Data Structures and Algorithms Interview Question: Implement a function that converts a binary tree into its mirror image. (recursive or non-recursive implementation)

Data Structures and Algorithms Interview Question: Implement a function that converts a binary tree into its mirror image. (recursive or non-recursive implementation)

Introduction: Implement a function that converts a binary tree into its mirror image. (recursive or non-recursive implementation)

The implementation idea of ​​the algorithm is as follows:

1. For the current node, swap its left and right subtrees.
2. Recursively mirrors the left and right subtrees of this node.

The following is the code to convert a binary tree to its mirror image (non-recursive implementation) using C++, with detailed comments:

#include <iostream>
#include <stack>

using namespace std;

// 定义二叉树结构
struct TreeNode {
    
    
    int val;
    TreeNode* left;
    TreeNode* right;
    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {
    
    }
};

// 将一棵二叉树转换为它的镜像（非递归实现）
void mirror_iterative(TreeNode* root) {
    
    
    if (root == nullptr) return;

    stack<TreeNode*> s{
    
    {
    
    root}};
    while (!s.empty()) {
    
    
        TreeNode* node = s.top();
        s.pop();

        swap(node->left, node->right); // 交换左右子树

        if (node->left != nullptr) s.push(node->left);
        if (node->right != nullptr) s.push(node->right);
    }
}

int main() {
    
    
    // 构造一棵二叉树
    TreeNode* root = new TreeNode(4);
    root->left = new TreeNode(2);
    root->right = new TreeNode(7);
    root->left->left = new TreeNode(1);
    root->left->right = new TreeNode(3);
    root->right->left = new TreeNode(6);
    root->right->right = new TreeNode(9);

    // 转换并输出镜像结果
    mirror_iterative(root);

    cout << root->val << endl;             // 4
    cout << root->left->val << " ";        // 7
    cout << root->left->left->val << " ";  // 9
    cout << root->left->right->val << " "; // 6
    cout << root->right->val << " ";       // 2
    cout << root->right->left->val << " "; // 3
    cout << root->right->right->val << endl;// 1

    return 0;
}

The following is the recursive implementation code of the same function, with detailed comments:

#include <iostream>

using namespace std;

// 定义二叉树结构
struct TreeNode {
    
    
    int val;
    TreeNode* left;
    TreeNode* right;
    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {
    
    }
};

// 将一棵二叉树转换为它的镜像（递归实现）
void mirror_recursive(TreeNode* root) {
    
    
    if (root == nullptr) return;

    swap(root->left, root->right); // 交换当前节点的左右子树

    // 递归对左右子树进行镜像操作
    mirror_recursive(root->left);
    mirror_recursive(root->right);
}

int main() {
    
    
    // 构造一棵二叉树
    TreeNode* root = new TreeNode(4);
    root->left = new TreeNode(2);
    root->right = new TreeNode(7);
    root->left->left = new TreeNode(1);
    root->left->right = new TreeNode(3);
    root->right->left = new TreeNode(6);
    root->right->right = new TreeNode(9);

    // 转换并输出镜像结果
    mirror_recursive(root);

    cout << root->val << endl;             // 4
    cout << root->left->val << " ";        // 7
    cout << root->left->left->val << " ";  // 9
    cout << root->left->right->val << " "; // 6
    cout << root->right->val << " ";       // 2
    cout << root->right->left->val << " "; // 3
    cout << root->right->right->val << endl;// 1

    return 0;
}

Both codes build a binary tree in a way that defines the structure of the binary tree. mirror_iterative()The function uses the stack for non-recursive implementation, thereby avoiding the stack depth of the function call and reducing the space complexity; while mirror_recursive()the function is implemented using recursion, the code is more concise and easy to understand. The idea of ​​the two functions is: for a node, after exchanging its left and right subtrees, recursively perform the same operation on its left and right subtrees.