树 - 二叉树

读了Robert Sedgewick的《算法:C语言实现》（第三版）的第五章，了解了许多关于树，特别是二叉树的知识。这里总结一下。直接看代码(C++)吧。

  1 #include <cstdio>
  2 #include <cstdlib>
  3 #include <queue>
  4 #include <stack>
  5
  6 #define null 0
  7 #define NEXTLINE printf("\n")
  8 #define MAX(x, y) ((x)>(y)?(x):(y))
  9
 10 int max = 1<<31;
 11 int min = ~(1<<31);
 12
 13 typedef int Item;
 14 typedef struct node *link;
 15 struct node {
 16     Item item;
 17     link l, r;
 18 };
 19 // 初始化树
 20 link
 21 InitTree(Item item)
 22 {
 23     link t = (link)malloc(sizeof *t);
 24     if (t == null) {
 25         return null;
 26     }
 27     t->item = item;
 28     t->l = null;
 29     t->r = null;
 30     return t;
 31 }
 32 // 加入左子节点
 33 link
 34 AddLeftNode(link t, Item item)
 35 {
 36     if (t == null) {
 37         return null;
 38     }
 39     link newNode = (link)malloc(sizeof *newNode);
 40     if (newNode == null) {
 41         return null;
 42     }
 43     t->l = newNode;
 44     newNode->item = item;
 45     newNode->l = null;
 46     newNode->r = null;
 47     return newNode;
 48 }
 49 // 加入右子节点
 50 link
 51 AddRightNode(link t, Item item)
 52 {
 53     if (t == null) {
 54         return null;
 55     }
 56     link newNode = (link)malloc(sizeof *newNode);
 57     if (newNode == null) {
 58         return null;
 59     }
 60     t->r = newNode;
 61     newNode->item = item;
 62     newNode->l = null;
 63     newNode->r = null;
 64     return newNode;
 65 }
 66 // 打印节点中的内容
 67 void
 68 PrintItem(link t)
 69 {
 70     printf("%d\t", t->item);
 71 }
 72 // 前序遍历(递归)
 73 void
 74 PreTraverse(link t)
 75 {
 76     if (t == null) {
 77         return;
 78     }
 79     PrintItem(t);
 80     PreTraverse(t->l);
 81     PreTraverse(t->r);
 82 }
 83 // 中序遍历(递归)
 84 void
 85 InTraverse(link t)
 86 {
 87     if (t == null) {
 88         return;
 89     }
 90     InTraverse(t->l);
 91     PrintItem(t);
 92     InTraverse(t->r);
 93 }
 94 // 后序遍历(递归)
 95 void
 96 PostTraverse(link t)
 97 {
 98     if (t == null) {
 99         return;
100     }
101     PostTraverse(t->l);
102     PostTraverse(t->r);
103     PrintItem(t);
104 }
105 // 层次遍历(非递归)
106 void
107 LevelTraverse(link t)
108 {
109     if (t == null) {
110         return;
111     }
112     std::queue<link> linkQueue;
113     linkQueue.push(t);
114     while (!linkQueue.empty()) {
115         PrintItem(t = linkQueue.front());
116         linkQueue.pop();
117         if (t->l != null) linkQueue.push(t->l);
118         if (t->r != null) linkQueue.push(t->r);
119     }
120 }
121 // 前序遍历(非递归)
122 void
123 PreTraverseNR(link t)
124 {
125     if (t == null) {
126         return;
127     }
128     std::stack<link> linkStack;
129     linkStack.push(t);
130     while (!linkStack.empty()) {
131         PrintItem(t = linkStack.top());
132         linkStack.pop();
133         if (t->r != null) linkStack.push(t->r);
134         if (t->l != null) linkStack.push(t->l);
135     }
136 }
137 // 找最大节点
138 void
139 FindMax(link t)
140 {
141     if (t == null) {
142         return;
143     }
144     if (max < t->item) {
145         max = t->item;
146     }
147     FindMax(t->l);
148     FindMax(t->r);
149 }
150 // 找最小节点
151 void
152 FindMin(link t)
153 {
154     if (t == null) {
155         return;
156     }
157     if (min > t->item) {
158         min = t->item;
159     }
160     FindMin(t->l);
161     FindMin(t->r);
162 }
163 // 计算深度(从0开始计算)
164 int
165 CountDepth(link t)
166 {
167     if (t == null) {
168         return -1;
169     }
170     return MAX(CountDepth(t->l), CountDepth(t->r)) + 1;
171 }
172 // 计算所有节点数目
173 int
174 CountNodes(link t)
175 {
176     if (t == null) {
177         return 0;
178     }
179     return CountNodes(t->l) + CountNodes(t->r) + 1;
180 }
181 // 计算叶子节点数目
182 int
183 CountLeaves(link t)
184 {
185     if (t == null) {
186         return 0;
187     }
188     if (!CountLeaves(t->l) && !CountLeaves(t->r)) {
189         return 1;
190     }
191     return CountLeaves(t->l) + CountLeaves(t->r);
192 }
193 // 清空一棵树
194 void
195 DeleteTree(link t)
196 {
197     if (t == null) {
198         return;
199     }
200     if (!(t->l) && !(t->r)) {
201         free(t);
202         return;
203     }
204     DeleteTree(t->l);
205     DeleteTree(t->r);
206     free(t);
207 }
208
209 int
210 main(int argc, char** argv)
211 {
212     link t, t1, t2, t3, t4;
213     t = InitTree(1);
214     t1 = AddLeftNode(t, 2);
215     t2 = AddRightNode(t, 3);
216     t3 = AddLeftNode(t1, 4);
217     t4 = AddRightNode(t1, 5);
218
219
220     PreTraverse(t);
221     NEXTLINE;
222     InTraverse(t);
223     NEXTLINE;
224     PostTraverse(t);
225     NEXTLINE;
226     LevelTraverse(t);
227     NEXTLINE;
228     PreTraverseNR(t);
229     NEXTLINE;
230
231     FindMax(t);
232     FindMin(t);
233     printf("Maxima Item in tree: %d\n", max);
234     printf("Minima Item in tree: %d\n", min);
235
236     printf("Depth of the tree(start from 0): %d\n", CountDepth(t));
237
238     printf("Number of the nodes of the tree: %d\n", CountNodes(t));
239
240     printf("Number of the leaves of the tree: %d\n", CountLeaves(t));
241
242
243     DeleteTree(t);
244
245     system("pause");
246     return 0;
247 }