[BinaryTree] 二叉树类的实现

二叉树结点的抽象数据类型：

 1 template<class T>
 2 class BinaryTreeNode
 3 {
 4     friend class BinaryTree<T>;
 5 private:
 6     T element;                      //结点的数据域
 7     BinaryTreeNode<T>* LeftChild;   //结点的左孩子结点
 8     BinaryTreeNode<T>* RightChild;  //结点的右孩子结点
 9 public:
10     BinaryTreeNode();
11     BinaryTreeNode(const T& ele);
12     BinaryTreeNode(const T& ele, BinaryTreeNode<T>* l, BinaryTreeNode<T>* r);
13     bool isLeaf() const;            //判断该结点是否是叶子结点，若是，则返回true
14 };

二叉树结点函数功能实现：

 1 template<class T>
 2 BinaryTreeNode<T>::BinaryTreeNode()
 3 {
 4     LeftChild = RightChild = NULL;
 5 }
 6 template<class T>
 7 BinaryTreeNode<T>::BinaryTreeNode(const T& ele)
 8 {
 9     element = ele;
10     LeftChild = RightChild = NULL;
11 }
12 template<class T>
13 BinaryTreeNode<T>::BinaryTreeNode(const T& ele, BinaryTreeNode<T>* l, BinaryTreeNode<T>* r)
14 {
15     element = ele;
16     LeftChild = l;
17     RightChild = r;
18 }
19 template<class T>
20 bool BinaryTreeNode<T>::isLeaf() const
21 {
22     if (LeftChild == NULL && RightChild == NULL)
23         return true;
24     else return false;
25 }

二叉树的抽象数据类型：

 1 template<class T>
 2 class BinaryTree
 3 {
 4 private:
 5     BinaryTreeNode<T>* root;
 6 public:
 7     BinaryTree();
 8     ~BinaryTree() {}
 9     bool IsEmpty() const;                           //判断二叉树是否为空树
10     BinaryTreeNode<T>* getRoot() const;             //返回二叉树的根结点
11     void breadthFirstOrder(BinaryTreeNode<T>* root);//广度优先遍历以root为根结点的子树
12     void preOrder(BinaryTreeNode<T>* root);         //先序遍历以root为根结点的子树
13     void inOrder(BinaryTreeNode<T>* root);          //中序遍历以root为根结点的子树
14     void postOrder(BinaryTreeNode<T>* root);        //后序遍历以root为根结点的子树
15     void deleteBinaryTree(BinaryTreeNode<T>* root); //删除以root为根结点的子树
16     void visit(BinaryTreeNode<T>* pointer);         //访问当前结点
17     BinaryTreeNode<T>* build_from_pre_and_in(char* preorder, char* inorder, int n);
18     //根据前序和中序遍历表达式构造二叉树
19     BinaryTreeNode<T>* build_from_post_and_in(char* postorder, char* inorder, int m);
20     //根据后序和中序遍历表达式构造二叉树
21     int getRootId1(char *preorder, char *inorder, int n);   //返回根结点在中序遍历表达式中序号
22     int getRootId2(char *postorder, char *inorder, int m);  //返回根结点在中序遍历表达式中序号
23 };

广度优先遍历(队列)：

【思路】根结点入队，队列不空循环，访问队头并出队，左子树不空则入队，右子树不空则入队。

 1 template<class T>
 2 void BinaryTree<T>::breadthFirstOrder(BinaryTreeNode<T>* root)
 3 {
 4     queue<BinaryTreeNode<T> *> nodeQueue;
 5     BinaryTreeNode<T> * pointer = root;
 6     if (pointer)
 7         nodeQueue.push(pointer);
 8     while (!nodeQueue.empty())
 9     {
10         pointer = nodeQueue.front();
11         visit(pointer);
12         nodeQueue.pop();
13         if (pointer->LeftChild)
14             nodeQueue.push(pointer->LeftChild);
15         if (pointer->RightChild)
16             nodeQueue.push(pointer->RightChild);
17     }
18 }

先序遍历：

【思路】

1.访问当前结点

2.当前结点的右儿子结点非空，则入栈

3.左儿子结点非空，使之作为当前结点，否则弹出栈顶元素，使之作为当前结点

4.反复执行1、2、3，至栈空为止

 1 template<class T>
 2 void BinaryTree<T>::preOrder(BinaryTreeNode<T>* root)
 3 {
 4     stack<BinaryTreeNode<T> *> nodeStack;
 5     BinaryTreeNode<T> * pointer = root;
 6     while (!nodeStack.empty() || pointer)
 7     {
 8         if (pointer)
 9         {
10             visit(pointer);
11             if (pointer->RightChild != NULL)
12                 nodeStack.push(pointer->RightChild);
13             pointer = pointer->LeftChild;
14         }
15         else
16         {
17             pointer = nodeStack.top();
18             nodeStack.pop();
19         }
20     }
21 }

中序遍历：

【思路】

1.每遇到一个结点就把它压栈，然后去遍历其左子树

2.遍历完左子树后，从栈顶弹出这个结点并访问之

3.然后遍历该结点的右子树

 1 template<class T>
 2 void BinaryTree<T>::inOrder(BinaryTreeNode<T>* root)
 3 {
 4     stack<BinaryTreeNode<T> *> nodeStack;
 5     BinaryTreeNode<T> * pointer = root;
 6     while (!nodeStack.empty() || pointer)
 7     {
 8         if (pointer)
 9         {
10             nodeStack.push(pointer);
11             pointer = pointer->LeftChild;
12         }
13         else
14         {
15             pointer = nodeStack.top();
16             visit(pointer);
17             pointer = pointer->RightChild;
18             nodeStack.pop();
19         }
20     }
21 }

后序遍历：

【基本思想】

1.每遇到一个结点，先把它推入栈中，去遍历它的左子树

2.遍历完它的左子树后，应继续遍历该结点的右子树

3.遍历完右子树之后，才从栈顶弹出该结点并访问它

【解决方案】

0.将根结点作为当前结点

1.进栈过程：

  a.如果当前结点不空且具有左子树，将当前结点压入栈中，否则进入2

  b.将当前结点的左子树的根结点设置为当前结点

  c.重复 a

2.出栈过程：

  a.如果当前结点不空且没有右子树，或者其右子树的根结点已经访问，访问之，否则进入3

  b.若栈空，结束，否则取出当前栈顶结点作为当前结点

  c.重复 a

3.将当前结点压入栈中

4.将当前结点的右子树的根结点设为当前结点，重复 1

 1 template<class T>
 2 void BinaryTree<T>::postOrder(BinaryTreeNode<T>* root)
 3 {
 4     stack<BinaryTreeNode<T> * > nodeStack;
 5     BinaryTreeNode<T> *pre = root, *pointer = root;
 6     while (pointer)
 7     {
 8         //入栈过程
 9         for (; pointer->LeftChild != NULL; pointer = pointer->LeftChild)
10         {
11             nodeStack.push(pointer);
12         }
13         //出栈过程
14         while (pointer != NULL && (pointer->RightChild == NULL || pointer->RightChild == pre))
15         //当前结点右孩子为空或右孩子刚被访问过，则访问该结点
16         {
17             visit(pointer);
18             pre = pointer;
19             if (nodeStack.empty())
20                 return;
21             pointer = nodeStack.top();
22             nodeStack.pop();
23         }
24         //将当前结点压入栈中
25         nodeStack.push(pointer);
26         //将当前结点的右子树的根结点设为当前结点
27         pointer = pointer->RightChild;
28     }
29 }

删除以root为根结点的子树：

 1 template<class T>
 2 void BinaryTree<T>::deleteBinaryTree(BinaryTreeNode<T>* root)
 3 {
 4     if (root->LeftChild != NULL)
 5         deleteBinaryTree(root->LeftChild);
 6     if (root->RightChild != NULL)
 7         deleteBinaryTree(root->RightChild);
 8     delete root;
 9     root = NULL;
10 }

根据前序和中序遍历表达式构造二叉树：

【思路】根据前序序列，找到根结点在中序序列中的位置，递归根结点的左子树序列和右子树序列。

 1 template<class T>
 2 BinaryTreeNode<T>* BinaryTree<T>::build_from_pre_and_in(char* preorder, char* inorder, int n)
 3 {
 4     if (n == 0)
 5         return NULL;
 6     char root_element = preorder[0];
 7     int i = 0;
 8     for( ;i < n;i ++)
 9     {
10         if(root_element == inorder[i])
11             break;
12     }
13     BinaryTreeNode<T>* root = new BinaryTreeNode<T>;
14     root->element = root_element;
15     root->LeftChild = build_from_pre_and_in(preorder + 1, inorder, i);
16     root->RightChild = build_from_pre_and_in(preorder + i + 1, inorder + i + 1, n - i - 1);
17     return root;
18 }

根据后序和中序遍历表达式构造二叉树：

【思路】根据后序序列，找到根结点在中序序列中的位置，递归根结点的左子树序列和右子树序列。

 1 template<class T>
 2 BinaryTreeNode<T>* BinaryTree<T>::build_from_post_and_in(char* postorder, char* inorder, int m)
 3 {
 4     if (m == 0)
 5         return NULL;
 6     char root_element = postorder[m - 1];
 7     int i = 0;
 8     for( ;i < m;i ++)
 9     {
10         if(root_element == inorder[i])
11             break;
12     }
13     BinaryTreeNode<T>* root = new BinaryTreeNode<T>;
14     root->element = root_element;
15     root->LeftChild = build_from_post_and_in(postorder, inorder, i);
16     root->RightChild = build_from_post_and_in(postorder+i, inorder + i+1, m-i-1);
17     return root;
18 }

测试函数：

 1 int main()
 2 {
 3     BinaryTreeNode<char> *zero = 0;
 4     BinaryTreeNode<char> f('F'), g('G'), h('H');
 5     BinaryTreeNode<char> d('D', &f, &g), e('E', zero, &h);
 6     BinaryTreeNode<char> b('B', zero, &d), c('C', zero, &e);
 7     BinaryTreeNode<char> a('A', &b, &c);
 8     BinaryTree<char> Tree;
 9     cout << "广度优先遍历为:" << endl;
10     Tree.breadthFirstOrder(&a);
11     cout << endl << "先序遍历为:" << endl;
12     Tree.preOrder(&a);
13     cout << endl << "中序遍历为:" << endl;
14     Tree.inOrder(&a);
15     cout << endl << "后序遍历为:" << endl;
16     Tree.postOrder(&a);
17     char *preorder = "ABDFGCEH";
18     char *inorder = "BFDGACEH";
19     char *postorder = "FGDBHECA";
20     int n = strlen(preorder);
21     int m = strlen(postorder);
22     BinaryTreeNode<char>* root1 = Tree.build_from_pre_and_in(preorder, inorder, n);
23     cout << endl << "先序中序构造后广度优先遍历为:" << endl;
24     Tree.breadthFirstOrder(root1);
25     BinaryTreeNode<char>* root2 = Tree.build_from_post_and_in(postorder, inorder, m);
26     cout << endl << "后序中序构造后广度优先遍历为:" << endl;
27     Tree.breadthFirstOrder(root2);
28     return 0;
29 }
30 //    测试的二叉树
31 //           A
32 //    B             C
33 //       D              E
34 //     F   G               H

测试结果：

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原文地址：https://www.cnblogs.com/lca1826/p/6358418.html