首先，我已经阅读了C++ 二叉搜索树状态访问冲突错误，其中包括添加节点和插入二叉搜索树访问冲突错误，但我仍然无法完全实现我的二叉树。我目前在我的 get height 类中遇到访问冲突，但不知道为什么。
template <typename Item, typename Key>
std::size_t BinarySearchTree<Item, Key>::height(TreeNode* node) const{
if (node == NULL)
return 0;
//Debug
if(node == NULL)
std::cout<< "node = Null"<< endl;
else
std::cout<< "node != Null"<< endl;
if(node->left == NULL)
std::cout<< "left = Null"<< endl;
else
std::cout<< "left != Null"<< endl;
if(node->right == NULL)
std::cout<< "right = Null"<< endl;
else
std::cout<< "right != Null"<< endl;
//This will go through the list adding 1 at each layer it passes through
std::size_t left = height(node->left);
std::size_t right = height(node->right);
//This will return the branch with the greatest height
return 1 + std::max(left, right);
}
这就是我向树中添加元素的方式
template <typename Item, typename Key>
void BinarySearchTree<Item, Key>::insert(const Item& value){
insert(root, value);//start at the root node
}//end insert
template <typename Item, typename Key>
void BinarySearchTree<Item, Key>::insert(TreeNode* node, const Item& value){
//if item == tree->data then stop the method
if (node == NULL){
//Populate the null leaf node
TreeNode* target = new TreeNode(value);//create a new node for the inserted parameter
target->data = value;//the data is stored in the target node
//increment the size counter
treeSize++;
}else if (value < node->data)
//If the item is less than the current nodes data then insert again
insert(node->left, value);
else
//If the item is greater than the current nodes data then insert again
insert(node->right, value);
}
我不知道我怎么会遇到访问冲突，因为我在调用左节点或右节点之前检查了空指针。任何见解将不胜感激。
编辑：我还应该注意节点的左叶和右叶被初始化为NULL。
完整代码：
#pragma once
#include <cstdlib>
namespace MySpace{
template <typename Item, typename Key = Item>
class BinarySearchTree{
// private node class (only visible inside the BinarySearchTree class)
struct TreeNode {
TreeNode(const Item& data = Item()) :
data(data), left(NULL), right(NULL) { }
~TreeNode(){
delete left; delete right;
left = NULL; right = NULL;
}
Item data;//This is the object
TreeNode* left; // left child
TreeNode* right; // right child
};
public:
//==========================Constructor=============================
// creates an empty tree
BinarySearchTree(){root = NULL; treeSize = 0;}
// Postcondition: A copy of the binary search tree
BinarySearchTree(BinarySearchTree<Item, Key>& source);
//==========================Destructor================================
~BinarySearchTree(){delete root; root = NULL;}//will delete all branches recursively
//=========================Public Methods============================
// Postcondition: the current tree has been replaced with a copy of
// the source binary serch tree. The return value is the calling object
BinarySearchTree<Item, Key>& operator =(BinarySearchTree<Item, Key>& source);
// returns the number of nodes in the tree
std::size_t size() const{return treeSize;}
// returns the height of the tree
std::size_t height() const;
// returns the minimum value in the tree
const Item& min() const;
// returns the maximum value in the tree
const Item& max() const;
// inserts a copy of the given value into the tree, unless one already exists
void insert(const Item& value);
// removes an entry with the given key, if present in the tree
bool remove(const Key& key);
// returns a pointer to an entry with the given key (if it exists), or NULL
Item* search(const Key& key) const;
// if an entry with the key exists, applies the function
template <typename Function>
bool apply(const Key& key, Function f);
// applies a function to each value in the tree, via preorder traversal
template <typename Function>
void preorder(Function f);
// applies a function to each value in the tree, via inorder traversal
template <typename Function>
void inorder(Function f);
// applies a function to each value in the tree, via postorder traversal
template <typename Function>
void postorder(Function f);
//Copy the nodes of a BST
TreeNode* copy(const TreeNode *node){
//If the passed node is Null then return null
if (node == NULL)
return NULL;
Item nodeData = node->data;
TreeNode* copyNode = new TreeNode(nodeData);//create a new node with the data from the last one
copyNode->data = node->data;
copyNode->left = copy(node->left);
copyNode->right = copy(node->right);
return copyNode;
}
//=========================Accessor============================
TreeNode* getRoot(){return root;}
private:
//This is the root node for the binary tree
TreeNode* root;
std::size_t treeSize;
//Checks the size of the BST to see if it is empty or not
bool isEmpty() const{return(treeSize == 0)?true:false;}
//These methods are used for recursion
Item* search(TreeNode* node, const Key& key) const;
void insert(TreeNode* node, const Item& value);
bool remove(TreeNode* node, const Key& key);
std::size_t height(TreeNode* node) const;
const Item& min(TreeNode* node) const;
const Item& max(TreeNode* node) const;
template <typename Function>
void preorder(TreeNode* node, Function f);
template <typename Function>
void inorder(TreeNode* node, Function f);
template <typename Function>
void postorder(TreeNode* node, Function f);
};
//------------------------This is where the methods will get implemented------------------------
//Copy constructor
template <typename Item, typename Key>
BinarySearchTree<Item, Key>::BinarySearchTree(BinarySearchTree<Item, Key>& source){
treeSize = source.size();
TreeNode* tempNode = source.getRoot();
//copy(tempNode);
}
template <typename Item, typename Key>
BinarySearchTree<Item, Key>& BinarySearchTree<Item, Key>::operator =(BinarySearchTree<Item, Key>& source){
if(&source == this)
return *this;
treeSize = source.size();
TreeNode* tempNode = source.getRoot();
//copy(tempNode);
return *this;
}
template <typename Item, typename Key>
std::size_t BinarySearchTree<Item, Key>::height() const{
if(root == NULL)
std::cout<< "AAAAAAHHHHHHH!"<< endl;
else
std::cout<< "okay!"<< endl;
return height(root);//start at the root
}
template <typename Item, typename Key>
std::size_t BinarySearchTree<Item, Key>::height(TreeNode* node) const{
if (node == NULL)
return 0;
//Debug
if(node == NULL)
std::cout<< "node = Null"<< endl;
else
std::cout<< "node != Null"<< endl;
if(node->left == NULL)
std::cout<< "left = Null"<< endl;
else
std::cout<< "left != Null"<< endl;
if(node->right == NULL)
std::cout<< "right = Null"<< endl;
else
std::cout<< "right != Null"<< endl;
//This will go through the list adding 1 at each layer it passes through
std::size_t left = height(node->left);
std::size_t right = height(node->right);
//This will return the branch with the greatest height
return 1 + std::max(left, right);
}
template <typename Item, typename Key>
const Item& BinarySearchTree<Item, Key>::min() const{
return min(root);//start at the root
}
template <typename Item, typename Key>
const Item& BinarySearchTree<Item, Key>::min(TreeNode* node) const{
if(!isEmpty()){
//goes recursively until the left most leaf is found
if(node->left == NULL)
return node->data;
else
min(node->left);
}
return Item();
}
template <typename Item, typename Key>
const Item& BinarySearchTree<Item, Key>::max() const{
return max(root);//start at the root
}
template <typename Item, typename Key>
const Item& BinarySearchTree<Item, Key>::max(TreeNode* node) const{
if(!isEmpty()){
//goes recursively until the right most leaf is found
if(node->right == NULL)
return node->data;
else
max(node->right);
}
return Item();
}
template <typename Item, typename Key>
void BinarySearchTree<Item, Key>::insert(const Item& value){
insert(root, value);//start at the root node
}//end insert
template <typename Item, typename Key>
void BinarySearchTree<Item, Key>::insert(TreeNode* node, const Item& value){
//if item == tree->data then stop the method
if (node == NULL){
//Populate the null leaf node
TreeNode* target = new TreeNode(value);//create a new node for the inserted parameter
target->data = value;//the data is stored in the target node
node = target;
//increment the size counter
treeSize++;
}else if (value < node->data)
//If the item is less than the current nodes data then insert again
insert(node->left, value);
else
//If the item is greater than the current nodes data then insert again
insert(node->right, value);
}
template <typename Item, typename Key>
bool BinarySearchTree<Item, Key>::remove(const Key& key){
return remove(root, key);//default is to return false
}
template <typename Item, typename Key>
bool BinarySearchTree<Item, Key>::remove(TreeNode* node, const Key& key){
//If the tree is not empty
if(!isEmpty()){
if (key < node->data)
//If the key is less than the Item than go to the left branch
remove(node->left, key);
else if (key > node->data)
//If the key is less than the Item than go to the right branch
remove(node->right, key);
else{
//If the key is equal to the Item then...
//decrement size
treeSize--;
// There are several cases I have to deal with
// 1) a leaf node - easy
// 2) a node with 1 child - left or right
// 3) a node with 2 children - left and right
if(node->left == NULL && node->right == NULL){
delete node;//If the node was a leaf then just delete it
node = NULL;
}else if(node->left != NULL || node->right != NULL){
TreeNode* tempNode = node;
//If either branch is empty, then delete the node
delete node;
//now set the node to the non empty branch
node = (tempNode->left != NULL)?tempNode->left:tempNode->right;
}else{
//if there are two branches then make the right branch the node
TreeNode* switchNode = node->right;
//gets the left most node on the right branch
while(switchNode->left != NULL){
switchNode = switchNode->left;
}
//This puts the data into the passed node, but does not delete it!
node->data = switchNode->data;
//I don't know how many children the switch node has(Either 0 or 1), so I have to run the
//method again on the switch node to remove it properly
remove(switchNode, switchNode->data);
}
return true;//return true since the item was deleted
}//end if
}//end if not empty
return false;
}
template <typename Item, typename Key>
Item* BinarySearchTree<Item, Key>::search(const Key& key) const{
return search(root, key);
}
template <typename Item, typename Key>
Item* BinarySearchTree<Item, Key>::search(TreeNode* node, const Key& key) const{
if (node == NULL){
//If there is no node at this location return null
return NULL;
}else if (key < node->data)
//If the key is less than the Item than go to the left branch
search(node->left, key);
else if (key > node->data)
//If the key is less than the Item than go to the right branch
search(node->right, key);
else
//If the key is equal to the Item than return the item
return &node->data;
}
template <typename Item, typename Key>
template <typename Function>
bool BinarySearchTree<Item, Key>::apply(const Key& key, Function f){
Item* data = search(key);
if(data != NULL){
f(*data);//do the function on the selected item
return true;
}
return false;
}
template <typename Item, typename Key>
template <typename Function>
void BinarySearchTree<Item, Key>::preorder(Function f){
preorder(root, f);//start at the root
}
template <typename Item, typename Key = Item>
template <typename Function>
void BinarySearchTree<Item, Key>::preorder(TreeNode* node, Function f){
//If the node is not null then do the method
if(node != NULL){
//Then apply the function to the data
f(node->data);
//Do the branches last
if(node->left) preorder(node->left, f);
if(node->right) preorder(node->right, f);
}else
return;
}
template <typename Item, typename Key>
template <typename Function>
void BinarySearchTree<Item, Key>::inorder(Function f){
inorder(root, f);//start at the root
}
template <typename Item, typename Key = Item>
template <typename Function>
void BinarySearchTree<Item, Key>::inorder(TreeNode* node, Function f){
//If the node is not null then do the method
if(node != NULL){
//Do the function in between the two branches
if(node->left) inorder(node->left, f);
//Then apply the function to the data
f(node->data);
if(node->right) inorder(node->right, f);
}else
return;
}
template <typename Item, typename Key = Item>
template <typename Function>
void BinarySearchTree<Item, Key>::postorder(Function f){
postorder(root, f);//start at the root
}
template <typename Item, typename Key = Item>
template <typename Function>
void BinarySearchTree<Item, Key>::postorder(TreeNode* node, Function f){
//If the node is not null then do the method
if(node != NULL){
//Do the function in between the two branches
if(node->left) postorder(node->left, f);
if(node->right) postorder(node->right, f);
//Then apply the function to the data
f(node->data);
}else
return;
}
}
这是主要功能所在
#include "BinarySearchTree.h"
#include <iostream>
#include <vector>
#include <cassert>
#include <algorithm>
#include <utility>
#include <cmath>
#include <sstream>
using namespace std;
using namespace MySpace;
using namespace rel_ops;
#define TreeType BinarySearchTree
#define BALANCED false
// #define ITERATORS
// returns the ideal height of a tree with n nodes
size_t balanced_height(size_t n) {
return (n < 2) ? n : 1 + (size_t) (log10((double) n) / log10(2.0));
}
// a simple compound data type
struct Person {
string name;
int age;
bool operator <(const Person& other) const { return (name < other.name); }
bool operator ==(const Person& other) const { return (name == other.name); }
operator string() const { return name; }
};
// operators for comparing a string to a Person (a Key to an Item)
bool operator <(const string& L, const Person& R) { return L < R.name; }
bool operator >(const string& L, const Person& R) { return L > R.name; }
bool operator ==(const string& L, const Person& R) { return L == R.name; }
bool operator !=(const string& L, const Person& R) { return L != R.name; }
bool operator <=(const string& L, const Person& R) { return L <= R.name; }
bool operator >=(const string& L, const Person& R) { return L >= R.name; }
// output operator for Person class
ostream& operator <<(ostream& out, const Person& p) { return out << p.name; }
template <typename Item, typename Key>
void test_tree(TreeType<Item, Key>, const vector<Item>&);
int main() {
const size_t NUM_VALUES = 15;
// create vectors containing the values to use
vector<int> nums(NUM_VALUES);
vector<Person> people(NUM_VALUES);
// populate them with values
for (size_t i = 0; i < NUM_VALUES; i++) {
nums[i] = people[i].age = i;
people[i].name = char('A' + i);
}
// create the empty trees
TreeType<int> t1;
TreeType<Person, string> t2;
// testing when the data type is also the key
cout << "Testing case when Item type is also the Key type... " << endl;
test_tree(t1, nums);
cout << "Passed!\n\n";
// testing when the Item type has a different Key type
cout << "Testing case with different Item and Key types... " << endl;
test_tree(t2, people);
cout << "Passed!\n\n";
// all tests passed
cout << "Nicely done!" << endl;
return EXIT_SUCCESS;
}
// simple stringstreams for testing purposes
stringstream s1, s2;
// outputs a value to the stringstream for testing
template <typename Item>
void output_value(Item& data) {
s1 << data;
}
// inserts the contents of the vector in way that yields a balanced tree
template <typename Item, typename Key>
void balanced_insert(TreeType<Item, Key>& tree, const vector<Item> values, int beg, int end) {
if (beg > end) return;
size_t mid = ceil((beg + end) / 2.0);
tree.insert(values[mid]);
if (beg != end) {
balanced_insert(tree, values, beg, mid - 1);
balanced_insert(tree, values, mid + 1, end);
}
}
// fills ss with data in preorder fashion
template <typename Item>
void vector_preorder(stringstream& ss, const vector<Item> values, int beg, int end) {
if (beg > end) return;
size_t mid = ceil((beg + end) / 2.0);
ss << values[mid];
if (beg != end) {
vector_preorder(ss, values, beg, mid - 1);
vector_preorder(ss, values, mid + 1, end);
}
}
// fills ss with data in inorder fashion
template <typename Item>
void vector_inorder(stringstream& ss, const vector<Item> values, int beg, int end) {
if (beg > end) return;
size_t mid = ceil((beg + end) / 2.0);
if (beg != end) vector_inorder(ss, values, beg, mid - 1);
ss << values[mid];
if (beg != end) vector_inorder(ss, values, mid + 1, end);
}
// fills ss with data in postorder fashion
template <typename Item>
void vector_postorder(stringstream& ss, const vector<Item> values, int beg, int end) {
if (beg > end) return;
size_t mid = ceil((beg + end) / 2.0);
if (beg != end) {
vector_postorder(ss, values, beg, mid - 1);
vector_postorder(ss, values, mid + 1, end);
}
ss << values[mid];
}
template <typename Item, typename Key>
void test_tree(TreeType<Item, Key> tree, const vector<Item>& values) {
// tree should initially be empty
assert(tree.size() == 0);
assert(tree.height() == 0);
std::cout<<"DIM TEST 1 COMPLETE!"<<endl;
// insert a single value (becomes root of tree)
tree.insert(values[0]);
// ensure that the tree has a size and height of 1...
assert(tree.size() == 1);
assert(tree.height() == 1);
std::cout<<"DIM TEST 2 COMPLETE!"<<endl;
// ensure the value appears in the tree...
assert(tree.search(values[0]));
// and that your function correctly returns a pointer to the value
assert(*tree.search(values[0]) == values[0]);
std::cout<<"SEARCH 1 COMPLETE!"<<endl;
// testing removing the root node (resulting in an empty tree)
assert(tree.remove(values[0]));
std::cout<<"REMOVE 1 COMPLETE!"<<endl;
// ensure that the tree is once again empty...
assert(tree.size() == 0);
assert(tree.height() == 0);
std::cout<<"DIM TEST 3 COMPLETE!"<<endl;
// ensure that removing a non-existent value doesn't fail (should return false)
assert(!tree.remove(values[0]));
std::cout<<"REMOVE 2 COMPLETE!"<<endl;
// ensure that the value no longer appears in the tree...
assert(!tree.search(values[0]));
std::cout<<"SEARCH 2 COMPLETE!"<<endl;
// insert all the values this time in sorted order...
for (size_t i = 0; i < values.size(); i++) {
tree.insert(values[i]);
// ensure the value appears in the tree...
assert(tree.search(values[i]));
// ensure that the size is correct...
assert(tree.size() == i + 1);
// height of tree depends on whether you're balancing as you go or not
assert(tree.height() == (BALANCED ? balanced_height(tree.size()) : tree.size()));
}
std::cout<<"INSERT 1 COMPLETE!"<<endl;
// ensure min and max work
assert(tree.min() == *min_element(values.begin(), values.end()));
assert(tree.max() == *max_element(values.begin(), values.end()));
// remove all the values, starting with the root
for (size_t i = 0; i < values.size(); i++) {
// remove the value
tree.remove(values[i]);
// ensure the value no longer appears in the tree...
assert(!tree.search(values[i]));
// ensure that the size is correct...
assert(tree.size() == values.size() - i - 1);
// height of tree depends on whether you're balancing as you go or not
assert(tree.height() == (BALANCED ? balanced_height(tree.size()) : tree.size()));
}
std::cout<<"REMOVE 3 COMPLETE!"<<endl;
// insert all the values this time in balanced order...
balanced_insert(tree, values, 0, values.size() - 1);
std::cout<<"INSERT 2 COMPLETE!"<<endl;
// make sure the size is still right...
assert(tree.size() == values.size());
// height of tree should be ceil(log2(n))
assert(tree.height() == balanced_height(tree.size()));
std::cout<<"DIM TEST 4 COMPLETE!"<<endl;
// can't insert duplicate values (size & height shouldn't increase)
// operation should simply fail silently (do nothing)
tree.insert(values[0]);
assert(tree.size() == values.size());
assert(tree.height() == balanced_height(values.size()));
// ensure min and max (still) work
assert(tree.min() == *min_element(values.begin(), values.end()));
assert(tree.max() == *max_element(values.begin(), values.end()));
std::cout<<"MIN MAX 1 COMPLETE!"<<endl;
// testing copy constructor
TreeType<Item, Key>* copy = new TreeType<Item, Key>(tree);
assert(copy->size() == tree.size());
assert(copy->height() == tree.height());
std::cout<<"DIM TEST 5 COMPLETE!"<<endl;
// original should remain unchanged after copy modification
copy->remove(values[1]);
copy->remove(values[values.size() - 2]);
assert(copy->size() == tree.size() - 2);
assert(tree.search(values[1]));
assert(tree.search(values[values.size() - 2]));
std::cout<<"REMOVE 4 COMPLETE!"<<endl;
// testing destructor
delete copy;
// the original should remain unchanged
for (size_t i = 0; i < values.size(); i++) {
assert(tree.search(values[i]));
}
// testing assignment operator
copy = new TreeType<Item, Key>;
*copy = tree;
// original should remain unchanged after copy modification
copy->remove(values[1]);
copy->remove(values[values.size() - 2]);
assert(copy->size() == tree.size() - 2);
assert(tree.search(values[1]));
assert(tree.search(values[values.size() - 2]));
// testing destructor
delete copy;
// the original should remain unchanged
for (size_t i = 0; i < values.size(); i++) {
assert(tree.search(values[i]));
}
// testing preorder traversal
s1.str(""); s2.str("");
vector_preorder(s2, values, 0, values.size() - 1);
tree.preorder(output_value<Item>);
assert(s1.str() == s2.str());
// testing inorder traversal
s1.str(""); s2.str("");
vector_inorder(s2, values, 0, values.size() - 1);
tree.inorder(output_value<Item>);
assert(s1.str() == s2.str());
// testing postorder traversal
s1.str(""); s2.str("");
vector_postorder(s2, values, 0, values.size() - 1);
tree.postorder(output_value<Item>);
assert(s1.str() == s2.str());
// testing apply
s1.str(""); s2.str("");
s2 << values[0];
tree.apply(values[0], output_value<Item>);
assert(s1.str() == s2.str());
#ifdef ITERATORS
// testing iterators (smallest-to-largest order)
typename TreeType<Item, Key>::iterator t = tree.begin();
typename vector<Item>::const_iterator v = values.begin();
while (t != tree.end()) {
assert(*t == *v);
++t;
++v;
}
assert(v == values.end());
#endif
}