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The author of this article, Noah Lazy Yangyang, a classmate of MF22, HKUST, provides a homework idea for everyone, please do not copy directly ! ! ! Let's learn together~
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Table of contents
2. Description of the algorithm
2.1 Description of data structure
2.2 Description of program structure
4. Spatio-temporal analysis of the algorithm
6. Experimental experience and harvest
1. Description of the problem
1.1 Basic functions
1. Create a binary tree (10')
You can use the preorder traversal input, and you can use # to indicate that there are no nodes.
For example, you can enter 6423####51##7## in the picture below. Here the first two #s indicate that the left and right children of node 3 are empty, the third # indicates that the right child of node 2 is empty, the fourth # indicates that the right child of node 4 is empty, and the two #s after 1 and 7 represent nodes respectively The left and right child nodes of 1 and 7 are empty.
You can also choose other ways to input, but you should make it clear in the readme file and the experiment report.
2. Traversing a binary tree (preorder, inorder, postorder, layer order traversal) (20')
Preorder traversal: 6423517
Inorder traversal: 3246157
Post-order traversal: 3241756
Layer sequence traversal: 6452173
3. Calculation of binary tree (number of nodes, number of leaves, height, width, etc.) of binary tree (20')
Number of nodes: 7
Number of leaves: 3
Height: 4
Width: 3
4. Binary tree processing (copying, destroying) (20')
Copying creates a new binary tree, and the destruction operations between the original binary tree and the copied binary tree cannot affect each other.
1.2 Robustness
- For the case that the created binary tree is empty, the program must be able to run normally and recognize it. (5 points)
- For an empty tree, other functions must be able to identify and output corresponding information, and the program cannot terminate abnormally. (5 points)
1.3 Normative
- code comment
- program modularization
- Friendly human-computer interaction
2. Description of the algorithm
2.1 Description of data structure
The main data structure used in the program is a binary tree (binary linked list).
Explanation of main variables:
| variable |
type |
illustrate |
| Node、BiTNode |
structure |
The structure of the binary tree node |
| *BiTree |
Binary tree node pointer |
A pointer to a binary tree node |
| data |
Variable (determined by the macro definition TElemType, char in the example) |
Data Fields in Binary Tree Nodes |
| *lchild |
Binary tree node pointer |
node's left child |
| *rchild |
Binary tree node pointer |
node's right child |
| TElemType |
macro definition |
Types of binary tree node data fields |
2.2 Description of program structure
The program mainly includes the Noah_BiTree.h header file and the main.cpp main file, where Noah_BiTree.h is the implementation code header file of the binary linked list data structure, N, and main.cpp mainly realizes the interaction between the menu and the function interface and the functions in the header file call. Its specific structure is shown in the figure below.
3. Debugging analysis
Debugging function 1: Create a binary tree and show the tree structure
Create a binary tree and display the structure of the tree
Test data selection:
- 6423####51##7##
- 124##5##36##7##
- #
- 1234######
Problems and solutions:
none
Debugging function 2: Create a binary tree and show show the preoeder, inorder, postorder and levelorder
Create a binary tree showing preorder, inorder postorder, and level traversal.
Test data selection:
- 6423####51##7##
- 124##5##36##7##
- 1234######
Problems and solutions:
none
调试功能三：Create a binary tree and calculate the number of nodes, leaves, height and width
Create a binary tree, count the number of nodes, leaves, height and width
Test data selection:
- 6423####51##7##
- 124##5##36##7##
- 1234######
Problems and solutions:
none
调试功能四：Create a binary tree, copy it, destory the original one and show the new tree
Create a binary tree, copy it, destroy the original tree, and display the new tree
Test data selection:
- 6423####51##7##
- 124##5##36##7##
- 1234######
Problems and solutions:
none
4. Spatio-temporal analysis of the algorithm
(1) CreateBiTree_withhint(BiTree &T)
Time complexity: O(n)
Space complexity: O(n)
(2) preorder(BiTree T)
Time complexity: O(n)
Space complexity: O(n)
(3) inorder(BiTree T)
Time complexity: O(n)
Space complexity: O(n)
(4) mail order (BiTree T)
Time complexity: O(n)
Space complexity: O(n)
(5) levelorder(BiTree T)
Time complexity: O(n)
Space complexity: O(n)
(6) NumofNode (BiTree T)
Time complexity: O(n)
Space complexity: O(n)
(7) BiHight (BiTree T)
Time complexity: O(n)
Space complexity: O(n)
(7) Numofleaves (BiTree T)
Time complexity: O(n)
Space complexity: O(n)
(7) BiWidth (BiTree T)
Time complexity: O(n)
Space complexity: O(n)
(7) CopyBitree (BiTree T)
Time complexity: O(n)
Space complexity: O(n)
(7) DestroyBiTree (BiTree T)
Time complexity: O(n)
Space complexity: O(n)
5. Test results and analysis
Test function one: Create a binary tree and show the tree structure
| test case |
result |
analyze |
| 6423####51##7## |
|
√ |
| 124##5##36##7## |
|
√ |
| # |
|
√ |
| 1234###### |
|
√ |
Debugging function 2: Create a binary tree and show show the preoeder, inorder, postorder and levelorder
| test case |
result |
analyze |
| 6423####51##7## |
|
√ |
| 124##5##36##7## |
|
√ |
| 1234###### |
|
√ |
测试功能三：Create a binary tree and calculate the number of nodes, leaves, height and width
| test case |
result |
analyze |
| 6423####51##7## |
|
√ |
| 124##5##36##7## |
|
√ |
| 1234###### |
|
√ |
调试功能四：Create a binary tree, copy it, destory the original one and show the new tree
| test case |
result |
analyze |
| 6423####51##7## |
|
√ |
| 124##5##36##7## |
|
√ |
| 1234###### |
|
√ |
6. Experimental experience and harvest
- Master the recursive properties of binary trees
- Master the common storage structure of binary tree----binary linked list
- Master basic operations such as binary tree creation and traversal
- Understand the execution process of recursive functions and learn to write recursive programs
the code
Noah_BiTree.h
1. #ifndef __NOAH_BITREE_H__
2. #define __NOAH_BITREE_H__
3. #include <stdlib.h>
4. #include <iostream>
5. #include <cstring>
6. #include <queue>
7. #include <string>
8. #include <iostream>
9. using namespace std;
10. #define TElemType char
11. /*
12. 1. 对于创建的二叉树为空的情况，要能程序要能正常运行并识别。（5分）
13. 2. 对于空树，其他功能要可以识别、输出相应信息，并且程序不能异常终止。（5分）
14. */
15. typedef struct Node
16. {
17. TElemType data;
18. struct Node *lchild,*rchild;//左右孩子指针
19. }BiTNode,*BiTree;
20.
21. void CreateBiTree_Preorder(BiTree &T){
22. //使用先序遍历的输入创建一个二叉树，例如6423####51##7##
23. char x;
24. cin>>x;
25. if(x==' '||x=='#'){
26. T = NULL;
27. }
28. else {
29. T = (BiTree)malloc(sizeof(BiTNode));
30. if(x !='#')
31. T->data = (TElemType)x;
32. CreateBiTree_Preorder(T->lchild);
33. CreateBiTree_Preorder(T->rchild);
34. }
35. }
36.
37. void CreateBiTree_withhint(BiTree &T){
38. //向屏幕输出初始化二叉树的提示信息，调用CreateBiTree_Preorder()
39. cout<<"Please input a preorder sequence of a binary tree(example:6423####51##7##):"<<endl;
40. CreateBiTree_Preorder(T);
41. if(T==NULL) cout<<"Input is an empty BiTree."<<endl;
42. }
43.
44. int isBiTreeEmpty(BiTree T){
45. //判断二叉树是否为空，为空返回1，不为空返回0
46. if((T->data == NULL && T->lchild && T->rchild)||T==NULL)
47. return 1;
48. else
49. return 0;
50. }
51.
52. void preorder(BiTree T){
53. //使用先序遍历输出二叉树
54. if(T){
55. cout<<T->data;
56. preorder(T->lchild);
57. preorder(T->rchild);
58. }
59. else
60. return;
61. //cout<<"Empty BiTree."<<endl;
62. }
63.
64. void inorder(BiTree T){
65. //使用中序遍历输出二叉树
66. if(T){
67. inorder(T->lchild);
68. cout<<T->data;
69. inorder(T->rchild);
70. }
71. }
72.
73. void postorder(BiTree T){
74. //使用后序遍历输出二叉树
75. if(T){
76. postorder(T->lchild);
77. postorder(T->rchild);
78. cout<<T->data;
79. }
80. }
81.
82. void leverorder(BiTree T){
83. //使用层次遍历输出二叉树
84. if(T){
85. queue<BiTree> q;
86. q.push(T);
87. while(!q.empty()){//当队列非空时，还有没有遍历的parent结点
88. BiTree temp = q.front();
89. q.pop();
90. cout<<temp->data;
91. if(temp->lchild!=NULL) q.push(temp->lchild);
92. if(temp->rchild!=NULL) q.push(temp->rchild);
93. }
94. }
95. }
96.
97. int NumofNode(BiTree T){
98. //返回二叉树节点数
99. if(!T) return 0;
100. else return 1 + NumofNode(T->lchild) + NumofNode(T->rchild);
101. }
102.
103. int Numofleaves(BiTree T){
104. //返回二叉树叶子数
105. int num = 0;
106. if(!T) return 0;
107. else{
108. if(T->lchild!=NULL) num = num + Numofleaves(T->lchild);
109. if(T->rchild!=NULL) num = num + Numofleaves(T->rchild);
110. if(T->lchild==NULL && T->rchild==NULL) return 1;
111. }
112. return num;
113. }
114.
115. int BiHight(BiTree T){
116. //返回二叉树高度
117. if(!T) return 0;
118. else{
119. int lefthight = BiHight(T->lchild);
120. int righthight = BiHight(T->rchild);
121. return (lefthight>=righthight)?lefthight+1:righthight+1;
122. }
123. }
124.
125. int BiWidth(BiTree T){
126. //返回二叉树宽度
127. if (isBiTreeEmpty(T)) {
128. return 0;
129. }
130. queue<BiTree> q;
131. int maxWidth = 1;
132. q.push(T);
133.
134. while (1) {
135. int len = q.size();
136. if (!len) {
137. break;
138. }
139. while (len--) {
140.
141. BiTree temp = q.front();
142. q.pop();
143. if (temp->lchild) {
144. q.push(temp->lchild);
145. }
146. if (temp->rchild) {
147. q.push(temp->rchild);
148. }
149. }
150. maxWidth = max(maxWidth, (int) q.size());
151. }
152. return maxWidth;
153. }
154.
155. void CopyBitree(BiTree source,BiTree &target){
156. //将source中的二叉树复制给target，原二叉树和复制的二叉树之间销毁操作不能互相影响
157. if(!source){
158. target = NULL;
159. return;
160. }
161.
162. else{
163. target = (BiTNode *)malloc(sizeof(BiTNode));
164. target->data = (TElemType)source->data;
165. CopyBitree(source->lchild,target->lchild);
166. CopyBitree(source->rchild,target->rchild);
167. }
168. }
169.
170.
171. void DestroyBiTree(BiTree &T){
172. //销毁二叉树并释放内存
173. if(isBiTreeEmpty(T)){
174. cout<<"DestroyBiTree succeed."<<endl;
175. return;
176. }
177. else{
178. if(T->lchild!=NULL) DestroyBiTree(T->lchild);
179. if(T->rchild!=NULL) DestroyBiTree(T->rchild);
180. free(T);
181. T = NULL;
182. }
183. }
184.
185. void DisplayBitree_control(BiTree n, bool left, string const& indent){
186. //DisplayBitree()函数的中间控制函数
187. if (n->rchild)
188. {
189. DisplayBitree_control(n->rchild, false, indent + (left ? "| " : " "));
190. }
191. cout << indent;
192. cout << (left ? '\\' : '/');
193. cout << "-----";
194. cout << n->data << endl;
195. if (n->lchild)
196. {
197. DisplayBitree_control(n->lchild, true, indent + (left ? " " : "| "));
198. }
199. }
200. void DisplayBitree(BiTree root){
201. //以树形结构形式输出二叉树
202. if(!root){
203. cout<<"An empty tree."<<endl;
204. return;
205. }
206. if (root->rchild)
207. {
208. DisplayBitree_control(root->rchild, false, "");
209. }
210. cout << root->data << endl;
211. if (root->lchild)
212. {
213. DisplayBitree_control(root->lchild, true, "");
214. }
215. }
216. #endif
main.cpp
1. #include <stdio.h>
2. #include <string.h>
3. #include <stdlib.h>
4. #include <iostream>
5. using namespace std;
6. #include "Noah_BiTree.h"
7. void Menue_gui();
8. void func1();
9. void func2();
10. void func3();
11. void func4();
12.
13. int main()
14. {
15. while(1){
16. Menue_gui();
17. int func;
18. scanf("%d",&func);
19. switch(func){
20. case 0:
21. exit(0);
22. case 1:
23. func1();break;
24. case 2:
25. func2();break;
26. case 3:
27. func3();break;
28. case 4:
29. func4();break;
30. default:
31. printf("Input error! Please try again!");
32. }
33. printf("\n");
34. system("pause");
35. }
36. return 0;
37. }
38.
39. //主界面
40. void Menue_gui(){
41. system("cls");
42. printf("**********************************Binary Tree calcuator**************************************\n");
43. printf("*********************************************************************************************\n");
44. printf("Menue:\n");
45. printf("\nExit this program------------------------------------------------------------------0.\n");
46. printf("\nCreate a binary tree and show the tree structure-----------------------------------1.\n");
47. printf("\nCreate a binary tree and show show the preoeder, inorder, postorder and levelorder-2.\n");
48. printf("\nCreate a binary tree and calculate the number of nodes, leaves, height and width---3.\n");
49. printf("\nCreate a binary tree, copy it, destory the original one and show the new tree------4.\n");
50. printf("\n**********************************************************************************************\n");
51. printf("Choose the function you want to use(input number):\n");
52. }
53.
54. void func1(){
55. system("cls");
56. printf("-----ENTER FUNCTION : Create a binary tree and show the tree structure--1.-----\n");
57. BiTree T1;
58. CreateBiTree_withhint(T1);
59. DisplayBitree(T1);
60. }
61. void func2(){
62. system("cls");
63. printf("-----ENTER FUNCTION : Create a binary tree and show show the preoeder, inorder, postorder and levelorder--2.-----\n");
64. BiTree T1;
65. CreateBiTree_withhint(T1);
66. cout<<endl<<"The tree form of the Binary Tree is:"<<endl;
67. DisplayBitree(T1);
68. cout<<endl<<"The preorder of the Binary Tree is:"<<endl;
69. preorder(T1);
70. cout<<endl<<"The inorder of the Binary Tree is:"<<endl;
71. inorder(T1);
72. cout<<endl<<"The postorder of the Binary Tree is:"<<endl;
73. postorder(T1);
74. cout<<endl<<"The levelorder of the Binary Tree is:"<<endl;
75. leverorder(T1);
76. }
77. void func3(){
78. system("cls");
79. printf("-----ENTER FUNCTION : Create a binary tree and calculate the number of nodes, leaves, height and width--3.-----\n");
80. BiTree T1;
81. CreateBiTree_withhint(T1);
82. cout<<endl<<"The tree form of the Binary Tree is:"<<endl;
83. DisplayBitree(T1);
84. cout<<endl<<"The number of nodes is:"<<NumofNode(T1)<<endl;
85. cout<<endl<<"The number of leaves is:"<<Numofleaves(T1)<<endl;
86. cout<<endl<<"The height is:"<<BiHight(T1)<<endl;
87. cout<<endl<<"The width is:"<<BiWidth(T1)<<endl;
88. }
89. void func4(){
90. system("cls");
91. printf("-----ENTER FUNCTION : Create a binary tree, copy it, destory the original one and show the new tree--4.-----\n");
92. BiTree T1;
93. CreateBiTree_withhint(T1);
94. cout<<endl<<"The tree form of the [ORIGINAL] Binary Tree is:"<<endl;
95. DisplayBitree(T1);
96. BiTree T2;
97. CopyBitree(T1,T2);//复制T1到T2
98. DestroyBiTree(T1);//销毁T1
99. cout<<endl<<"After destroy, the tree form of the [ORIGINAL] Binary Tree is:"<<endl;
100. DisplayBitree(T1);
101. cout<<endl<<"The tree form of the [NEW] Binary Tree is:"<<endl;
102. DisplayBitree(T2);
103. }