《剑指offer》第二十八题：对称的二叉树

// 面试题28：对称的二叉树
// 题目：请实现一个函数，用来判断一棵二叉树是不是对称的。如果一棵二叉树和
// 它的镜像一样，那么它是对称的。

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

bool isSymmetrical(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2);

bool isSymmetrical(BinaryTreeNode* pRoot)
{
    return isSymmetrical(pRoot, pRoot); //函数重载
}

bool isSymmetrical(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2)
{
    if (pRoot1 == nullptr && pRoot2 == nullptr) //如果子节点都为空
        return true;

    if (pRoot1 == nullptr || pRoot2 == nullptr) //如果一个子节点为空
        return false;

    if (pRoot1->m_nValue != pRoot2->m_nValue) //两个节点不相等
        return false;

    return isSymmetrical(pRoot1->m_pLeft, pRoot2->m_pRight)
        && isSymmetrical(pRoot1->m_pRight, pRoot2->m_pLeft);
}

// ====================测试代码====================
void Test(const char* testName, BinaryTreeNode* pRoot, bool expected)
{
    if (testName != nullptr)
        printf("%s begins: ", testName);

    if (isSymmetrical(pRoot) == expected)
        printf("Passed.
");
    else
        printf("FAILED.
");
}

//            8
//        6      6
//       5 7    7 5
void Test1()
{
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNode61 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode62 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode51 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode71 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode72 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode52 = CreateBinaryTreeNode(5);

    ConnectTreeNodes(pNode8, pNode61, pNode62);
    ConnectTreeNodes(pNode61, pNode51, pNode71);
    ConnectTreeNodes(pNode62, pNode72, pNode52);

    Test("Test1", pNode8, true);

    DestroyTree(pNode8);
}

//            8
//        6      9
//       5 7    7 5
void Test2()
{
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNode61 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode9 = CreateBinaryTreeNode(9);
    BinaryTreeNode* pNode51 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode71 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode72 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode52 = CreateBinaryTreeNode(5);

    ConnectTreeNodes(pNode8, pNode61, pNode9);
    ConnectTreeNodes(pNode61, pNode51, pNode71);
    ConnectTreeNodes(pNode9, pNode72, pNode52);

    Test("Test2", pNode8, false);

    DestroyTree(pNode8);
}

//            8
//        6      6
//       5 7    7
void Test3()
{
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
    BinaryTreeNode* pNode61 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode62 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode51 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode71 = CreateBinaryTreeNode(7);
    BinaryTreeNode* pNode72 = CreateBinaryTreeNode(7);

    ConnectTreeNodes(pNode8, pNode61, pNode62);
    ConnectTreeNodes(pNode61, pNode51, pNode71);
    ConnectTreeNodes(pNode62, pNode72, nullptr);

    Test("Test3", pNode8, false);

    DestroyTree(pNode8);
}

//               5
//              / 
//             3   3
//            /     
//           4       4
//          /         
//         2           2
//        /             
//       1               1
void Test4()
{
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode21 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode11 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode12 = CreateBinaryTreeNode(1);

    ConnectTreeNodes(pNode5, pNode31, pNode32);
    ConnectTreeNodes(pNode31, pNode41, nullptr);
    ConnectTreeNodes(pNode32, nullptr, pNode42);
    ConnectTreeNodes(pNode41, pNode21, nullptr);
    ConnectTreeNodes(pNode42, nullptr, pNode22);
    ConnectTreeNodes(pNode21, pNode11, nullptr);
    ConnectTreeNodes(pNode22, nullptr, pNode12);

    Test("Test4", pNode5, true);

    DestroyTree(pNode5);
}


//               5
//              / 
//             3   3
//            /     
//           4       4
//          /         
//         6           2
//        /             
//       1               1
void Test5()
{
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode11 = CreateBinaryTreeNode(1);
    BinaryTreeNode* pNode12 = CreateBinaryTreeNode(1);

    ConnectTreeNodes(pNode5, pNode31, pNode32);
    ConnectTreeNodes(pNode31, pNode41, nullptr);
    ConnectTreeNodes(pNode32, nullptr, pNode42);
    ConnectTreeNodes(pNode41, pNode6, nullptr);
    ConnectTreeNodes(pNode42, nullptr, pNode22);
    ConnectTreeNodes(pNode6, pNode11, nullptr);
    ConnectTreeNodes(pNode22, nullptr, pNode12);

    Test("Test5", pNode5, false);

    DestroyTree(pNode5);
}

//               5
//              / 
//             3   3
//            /     
//           4       4
//          /         
//         2           2
//                      
//                       1
void Test6()
{
    BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode(3);
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode(4);
    BinaryTreeNode* pNode21 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode(2);
    BinaryTreeNode* pNode12 = CreateBinaryTreeNode(1);

    ConnectTreeNodes(pNode5, pNode31, pNode32);
    ConnectTreeNodes(pNode31, pNode41, nullptr);
    ConnectTreeNodes(pNode32, nullptr, pNode42);
    ConnectTreeNodes(pNode41, pNode21, nullptr);
    ConnectTreeNodes(pNode42, nullptr, pNode22);
    ConnectTreeNodes(pNode21, nullptr, nullptr);
    ConnectTreeNodes(pNode22, nullptr, pNode12);

    Test("Test6", pNode5, false);

    DestroyTree(pNode5);
}

// 只有一个结点
void Test7()
{
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(1);
    Test("Test7", pNode1, true);

    DestroyTree(pNode1);
}

// 没有结点
void Test8()
{
    Test("Test8", nullptr, true);
}

// 所有结点都有相同的值，树对称
//               5
//              / 
//             5   5
//            /     
//           5       5
//          /         
//         5           5
void Test9()
{
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode21 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode(5);

    ConnectTreeNodes(pNode1, pNode21, pNode22);
    ConnectTreeNodes(pNode21, pNode31, nullptr);
    ConnectTreeNodes(pNode22, nullptr, pNode32);
    ConnectTreeNodes(pNode31, pNode41, nullptr);
    ConnectTreeNodes(pNode32, nullptr, pNode42);
    ConnectTreeNodes(pNode41, nullptr, nullptr);
    ConnectTreeNodes(pNode42, nullptr, nullptr);

    Test("Test9", pNode1, true);

    DestroyTree(pNode1);
}

// 所有结点都有相同的值，树不对称
//               5
//              / 
//             5   5
//            /     
//           5       5
//          /       /
//         5       5
void Test10()
{
    BinaryTreeNode* pNode1 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode21 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode(5);
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode(5);

    ConnectTreeNodes(pNode1, pNode21, pNode22);
    ConnectTreeNodes(pNode21, pNode31, nullptr);
    ConnectTreeNodes(pNode22, nullptr, pNode32);
    ConnectTreeNodes(pNode31, pNode41, nullptr);
    ConnectTreeNodes(pNode32, pNode42, nullptr);
    ConnectTreeNodes(pNode41, nullptr, nullptr);
    ConnectTreeNodes(pNode42, nullptr, nullptr);

    Test("Test10", pNode1, false);

    DestroyTree(pNode1);
}

void main(int argc, char* argv[])
{
    Test1();
    Test2();
    Test3();
    Test4();
    Test5();
    Test6();
    Test7();
    Test8();
    Test9();
    Test10();
}

分析：妙啊！

/*
struct TreeNode {
    int val;
    struct TreeNode *left;
    struct TreeNode *right;
    TreeNode(int x) :
            val(x), left(NULL), right(NULL) {
    }
};
*/
class Solution {
public:
    bool isSymmetrical(TreeNode* pRoot)
    {
        return isSymmetrical(pRoot, pRoot);
    }
    bool isSymmetrical(TreeNode* pRoot1, TreeNode* pRoot2)
    {
        if (pRoot1 == nullptr && pRoot2 == nullptr)
            return true;
        
        if (pRoot1 == nullptr || pRoot2 == nullptr)
            return false;
        
        if (pRoot1->val != pRoot2->val)
            return false;
        
        return isSymmetrical(pRoot1->left, pRoot2->right)
            && isSymmetrical(pRoot1->right, pRoot2->left);
    }
};