《剑指offer》第二十七题：二叉树的镜像

// 面试题27：二叉树的镜像
// 题目：请完成一个函数，输入一个二叉树，该函数输出它的镜像。

#include <cstdio>
#include "BinaryTree.h"
#include <stack>

void MirrorRecursively(BinaryTreeNode* pNode) //自底向上
{
    if (pNode == nullptr || (pNode->m_pLeft == nullptr && pNode->m_pRight == nullptr))
        return;

    //交换父节点的两个子节点
    BinaryTreeNode* pTemp = pNode->m_pLeft;
    pNode->m_pLeft = pNode->m_pRight;
    pNode->m_pRight = pTemp;

    if (pNode->m_pLeft) //交换左子节点的子节点
        MirrorRecursively(pNode->m_pLeft);
    if (pNode->m_pRight) //交换右子节点的子节点
        MirrorRecursively(pNode->m_pRight);
}

void MirrorIteratively(BinaryTreeNode* pRoot) //自顶向下
{
    if (pRoot == nullptr)
        return;

    std::stack<BinaryTreeNode*> treeNodeStack; //存放未交换的根节点
    treeNodeStack.push(pRoot);

    while (treeNodeStack.size() > 0)
    {
        BinaryTreeNode* pNode = treeNodeStack.top();
        treeNodeStack.pop();

        //交换父节点的两个子节点
        BinaryTreeNode* pTemp = pNode->m_pLeft;
        pNode->m_pLeft = pNode->m_pRight;
        pNode->m_pRight = pTemp;

        if (pNode->m_pLeft)
            treeNodeStack.push(pNode->m_pLeft);
        if (pNode->m_pRight)
            treeNodeStack.push(pNode->m_pRight);
    }
}

// ====================测试代码====================
// 测试完全二叉树：除了叶子节点，其他节点都有两个子节点
//            8
//        6      10
//       5 7    9  11
void Test1()
{
    printf("=====Test1 starts:=====\n");
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode10 = CreateBinaryTreeNode(10);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode9 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNode11 = CreateBinaryTreeNode(11);

    ConnectTreeNodes(pNode8, pNode6, pNode10);
    ConnectTreeNodes(pNode6, pNode5, pNode7);
    ConnectTreeNodes(pNode10, pNode9, pNode11);

    PrintTree(pNode8);

    printf("=====Test1: MirrorRecursively=====\n");
    MirrorRecursively(pNode8);
    PrintTree(pNode8);

    printf("=====Test1: MirrorIteratively=====\n");
    MirrorIteratively(pNode8);
    PrintTree(pNode8);

    DestroyTree(pNode8);
}

// 测试二叉树：出叶子结点之外，左右的结点都有且只有一个左子结点
//            8
//          7   
//        6 
//      5
//    4
void Test2()
{
    printf("=====Test2 starts:=====\n");
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);

    ConnectTreeNodes(pNode8, pNode7, nullptr);
    ConnectTreeNodes(pNode7, pNode6, nullptr);
    ConnectTreeNodes(pNode6, pNode5, nullptr);
    ConnectTreeNodes(pNode5, pNode4, nullptr);

    PrintTree(pNode8);

    printf("=====Test2: MirrorRecursively=====\n");
    MirrorRecursively(pNode8);
    PrintTree(pNode8);

    printf("=====Test2: MirrorIteratively=====\n");
    MirrorIteratively(pNode8);
    PrintTree(pNode8);

    DestroyTree(pNode8);
}

// 测试二叉树：出叶子结点之外，左右的结点都有且只有一个右子结点
//            8
//             7   
//              6 
//               5
//                4
void Test3()
{
    printf("=====Test3 starts:=====\n");
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);

    ConnectTreeNodes(pNode8, nullptr, pNode7);
    ConnectTreeNodes(pNode7, nullptr, pNode6);
    ConnectTreeNodes(pNode6, nullptr, pNode5);
    ConnectTreeNodes(pNode5, nullptr, pNode4);

    PrintTree(pNode8);

    printf("=====Test3: MirrorRecursively=====\n");
    MirrorRecursively(pNode8);
    PrintTree(pNode8);

    printf("=====Test3: MirrorIteratively=====\n");
    MirrorIteratively(pNode8);
    PrintTree(pNode8);

    DestroyTree(pNode8);
}

// 测试空二叉树：根结点为空指针
void Test4()
{
    printf("=====Test4 starts:=====\n");
    BinaryTreeNode* pNode = nullptr;

    PrintTree(pNode);

    printf("=====Test4: MirrorRecursively=====\n");
    MirrorRecursively(pNode);
    PrintTree(pNode);

    printf("=====Test4: MirrorIteratively=====\n");
    MirrorIteratively(pNode);
    PrintTree(pNode);
}

// 测试只有一个结点的二叉树
void Test5()
{
    printf("=====Test5 starts:=====\n");
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);

    PrintTree(pNode8);

    printf("=====Test4: MirrorRecursively=====\n");
    MirrorRecursively(pNode8);
    PrintTree(pNode8);

    printf("=====Test4: MirrorIteratively=====\n");
    MirrorIteratively(pNode8);
    PrintTree(pNode8);
}

int main(int argc, char* argv[])
{
    Test1();
    Test2();
    Test3();
    Test4();
    Test5();

    return 0;
}

分析：基于循环的方法很巧妙。

/*
struct TreeNode {
    int val;
    struct TreeNode *left;
    struct TreeNode *right;
    TreeNode(int x) :
            val(x), left(NULL), right(NULL) {
    }
};*/
class Solution {
public:
    void Mirror(TreeNode *pRoot) {
        
        if (pRoot == nullptr || (pRoot->left == nullptr && pRoot->right == nullptr))
            return;
        
        TreeNode* treeTemp = pRoot->right;
        pRoot->right = pRoot->left;
        pRoot->left = treeTemp;
            
        if (pRoot->left)
            Mirror(pRoot->left);
        if (pRoot->right)
            Mirror(pRoot->right);
    }
};