建立以左右孩子链接结构表示的二叉树，实现二叉树的先序、中序、后序的递归和非递归方式遍历，分层遍历、统计树的高度。

好的，我可以为您解答。以下是基于左右孩子链接结构表示的二叉树的相关算法实现：

### 1. 二叉树结构定义

struct TreeNode {
    int val;
    TreeNode* left;
    TreeNode* right;
    TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};

### 2. 二叉树先序遍历

#### 2.1 递归实现

void preorderTraversal(TreeNode* root) {
    if (root == NULL) return;
    cout << root->val << " ";
    preorderTraversal(root->left);
    preorderTraversal(root->right);
}

#### 2.2 非递归实现

void preorderTraversal(TreeNode* root) {
    if (root == NULL) return;
    stack<TreeNode*> s;
    s.push(root);
    while (!s.empty()) {
        TreeNode* cur = s.top();
        s.pop();
        cout << cur->val << " ";
        if (cur->right) s.push(cur->right);
        if (cur->left) s.push(cur->left);
    }
}

### 3. 二叉树中序遍历

#### 3.1 递归实现

void inorderTraversal(TreeNode* root) {
    if (root == NULL) return;
    inorderTraversal(root->left);
    cout << root->val << " ";
    inorderTraversal(root->right);
}

#### 3.2 非递归实现

void inorderTraversal(TreeNode* root) {
    if (root == NULL) return;
    stack<TreeNode*> s;
    TreeNode* cur = root;
    while (cur != NULL || !s.empty()) {
        while (cur != NULL) {
            s.push(cur);
            cur = cur->left;
        }
        cur = s.top();
        s.pop();
        cout << cur->val << " ";
        cur = cur->right;
    }
}

### 4. 二叉树后序遍历

#### 4.1 递归实现

void postorderTraversal(TreeNode* root) {
    if (root == NULL) return;
    postorderTraversal(root->left);
    postorderTraversal(root->right);
    cout << root->val << " ";
}

#### 4.2 非递归实现

void postorderTraversal(TreeNode* root) {
    if (root == NULL) return;
    stack<TreeNode*> s;
    s.push(root);
    TreeNode* pre = NULL;
    while (!s.empty()) {
        TreeNode* cur = s.top();
        if ((cur->left == NULL && cur->right == NULL) || (pre != NULL && (pre == cur->left || pre == cur->right))) {
            cout << cur->val << " ";
            s.pop();
            pre = cur;
        } else {
            if (cur->right != NULL) s.push(cur->right);
            if (cur->left != NULL) s.push(cur->left);
        }
    }
}

### 5. 二叉树分层遍历

vector<vector<int>> levelOrder(TreeNode* root) {
    vector<vector<int>> res;
    if (root == NULL) return res;
    queue<TreeNode*> q;
    q.push(root);
    while (!q.empty()) {
        int size = q.size();
        vector<int> level;
        for (int i = 0; i < size; i++) {
            TreeNode* cur = q.front();
            q.pop();
            level.push_back(cur->val);
            if (cur->left) q.push(cur->left);
            if (cur->right) q.push(cur->right);
        }
        res.push_back(level);
    }
    return res;
}

### 6. 统计二叉树高度

int maxDepth(TreeNode* root) {
    if (root == NULL) return 0;
    int leftDepth = maxDepth(root->left);
    int rightDepth = maxDepth(root->right);
    return max(leftDepth, rightDepth) + 1;
}

希望以上算法能够帮助您解决问题。