二叉树的基本操作（递归版）

递归：

　　　　二叉树的创建，遍历，求高度，求结点数，求叶子数。 递归写法很简单，不多说了。

 

#include<iostream>
using namespace std;

struct Node {
    char data;
    Node * lchild;
    Node * rchild;
};

class Tree {
public:
    Tree();
    ~Tree();
    Node * getRoot();
    void preTree(Node *);
    void inTree(Node *);
    void postTree(Node *);
    int getHigh(Node *);
    int getLeaf(Node *);
    int getNode_number(Node *);
private:
    Node * root;
    Node * Create();
    void Delete(Node *);
};

int main() {

    Tree T;
    cout << "先序遍历:";
    T.preTree(T.getRoot());
    cout << endl << "中序遍历:";
    T.inTree(T.getRoot());
    cout << endl << "后序遍历:";
    T.postTree(T.getRoot());
    cout << endl << "高度:";
    cout << T.getHigh(T.getRoot());
    cout << endl << "结点数:";
    cout << T.getNode_number(T.getRoot());
    cout << endl << "叶子数:";
    cout << T.getLeaf(T.getRoot());

    system("pause");
}

int Tree::getLeaf(Node * root) {
    int Left = 0, Right = 0;
    if (root->lchild == NULL && root->rchild == NULL) {        // 左右孩子都为空，表示是叶子 ，返回叶子个数 1
        return 1;
    }
    else if (root->lchild == NULL) {    // 左孩子为空，就递归该结点的右子树
        Right = getLeaf(root->rchild);
        return Right;
    }
    else if(root->rchild == NULL) {        // 右孩子为空，就递归该结点的左子树
        Left = getLeaf(root->lchild);
        return Left;
    }
    else {                                // 左右孩子都不空，就先递归该结点的左子树，然后递归该结点的右子树
        Left =  getLeaf(root->lchild);
        Right = getLeaf(root->rchild);
        return Left + Right;
    }
}

int Tree::getHigh(Node * root) {
    int Left = 0, Right = 0;
    if (root == NULL) {
        return 0;
    }
    else {
        Left = getHigh(root->lchild);
        Right = getHigh(root->rchild);
        return Left > Right ? (Left + 1) : (Right + 1);
    }
}

int Tree::getNode_number(Node * root) {
    int Left = 0, Right = 0;
    if (root == NULL) {
        return 0;
    }
    else {
        Left = getNode_number(root->lchild);
        Right = getNode_number(root->rchild);
        return Left + Right + 1;
    }
}

Node * Tree::Create() {
    Node * node;
    char ch;
    cin >> ch;
    if (ch == '#') {
        node = NULL;
    }
    else {
        node = new Node();
        node->data = ch;
        node->lchild = Create();
        node->rchild = Create();
    }
    return node;
}

void Tree::Delete(Node * root) {
    if (root != NULL) {
        Delete(root->lchild);
        Delete(root->rchild);
        delete root;
    }
}

Tree::Tree() {
    root = Create();
}

Tree::~Tree() {
    Delete(root);
}

Node * Tree::getRoot() {
    return root;
}

void Tree::preTree(Node * root) {
    if (root == NULL) {
        return;
    }
    else {
        cout << root->data << " ";
        preTree(root->lchild);
        preTree(root->rchild);
    }
}

void Tree::inTree(Node * root) {
    if (root == NULL) {
        return;
    }
    else {
        inTree(root->lchild);
        cout << root->data << " ";
        inTree(root->rchild);
    }
}

void Tree::postTree(Node * root) {
    if (root == NULL) {
        return;
    }
    else {
        postTree(root->lchild);
        postTree(root->rchild);
        cout << root->data << " ";
    }
}