《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 <iostream>
#include "BinaryTree.h"
 
bool isSymmetrical(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2);
 
bool isSymmetrical(BinaryTreeNode* pRoot)
{
    return isSymmetrical(pRoot, pRoot);
}
 
bool isSymmetrical(BinaryTreeNode* pRoot1, BinaryTreeNode* pRoot2)
{
    if (pRoot1 == nullptr && pRoot2 == nullptr)//当二者都为空，true
        return true;
 
    if (pRoot1 == nullptr || pRoot2 == nullptr)//只有一个为空，flase
        return false;
 
    if (pRoot1->m_nValue != pRoot2->m_nValue)//当二者值不等，flase
        return false;
 
    return isSymmetrical(pRoot1->m_pLeft, pRoot2->m_pRight)
        && isSymmetrical(pRoot1->m_pRight, pRoot2->m_pLeft);//看看你镜像和我是不是一样~
}//注意这里有个关键是，要测试是否都是空的，详见test9和10
 
// ====================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.\n");
    else
        printf("FAILED.\n");
}
 
//            8
//        6      6
//       5 7    7 5
void Test1()
{
    BinaryTreeNode* pNode8 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode61 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode62 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode51 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode71 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode72 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode52 = CreateBinaryTreeNode();
 
    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();
    BinaryTreeNode* pNode61 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode9 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode51 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode71 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode72 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode52 = CreateBinaryTreeNode();
 
    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();
    BinaryTreeNode* pNode61 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode62 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode51 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode71 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode72 = CreateBinaryTreeNode();
 
    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();
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode21 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode11 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode12 = CreateBinaryTreeNode();
 
    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();
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode6 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode11 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode12 = CreateBinaryTreeNode();
 
    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();
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode21 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode12 = CreateBinaryTreeNode();
 
    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();
    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();
    BinaryTreeNode* pNode21 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode();
 
    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();
    BinaryTreeNode* pNode21 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode22 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode31 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode32 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode41 = CreateBinaryTreeNode();
    BinaryTreeNode* pNode42 = CreateBinaryTreeNode();
 
    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();
    system("pause");
}