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。
1》 stdafx.h
<span style="font-family: Arial, Helvetica, sans-serif;">#pragma once</span>
#include "targetver.h" #include <stdio.h> #include <tchar.h>
2>targetver.h
#pragma once // The following macros define the minimum required platform. The minimum required platform // is the earliest version of Windows, Internet Explorer etc. that has the necessary features to run // your application. The macros work by enabling all features available on platform versions up to and // including the version specified. // Modify the following defines if you have to target a platform prior to the ones specified below. // Refer to MSDN for the latest info on corresponding values for different platforms. #ifndef _WIN32_WINNT // Specifies that the minimum required platform is Windows Vista. #define _WIN32_WINNT 0x0600 // Change this to the appropriate value to target other versions of Windows. #endif
3>BinaryTree.h
#pragma once
struct BinaryTreeNode
{
int m_nValue;
BinaryTreeNode* m_pLeft;
BinaryTreeNode* m_pRight;
};
_declspec(dllexport)void PrintTree(BinaryTreeNode *pRoot);
_declspec(dllexport)void DestroyTree(BinaryTreeNode *pRoot);
4>BinaryTree.cpp
#include "stdafx.h"
#include "BinaryTree.h"
void PrintTreeNode(BinaryTreeNode *pNode);
void PrintTree(BinaryTreeNode *pRoot)
{
PrintTreeNode(pRoot);
//
if(pRoot != NULL)
{
if(pRoot->m_pLeft != NULL)
PrintTree(pRoot->m_pLeft);
if(pRoot->m_pRight != NULL)
PrintTree(pRoot->m_pRight);
}
}
void PrintTreeNode(BinaryTreeNode *pNode)
{
if(pNode != NULL)
{
printf("value of this node is : %d\n", pNode->m_nValue);
if(pNode->m_pLeft != NULL)
printf("value of its left child is: %d.\n", pNode->m_pLeft->m_nValue);
else
printf("left child is null.\n");
if(pNode->m_pRight != NULL)
printf("value of its right childe is : %d.\n", pNode->m_pRight->m_nValue);
else
printf("right child is null.\n");
}
else
{
printf("this node is null.\n");
}
printf("\n");
}
void DestroyTree(BinaryTreeNode *pRoot)
{
if(pRoot != NULL)
{
BinaryTreeNode *pLeft = pRoot->m_pLeft;
BinaryTreeNode *pRight = pRoot->m_pRight;
delete pRoot;
pRoot = NULL;
DestroyTree(pLeft);
DestroyTree(pRight);
}
}
5>ConstructBinaryTree.cpp
/*
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。
*/
#include "stdafx.h"
#include "BinaryTree.h"
//
#include "iostream" // 不能是 iostream.h
using namespace std;
/*
preorder 前序遍历
inorder 中序遍历
*/
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)
return NULL;
return ConstructCore(preorder, preorder + length - 1, inorder, inorder + length -1);
}
// startPreorder 前序遍历的第一个节点
// endPreorder 前序遍历的左后一个节点
// startInorder 中序遍历的第一个节点
// startInorder 中序遍历的最后一个节点
BinaryTreeNode* ConstructCore(int* startPreorder, int* endPreorder, int* startInorder, int* endInorder)
{
// 前序遍历序列的第一个数字是根结点的值
int rootValue = startPreorder[0];
BinaryTreeNode *root = new BinaryTreeNode();
root->m_nValue = rootValue;
root->m_pLeft = root->m_pRight = NULL;
if(startPreorder == endPreorder)
{
if(startInorder == endInorder && *startPreorder == *startInorder)
return root;
else
throw std::exception("Invalid input.");
}
//
// 在中序遍历中找到根结点的值
int *rootInorder = startInorder;
while(rootInorder <= endInorder && *rootInorder != rootValue)
++rootInorder;
if(rootInorder == endInorder && *rootInorder != rootValue)
throw std::exception("Invalid input");
//
int leftLength = rootInorder - startInorder;
//int rightLength = endInorder - rootInorder;
int *leftPreorderEnd = startPreorder + leftLength;
if(leftLength > 0)
{
// 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(char *testName, int *preorder, int *inorder, int length)
{
if(testName != NULL)
printf("%s Begins:\n", testName);
printf("The preorder sequence is: ");
for(int i = 0; i < length; ++i)
printf("%d ", preorder[i]);
printf("\n");
printf("The inorder sequence is:");
for(int i = 0; i < length; ++i)
printf("%d ", inorder[i]);
printf("\n");
try
{
BinaryTreeNode *root = Construct(preorder, inorder,length);
PrintTree(root);
DestroyTree(root);
}
catch(std::exception &expection)
{
printf("Invalid Input.\n");
}
}
// 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
/*
判断完全二叉树:完全二叉树：除最后一层外，每一层上的节点数均达到最大值；在最后一层上只缺少右边的若干结点。
完全二叉树(Complete Binary Tree)定义：
若设二叉树的深度为h，除第 h 层外，其它各层 (1～h-1) 的结点数都达到最大个数，第 h 层所有的结点都连续集中在最左边，这就是完全二叉树。
*/
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 _tmain(int argc, _TCHAR *argv[])
{
//Test1();
// Test2();
//Test3();
//Test4();
//Test6();
Test7();
//Test5();
system("pause");
return 0;
}