《剑指offer》第六题（重要！重建二叉树）

Posted 2021-02-11 cjt-blog

文件一：main.cpp

// 面试题：重建二叉树
// 题目：输入某二叉树的前序遍历和中序遍历的结果，请重建出该二叉树。假设输
// 入的前序遍历和中序遍历的结果中都不含重复的数字。例如输入前序遍历序列{1,
// 2, 4, 7, 3, 5, 6, 8}和中序遍历序列{4, 7, 2, 1, 5, 3, 8, 6}，则重建出
// 图2.6所示的二叉树并输出它的头结点。

#include <iostream>
#include "BinaryTree.h"
using namespace std;

BinaryTreeNode* ConstructCore(int* startPreorder, int* endPreorder, int* startInorder, int* endInorder);

BinaryTreeNode* Construct(int* preorder, int* inorder, int length)
{
    if (preorder == NULL || inorder == NULL || length <= 0)//确认输入存在
        return NULL;

    return ConstructCore(preorder, preorder + length - 1,inorder, inorder + length - 1);
}

BinaryTreeNode* ConstructCore(int* startPreorder, int* endPreorder,int* startInorder, int* endInorder)//注意传入的是地址
{
    // 前序遍历序列的第一个数字是根结点的值
    BinaryTreeNode* root = CreateBinaryTreeNode(startPreorder[0]);//建立根节点
    
    if (startPreorder == endPreorder)//如果这个树只有根节点
    {
        if (startInorder == endInorder && *startPreorder == *startInorder)
            return root;
        else                        //注意判断输入是否真的是对的
            throw exception("Invalid input.");
    }

    // 在中序遍历中找到根结点的值
    int* rootInorder = startInorder;
    while (rootInorder <= endInorder && *rootInorder != startPreorder[0])
        ++rootInorder;

    if (rootInorder == endInorder && *rootInorder != startPreorder[0])//如果中序遍历中没有根节点，就抛出异常
        throw exception("Invalid input.");

    int leftLength = rootInorder - startInorder;//计算左孩子子树个数
    int* leftPreorderEnd = startPreorder + leftLength;
    if (leftLength > 0)//递归的构建子树
    {
        // 构建左子树
        root->m_pLeft = ConstructCore(startPreorder + 1, leftPreorderEnd,startInorder, rootInorder - 1);
    }
    if (leftLength < endPreorder - startPreorder)
    {
        // 构建右子树
        root->m_pRight = ConstructCore(leftPreorderEnd + 1, endPreorder,rootInorder + 1, endInorder);
    }

    return root;
}

// ====================测试代码====================
void Test(const char* testName, int* preorder, int* inorder, int length)
{
    if (testName != NULL)
        cout << testName << " begins:
";

    cout << "The preorder sequence is: ";
    for (int i = 0; i < length; ++i)
        cout << preorder[i];
    cout << endl;

    cout << "The inorder sequence is: ";
    for (int i = 0; i < length; ++i)
        cout << inorder[i];
    cout << endl;

    try
    {
        BinaryTreeNode* root = Construct(preorder, inorder, length);
        PrintTree(root);

        DestroyTree(root);
    }
    catch (exception& exception)
    {
        cout << "Invalid Input.
";
    }
}

// 普通二叉树
//              1
//           /     //          2       3  
//         /       / //        4       5   6
//                  /
//          7       8
void Test1()
{
    const int length = 8;
    int preorder[length] = { 1, 2, 4, 7, 3, 5, 6, 8 };
    int inorder[length] = { 4, 7, 2, 1, 5, 3, 8, 6 };

    Test("Test1", preorder, inorder, length);
}

// 所有结点都没有右子结点
//            1
//           / 
//          2   
//         / 
//        3 
//       /
//      4
//     /
//    5
void Test2()
{
    const int length = 5;
    int preorder[length] = { 1, 2, 3, 4, 5 };
    int inorder[length] = { 5, 4, 3, 2, 1 };

    Test("Test2", preorder, inorder, length);
}

// 所有结点都没有左子结点
//            1
//              
//              2   
//                
//                3 
//                 //                  4
//                   //                    5
void Test3()
{
    const int length = 5;
    int preorder[length] = { 1, 2, 3, 4, 5 };
    int inorder[length] = { 1, 2, 3, 4, 5 };

    Test("Test3", preorder, inorder, length);
}

// 树中只有一个结点
void Test4()
{
    const int length = 1;
    int preorder[length] = { 1 };
    int inorder[length] = { 1 };

    Test("Test4", preorder, inorder, length);
}

// 完全二叉树
//              1
//           /     //          2       3  
//         /      / //        4   5   6   7
void Test5()
{
    const int length = 7;
    int preorder[length] = { 1, 2, 4, 5, 3, 6, 7 };
    int inorder[length] = { 4, 2, 5, 1, 6, 3, 7 };

    Test("Test5", preorder, inorder, length);
}

// 输入空指针
void Test6()
{
    Test("Test6", NULL, NULL, 0);
}

// 输入的两个序列不匹配
void Test7()
{
    const int length = 7;
    int preorder[length] = { 1, 2, 4, 5, 3, 6, 7 };
    int inorder[length] = { 4, 2, 8, 1, 6, 3, 7 };

    Test("Test7: for unmatched input", preorder, inorder, length);
}

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

    system("pause");
}

文件二：BinaryTree.h

#ifndef BINARY_TREE_H
#define BINARY_TREE_H

struct BinaryTreeNode
{
    int                    m_nValue;
    BinaryTreeNode*        m_pLeft;
    BinaryTreeNode*        m_pRight;
};

BinaryTreeNode* CreateBinaryTreeNode(int value);
void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight);
void PrintTreeNode(const BinaryTreeNode* pNode);
void PrintTree(const BinaryTreeNode* pRoot);
void DestroyTree(BinaryTreeNode* pRoot);

#endif

文件三：BinaryTree.cpp

#include <iostream>
#include "BinaryTree.h"
using namespace std;

BinaryTreeNode* CreateBinaryTreeNode(int value)//创建一个二叉树节点
{
    BinaryTreeNode* pNode = new BinaryTreeNode();
    pNode->m_nValue = value;
    pNode->m_pLeft = NULL;
    pNode->m_pRight = NULL;

    return pNode;
}

void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight)//将两个孩子连接到一个父节点
{
    if (pParent != NULL)
    {
        pParent->m_pLeft = pLeft;
        pParent->m_pRight = pRight;
    }
}

void PrintTreeNode(const BinaryTreeNode* pNode)//打印当前二叉树节点
{
    if (pNode != NULL)//判断该节点存在否
    {
        cout << "value of this node is:" << pNode->m_nValue << endl;//打印父节点

        if (pNode->m_pLeft != NULL)//打印左孩子节点
            cout << "value of its left child is:" << pNode->m_pLeft->m_nValue << endl;
        else
            cout << "left child is NULL.
";

        if (pNode->m_pRight != NULL)//打印右孩子节点
            cout << "value of its right child is:" << pNode->m_pRight->m_nValue << endl;
        else
            cout << "right child is NULL.
";
    }
    else
    {
        cout << "this node is nullptr.
";
    }

    cout << endl;
}

void PrintTree(const BinaryTreeNode* pRoot)//打印整个树
{
    PrintTreeNode(pRoot);//打印根节点

    if (pRoot != NULL)//递归打印左右孩子节点，但是注意判断节点是否存在
    {
        if (pRoot->m_pLeft != NULL)
            PrintTree(pRoot->m_pLeft);

        if (pRoot->m_pRight != NULL)
            PrintTree(pRoot->m_pRight);
    }
}

void DestroyTree(BinaryTreeNode* pRoot)//删除整个树
{
    if (pRoot != NULL)
    {
        BinaryTreeNode* pLeft = pRoot->m_pLeft;
        BinaryTreeNode* pRight = pRoot->m_pRight;

        delete pRoot;
        pRoot = NULL;

        DestroyTree(pLeft);//递归调用该函数，分别把左右孩子节点作为父节点
        DestroyTree(pRight);
    }
}