二叉查找树_前序遍历_中序_后序_递归与非递归写法_层次遍历_以及树形显示

#include <iostream>
#include <stack>
using namespace std;

template<typename T>
struct BinaryNode
{
    T element;
    BinaryNode<T> *left;
    BinaryNode<T> *right;

    BinaryNode(const T &theElement, BinaryNode *lt, BinaryNode *rt)
        : element(theElement), left(lt), right(rt) {}
};


template<typename T>
class BinarySearchTree
{
public:
    BinarySearchTree() {
        root = nullptr;
    }
    BinarySearchTree(const BinarySearchTree& rhs) {  //复制构造函数
        root = clone(rhs.root);
    }
    ~BinarySearchTree();

    const T &findMin() const {
        return findMin(root)->element;
    }
    const T &findMax() const {
        return findMax(root)->element;
    }
    
    bool contains(const T& x) const;
    T& getNode(const T& e) {                        //得到元素为e的结点 
        return getNode(e, root)->element;
    }
    
    bool isEmpty() const {
        if (root == nullptr)
            return true;
        return false;
    }
    void PreprintTree() const {
        PreprintTree(root);
    }
    
    void InprintTree() const {
        InprintTree(root);
    }
    
    void PostprintTree() const {
        PostprintTree(root);
    }
    
    void LevelprintTree() const {
        LevelprintTree(root);
    }
    
    void PreprintTree_N() const {
        PreprintTree_N(root); 
    }
    
    void InprintTree_N() const {
        InprintTree_N(root);
    }
    
    void PostprintTree_N() const {
        PostprintTree_N(root);
    }
    
    void DisplayTreeShape(int level = 1) const {
        DisplayTreeShape(root, level);
    }

    void makeEmpty();
    void insert(const T &x);
    void remove(const T &x);
    int Depth(); 
    int CountLeaf() {
        BinaryNode<T> *p = root;
        int count = 0;
        CountLeaf(p, count);
        return count;
    }
    
    const BinarySearchTree& operator = (const BinarySearchTree& rhs);

private:

    BinaryNode<T> *root;                      //指向树根结点的指针

    void insert(const T & x, BinaryNode<T> * & t);  
    void remove(const T & x, BinaryNode<T> * & t);
    BinaryNode<T> * findMin(BinaryNode<T> *t) const;
    BinaryNode<T> * findMax(BinaryNode<T> *t ) const;
    
    bool contains(const T & x, BinaryNode<T> *t) const;
    BinaryNode<T> * getNode(const T &x, BinaryNode<T> *t);
    
    void makeEmpty( BinaryNode<T> * & t );                  
    //利用 递归 算法 计算树的 深度 
    int Depth( BinaryNode<T> * t, int level, int &depth);
    //利用 递归 算法 计算树的 高度
    void CountLeaf(BinaryNode<T> * t, int &count);
    
        
    void PreprintTree( BinaryNode<T> * t ) const;           //先序遍历 
    void InprintTree( BinaryNode<T> *t ) const;             //中序遍历   
    void PostprintTree( BinaryNode<T> * t ) const;          //后序遍历
    void LevelprintTree( BinaryNode<T> * t) const;          //层次遍历 
    
    void PreprintTree_N( BinaryNode<T> * t) const;          //非递归先序遍历
    void InprintTree_N( BinaryNode<T> * t) const;           //非递归中序遍历二叉树 
    void PostprintTree_N( BinaryNode<T> * t) const;         //非递归后序遍历二叉树 
    void DisplayTreeShape(BinaryNode<T> *bt, int level) const;    //二叉树的树形显示算法 
    
      
    BinaryNode<T> * clone( BinaryNode<T> * t ) const;
};

template<typename T>
bool BinarySearchTree<T>::contains(const T& x) const
{
    return contains(x, root);
}

template<typename T>
bool BinarySearchTree<T>::contains(const T & x, BinaryNode<T> *t) const
{
    if (t == nullptr)
        return false;
    else if (x < t->element)          // x 小， 说明应该在左边找
        return contains(x, t->left);
    else if (t->element < x)          // x 大， 说明应该在右面找
        return contains(x, t->right);
    else 
        return true;
}

template<typename T>
BinaryNode<T>* BinarySearchTree<T>::getNode(const T & x, BinaryNode<T> *t)
{
    if (t == nullptr) 
        return nullptr;
    else if (x < t->element)
        return getNode(x, t->left);
    else if (t->element < x)
        return getNode(x, t->right);
    return t;
}


//findMin--返回指向树中包含最小元的结点的指针
template<typename T>
BinaryNode<T> * BinarySearchTree<T>::findMin(BinaryNode<T> *t) const
{
    if (t == nullptr)
        return  nullptr;
    if (t->left == nullptr)
        return t;
    return findMin(t->left);
}

template<typename T>
BinaryNode<T>* BinarySearchTree<T>::findMax(BinaryNode<T> *t) const
{
    if (t != nullptr)
        while (t->right != nullptr) {
            t = t->right;
        }
    return t;
}

template<typename T>
void BinarySearchTree<T>::insert(const T &x)
{
    insert(x, root);
}

/************************************************************************/
/* x is the item to insert        */
/* t is the node that roots the subtree*/
/* Set the new root of the subtree*/
///* 只有当一个新树叶生成时候，t才改变.
///* t 是到p->left或p->right的引用.==> 意味着p->left或p->right将会改变为指向新结点.
/************************************************************************/
template<typename T>
void BinarySearchTree<T>::insert(const T & x, BinaryNode<T> * & t)
{
    if (t == nullptr)         //没有结点，在该位置处添加新结点
        t = new BinaryNode<T>(x, nullptr, nullptr);
    else if (x < t->element)  //x 小， 在左子树查询
        insert(x, t->left);  
    else if (t->element < x)  //x 大， 在右子树查询
        insert(x, t->right);
    else;                     //Duplicate, do nothing;
}

template<typename T>
void BinarySearchTree<T>::remove(const T &x)
{
    remove(x, root);
}

/************************************************************************/
/* x is item to remove                                                  */
/* t is the node that roots the subtree                                 */
/* Set the new root of the subtree                                      */
/* 1.结点是一片树叶时 -- 可被立即删除*/
/* 2.结点有一个儿子, 则该结点可以在其父节点调整他的链 以绕过该结点后被删除 */
/* 3.结点有两个儿子, 则其右子树的最小数据代替该结点的数据，并递归删除那个结点 */
/* 注: 右子树中的最小的结点不可能有左结点                               */
/************************************************************************/
template<typename T>
void BinarySearchTree<T>::remove(const T &x, BinaryNode<T> * & t)
{
    if (t == nullptr) return;     //Item not found; do nothing
    if (x < t->element)           //x 小，在左子树递归查找
        remove(x, t->left);
    else if (t->element < x)      //x 大，在右子树递归查找
        remove(x, t->right); 
    else if (t->left != nullptr && t->right != nullptr)  //two children
    {
        //在右子树中查找最小数据代替该结点数据.;
        t->element = findMin(t->right)->element;
        remove(t->element, t->right);                    //删除该结点
    }
    else                         //只有一个结点或是树叶. 调整它的链,以绕过该结点后被删除.
    {                          
        BinaryNode<T> *oldNode = t;
        t = (t->left != nullptr) ? t->left : t->right;
        delete oldNode;
    }
}

/************************************************************************/
///* Destructor for the tree
/************************************************************************/
template<typename T>
BinarySearchTree<T>::~BinarySearchTree()
{
    makeEmpty();
}

template<typename T>
void BinarySearchTree<T>::makeEmpty()       //公有函数
{
    makeEmpty(root);
}

/************************************************************************/
///* Internal method to make subtree empty -- 私有函数
/************************************************************************/
template<typename T>
void BinarySearchTree<T>::makeEmpty(BinaryNode<T> * & t)   
{
    if (t != nullptr)
    {
        makeEmpty(t->left);
        makeEmpty(t->right);
        delete t;
    }
    t = nullptr;
}

/************************************************************************/
///* Deep copy
/************************************************************************/
template<typename T>
const BinarySearchTree<T>& BinarySearchTree<T>::operator = (const BinarySearchTree &rhs)
{
    if (this != &rhs) {
        makeEmpty();
        root = clone(rhs.root);
    }
    return *this;
}

/************************************************************************/
///* Internal method to clone subtree.  --  递归复制结点
/************************************************************************/
template<typename T>
BinaryNode<T>* BinarySearchTree<T>::clone(BinaryNode<T> * t) const
{
    if (t == nullptr)
        return nullptr;
    return new BinaryNode<T>( t->element, clone(t->left), clone(t->right) );
}

//利用递归计算树的深度 
template<typename T>
int BinarySearchTree<T>::Depth()
{
    BinaryNode<T> *t = root;
    int depth = 0;
    if (root == nullptr) 
        return 0;
    Depth(t, 1, depth);
    return depth;
}

//由public的函数Depth调用, 完成树的深度的计算，p是根结点，Level是层，depth用来返回树的深度 
template<typename T>
int BinarySearchTree<T>::Depth(BinaryNode<T> *t, int level, int &depth)
{
    if (level > depth) depth = level;                  //层数
    if (t->left) Depth(t->left, level + 1, depth);     //递归遍历左子树，且层数加1 
    if (t->right) Depth(t->right, level + 1, depth);   //递归遍历右子树, 且层数加1 
    return 0; 
}

template<typename T>
//利用 递归 算法 计算树的 高度
void BinarySearchTree<T>::CountLeaf(BinaryNode<T> * t, int &count)
{
    if (t == nullptr) return;               //为空时，退出

//    CountLeaf(t->left, count);
//    CountLeaf(t->right, count); 
    if (!(t->left) && !(t->right)) {        //儿子为空时 
        count++;
    }
    CountLeaf(t->left, count);
    CountLeaf(t->right, count); 
}


/************************************************************************/
///* printTree   ---    前序遍历 
/************************************************************************/
template<typename T>
void BinarySearchTree<T>::PreprintTree(BinaryNode<T> * t) const
{
    if (t != nullptr) {
        cout << t->element << ' ';     
        PreprintTree(t->left);
        PreprintTree(t->right);
    }
}

//中序遍历 
template<typename T>
void BinarySearchTree<T>::InprintTree(BinaryNode<T> * t ) const
{
    if (t != nullptr) {
        InprintTree(t->left);
        cout << t->element << ' ';
        InprintTree(t->right);
    }    
} 

//后序遍历 
template<typename T>
void BinarySearchTree<T>::PostprintTree(BinaryNode<T> * t) const 
{
    if (t != nullptr) {
        PostprintTree(t->left);
        PostprintTree(t->right);
        cout << t->element << ' ';
    }    
}

//利用队列Queue层次遍历二叉树 
template<typename T>
void BinarySearchTree<T>::LevelprintTree( BinaryNode<T> * t) const
{
    const int maxn = 1024;
    BinaryNode<T> *Queue[maxn];                          //一维数组作为队列 
    BinaryNode<T> *tmp;                         
    int front = 0, rear = 0;                             //队列初始为空 
    if (root) {
        Queue[rear++] = root;                            //二叉树的根结点指针入队列 
        while (front != rear)
        {
            tmp = Queue[front++];                        //队首的元素出队列
            if (tmp) cout << tmp->element << ' ';        //输出结点值
            if (tmp->left) Queue[rear++] = tmp->left; 
            if (tmp->right) Queue[rear++] = tmp->right; 
        }
    }
}

//先序遍历 
template<typename T>
void BinarySearchTree<T>::PreprintTree_N( BinaryNode<T> * t) const          //非递归先序遍历
{
    const int maxn = 1024;
    BinaryNode<T> *Stack[maxn];    
    int top = 0;
    BinaryNode<T> *tmp = root;            //将根结点的指针赋值给tmp 
    
//    cout << "Debug :
";
    while (tmp || top != 0)
    {
//        cout << "debug : 
";
        while (tmp) {
            cout << tmp->element << ' ';
            Stack[top++] = tmp;           //右孩子入栈 
            tmp = tmp->left;              //一直递归到最左的结点 
        }    
        if (top) {                        //栈不为空, 从栈中取出一个结点指针 
            tmp = Stack[--top];           
            tmp = tmp->right;                   
        }
    }    
}

//中序非递归遍历二叉树 (LDR)
template<typename T>
void BinarySearchTree<T>::InprintTree_N( BinaryNode<T> * t) const           //非递归中序遍历二叉树 
{
    const int maxn = 1024;
    BinaryNode<T> *Stack[maxn];
    int top = 0;
    BinaryNode<T> *tmp = root;
    
    while (tmp || top != 0)
    {
        while (tmp) {                  //迭代到最左的子树 
            Stack[top++] = tmp;        //左子树入栈 
            tmp = tmp->left;
        }
        if (top) {
            tmp = Stack[--top];            //出栈最左的子树 
            cout << tmp->element << ' ';   //输出该元素 
            tmp = tmp->right;              //并指向右结点开始迭代 
        }
    }
     
}

//非递归后序遍历二叉树 (LRD)
template<typename T>
void BinarySearchTree<T>::PostprintTree_N( BinaryNode<T> * t) const         
{
       const int maxn = 1024;
    struct Mystack {
        BinaryNode<T> * link;
        int flag;
    };
    
    Mystack Stack[maxn]; 
    BinaryNode<T> * p = root, *tmp;

    if (root == nullptr) return;

    int top = -1,                  //栈顶初始化 
        sign = 0;                  //为结点tmp 的标志量 
    
    while ( p != nullptr || top != -1)
    {
        while (p != nullptr)       //遍历到最左 
        {
            Stack[++top].link = p; //并且一直入栈 
            Stack[top].flag = 1;   //设置flag为第一次入栈 
            p = p->left;         
        }        
        
        if (top != -1)         
        {                          
            tmp = Stack[top].link; 
            sign = Stack[top].flag;
            top--;                 //出栈 
                                   
            if (sign == 1)         //结点第一次进栈 
            {
                top++;
                Stack[top].link = tmp;
                Stack[top].flag = 2;            //标记为第二次出栈 
                p = tmp->right;    
            }
            else {                 //第二次出栈就输出 
                cout << tmp->element << ' ';      //访问该结点数据域 
                p = nullptr;
            }
        }
    
    }
    
}

//树形显示二叉树，也是中序遍历 
template<typename T>
void BinarySearchTree<T>::DisplayTreeShape(BinaryNode<T> *bt, int level) const
{    
    if (bt)                                         //二叉树的树形显示算法
    {
        cout << endl;
        for (int i = 0; i < level - 1; i++)         
            cout << "   ";                            //确保在第level列显示结点 
        cout << bt->element;                        //显示结点 
        DisplayTreeShape(bt->left, level - 1);     //空二叉树不显示
//        cout << endl;                               //显示右子树
        DisplayTreeShape(bt->right, level + 2);      //显示左子树 
    } 
}

int main()
{
//    srand((unsigned)time(nullptr));
    int testData, t = 0;
    BinarySearchTree<int> test;
    cout << "输入数字个数: 
";
    cin >> t;
    cout << "输入数字: 
";
    while (t--)
    {
        testData = rand() % 500 + 1;
        test.insert(testData);
    }
    cout << "
全部元素为: 
";
    test.PreprintTree();
    
    cout << endl;
//    cin >> testData;                //不符合查找二叉树 
//    test.getNode(testData) = 10000;
    
    
    cout << "
Max = " << test.findMax() << endl;
    cout << "Min = " << test.findMin() << endl;

    cout << "输入查找元素: 
";
    cin >> testData;
    cout << "是否包含 " << testData  << " : " << test.contains(testData) << endl; 
    test.PreprintTree();
    
    cout << endl;
    cout << "输入删除元素: 
";
    cin >> testData;
    test.remove(testData);
    
    cout << "
树的高度: " << test.Depth() << endl;
    cout << "
叶子的个数: " << test.CountLeaf() << endl; 
    cout << endl;
    
    cout << "先序遍历树元素: 
";
    test.PreprintTree();
    
    cout << "

中序遍历树元素: 
";
    test.InprintTree();
    
    cout << "

后序遍历树元素: 
";
    test.PostprintTree();
    
    cout << "

层次遍历树元素: 
";
    test.LevelprintTree();
    
    cout << "

先序遍历树元素(非递归): 
";
    test.PreprintTree_N();
    
    cout << "

中序遍历树元素(非递归): 
";
    test.InprintTree_N();
    
    cout << "

后序遍历树元素(非递归): 
";
    test.PostprintTree_N();
    
    cout << "

二叉树的树形显示算法: 
";
    test.DisplayTreeShape(43);
    
    cout << endl;
    return 0;
}