二分搜索树删除节点

 

 

 

#include <iostream>
#include <queue>
#include <cassert>

using namespace std;

template <typename Key, typename Value>
class BST{

private:
struct Node{
Key key;
Value value;
Node *left;
Node *right;

Node(Key key, Value value){
this->key = key;
this->value = value;
this->left = this->right = NULL;
}

Node(Node *node){
this->key = node->key;
this->value = node->value;
this->left = node->left;
this->right = node->right;
}
};

Node *root;
int count;

public:
BST(){
root = NULL;
count = 0;
}
~BST(){
destroy( root );
}

int size(){
return count;
}

bool isEmpty(){
return count == 0;
}

void insert(Key key, Value value){
root = insert(root, key, value);
}

bool contain(Key key){
return contain(root, key);
}

Value* search(Key key){
return search( root , key );
}

// 前序遍历
void preOrder(){
preOrder(root);
}

// 中序遍历
void inOrder(){
inOrder(root);
}

// 后序遍历
void postOrder(){
postOrder(root);
}

// 层序遍历
void levelOrder(){

queue<Node*> q;
q.push(root);
while( !q.empty() ){

Node *node = q.front();
q.pop();

cout<<node->key<<endl;

if( node->left )
q.push( node->left );
if( node->right )
q.push( node->right );
}
}

// 寻找最小的键值
Key minimum(){
assert( count != 0 );
Node* minNode = minimum( root );
return minNode->key;
}

// 寻找最大的键值
Key maximum(){
assert( count != 0 );
Node* maxNode = maximum(root);
return maxNode->key;
}

// 从二叉树中删除最小值所在节点
void removeMin(){
if( root )
root = removeMin( root );
}

// 从二叉树中删除最大值所在节点
void removeMax(){
if( root )
root = removeMax( root );
}

// 从二叉树中删除键值为key的节点
void remove(Key key){
root = remove(root, key);
}

private:
// 向以node为根的二叉搜索树中,插入节点(key, value)
// 返回插入新节点后的二叉搜索树的根
Node* insert(Node *node, Key key, Value value){

if( node == NULL ){
count ++;
return new Node(key, value);
}

if( key == node->key )
node->value = value;
else if( key < node->key )
node->left = insert( node->left , key, value);
else // key > node->key
node->right = insert( node->right, key, value);

return node;
}

// 查看以node为根的二叉搜索树中是否包含键值为key的节点
bool contain(Node* node, Key key){

if( node == NULL )
return false;

if( key == node->key )
return true;
else if( key < node->key )
return contain( node->left , key );
else // key > node->key
return contain( node->right , key );
}

// 在以node为根的二叉搜索树中查找key所对应的value
Value* search(Node* node, Key key){

if( node == NULL )
return NULL;

if( key == node->key )
return &(node->value);
else if( key < node->key )
return search( node->left , key );
else // key > node->key
return search( node->right, key );
}

// 对以node为根的二叉搜索树进行前序遍历
void preOrder(Node* node){

if( node != NULL ){
cout<<node->key<<endl;
preOrder(node->left);
preOrder(node->right);
}
}

// 对以node为根的二叉搜索树进行中序遍历
void inOrder(Node* node){

if( node != NULL ){
inOrder(node->left);
cout<<node->key<<endl;
inOrder(node->right);
}
}

// 对以node为根的二叉搜索树进行后序遍历
void postOrder(Node* node){

if( node != NULL ){
postOrder(node->left);
postOrder(node->right);
cout<<node->key<<endl;
}
}

void destroy(Node* node){

if( node != NULL ){
destroy( node->left );
destroy( node->right );

delete node;
count --;
}
}

// 在以node为根的二叉搜索树中,返回最小键值的节点
Node* minimum(Node* node){
if( node->left == NULL )
return node;

return minimum(node->left);
}

// 在以node为根的二叉搜索树中,返回最大键值的节点
Node* maximum(Node* node){
if( node->right == NULL )
return node;

return maximum(node->right);
}

// 删除掉以node为根的二分搜索树中的最小节点
// 返回删除节点后新的二分搜索树的根
Node* removeMin(Node* node){

if( node->left == NULL ){

Node* rightNode = node->right;
delete node;
count --;
return rightNode;
}

node->left = removeMin(node->left);
return node;
}

// 删除掉以node为根的二分搜索树中的最大节点
// 返回删除节点后新的二分搜索树的根
Node* removeMax(Node* node){

if( node->right == NULL ){

Node* leftNode = node->left;
delete node;
count --;
return leftNode;
}

node->right = removeMax(node->right);
return node;
}

// 删除掉以node为根的二分搜索树中键值为key的节点
// 返回删除节点后新的二分搜索树的根
Node* remove(Node* node, Key key){

if( node == NULL )
return NULL;

if( key < node->key ){
node->left = remove( node->left , key );
return node;
}
else if( key > node->key ){
node->right = remove( node->right, key );
return node;
}
else{ // key == node->key

if( node->left == NULL ){
Node *rightNode = node->right;
delete node;
count --;
return rightNode;
}

if( node->right == NULL ){
Node *leftNode = node->left;
delete node;
count--;
return leftNode;
}

// node->left != NULL && node->right != NULL
Node *successor = new Node(minimum(node->right));  // 注意此处的new一个新的Node不然会被removeMin所删除；

count ++;

successor->right = removeMin(node->right);
successor->left = node->left;

delete node;
count --;

return successor;
}
}
};

void shuffle( int arr[], int n ){

srand( time(NULL) );
for( int i = n-1 ; i >= 0 ; i -- ){
int x = rand()%(i+1);
swap( arr[i] , arr[x] );
}
}

int main() {

srand(time(NULL));
BST<int,int> bst = BST<int,int>();

int n = 10000;
for( int i = 0 ; i < n ; i ++ ){
int key = rand()%n;
// 为了后续测试方便,这里value值取和key值一样
int value = key;
//cout<<key<<" ";
bst.insert(key,value);
}

// test remove
// remove elements in random order
int order[n];
for( int i = 0 ; i < n ; i ++ )
order[i] = i;
shuffle( order , n );

for( int i = 0 ; i < n ; i ++ )
if( bst.contain( order[i] )){
bst.remove( order[i] );
cout<<"After remove "<<order[i]<<" size = "<<bst.size()<<endl;
}

return 0;
}