C++ 二叉排序树BST（二叉查找树）

BST属于对无序集合排序查找算法中的一种，通过定义左小右大的规则放置无序集合中的元素，使得中序遍历能得到排序后的集合，并且任一子树都是二叉排序树。二叉排序树中右子树上任一元素大于该节点上左子树中全部元素，我是通过这个性质，写的删除，也叫后继删除。当然也可以前驱删除，从本质上来说是一样的。二叉排序树的建立、查找都是相当简单的，通过迭代、递归都可以实现，不断判断当前值是否大于小于当前节点，大于往右走，小于往左走，直到走到叶节点。删除要分为3种情况：1、叶节点可直接删除2、若只有右子树，则让右子树的根替换该节点，只有左子树的话同理3、有左右子树，找到删除节点的后继，用后继的值代替要删除节点的值，若后继有右子树又分为两种情况1、删除节点右子树上有左子树，用后继父节点的左指针指向后继的右子树2、删除节点的右子树没有左子树，那么右边的节点就代替了最左的后继，此时用后继父节点的右指针指向后继的右子树。具体就来看一看代码吧

#include<iostream>#include<ctime>using namespace std;struct Node{int data;Node* left;Node* right;};void InOrderTranversal(Node* root){if(root==0){return;}InOrderTranversal(root->left);cout<<root->data<<endl;InOrderTranversal(root->right);}void release(Node* root){if(root==0){return;}release(root->left);release(root->right);delete root;}void search(Node*& root,int key,Node**& _result){if(root==0){_result=0;return;}if(key<root->data){search(root->left,key,_result);}else if(key==root->data){_result=&root;//put purpoes's addr to result for changing the purpoes pointer point another addr by _deletereturn;}else{search(root->right,key,_result);}}void insert(Node*& root,int value){if(root==0){root=new Node;root->left=0;root->right=0;root->data=value;return;}if(value>root->data){insert(root->right,value);}else if(value==root->data){return;}else{insert(root->left,value);}}bool _delete(Node*& root,int key){Node** node;search(root,key,node);if(node==0){return false;}Node* temp=*node;if((*node)->left==0&&(*node)->right==0){//leaf node can remove now*node=0;cout<<"0"<<endl;delete temp;}else if((*node)->left==0){//if has no left,make parent link to right and remove itself*node=(*node)->right;delete temp;}else if((*node)->right==0){*node=(*node)->left;delete temp;}else{//it must have left and right//my method is subsequent move,walk to end of right's left//s init to right//s_prent init to rootNode* s=(*node)->right;Node* s_parent=*node;while(s->left!=0){s_parent=s;s=s->left;}temp->data=s->data;if(s->right!=0){//if end of right's left has right, it should replace end of right's leftif(s_parent==*node){//if s_parent does not change,s_parent has had left tree,so it should put s'right to s_parent's rights_parent->right=s->right;}else{s_parent->left=s->right;}}else{if(s_parent==root){s_parent->right=0;}else{s_parent->left=0;}}delete s;}return true; }int main(){srand(time(NULL));Node* root=new Node;root->left=0;root->right=0;root->data=10;for(int i=0;i<100;i++){insert(root,rand()%100);}InOrderTranversal(root);Node** _result;int value;cout<<"please cin the value you want to find:";cin>>value;search(root,value,_result);if(_result==0){cout<<"can't find purpoes!"<<endl;}else{cout<<"the result is:"<<(*_result)->data<<endl; }cout<<"please cin the value you want to delete:";cin>>value;if(_delete(root,value)){InOrderTranversal(root);cout<<"delete succeed!"<<endl;} else{cout<<"delete failed!"<<endl;}release(root);return 0;}