子树u {if(u->p==NULL)T=v;else if(u==u->p->left) u->p->left=v;else u->p->right=v;if(v)v->p=u->p; }  void tree_delete(TreeNode* T, TreeNode* z) { if(!z->left) transplant(T,z,z->right); else if(!z->right) transplant(T,z,z->left); else { TreeNode* y=tree_minmum(z->right); if(y->p!=z) { transplant(T,y,y->right); y->right=z->right; y->right->p=y; } transplant(T,z,y); y->left=z->left; y->left->p=y; } } int main(){ TreeNode* T=new TreeNode(15); //inorder_tree_walk(T); int a[10]={6,18,3,7,17,20,2,4,13,9}; for(int i=0;i<10;i++) {TreeNode* z=new TreeNode(a[i]);       tree_insert(T,z);} inorder_tree_walk(T);cout<<endl; preorder_tree_walk(T); TreeNode* min=tree_minmum(T); TreeNode* max=tree_maxmum(T);cout<<endl; cout<<"最大值："<<max->key<<"  最小值："<<min->key<<endl; cout<<"查找z=13的节点："; TreeNode* z=tree_search(T,13);cout<<z->key<<endl; TreeNode* prez=tree_predecessor(z); TreeNode* sucz=tree_successor(z); cout<<"z的前驱："<<prez->key<<" "<<"z的后继："<<sucz->key<<endl; tree_delete(T,z); cout<<"删除z之后：";  inorder_tree_walk(T);cout<<endl; }

说明：第一行是中序遍历，第二行是先序遍历。