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【遍历二叉树】03二叉树的后序遍历【Binary Tree Postorder Traversal】

2014-04-08 16:41 399 查看
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给定一个二叉树，返回他的后序遍历的节点的values。

例如：

给定一个二叉树 
{1,#,2,3}
,

1
\
2
/
3

返回 
[3,2,1]
.

笔记：

递归解决方案是微不足道的，你可以用迭代的方法吗？

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Given a binary tree, return the postorder traversal of its nodes' values.

For example:
Given binary tree 
{1,#,2,3}
,

1
\
2
/
3

return 
[3,2,1]
.

Note: Recursive solution is trivial, could you do it iteratively?

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【二叉树遍历模版】后序遍历-递归实现

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#include <iostream>
#include <cstdio>
#include <stack>
#include <vector>
#include "BinaryTree.h"

using namespace std;

/**
* Definition for binary tree
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
void postorder(TreeNode *root, vector<int> &path)
{
if(root != NULL)
{
postorder(root->left, path);
postorder(root->right, path);
path.push_back(root->val);
}
}
vector<int> postorderTraversal(TreeNode *root)
{

vector<int> path;
postorder(root, path);
return path;
}

// 树中结点含有分叉，
// 8
// / \
// 6 1
// / \
// 9 2
// / \
// 4 7
int main()
{
TreeNode *pNodeA1 = CreateBinaryTreeNode(8);
TreeNode *pNodeA2 = CreateBinaryTreeNode(6);
TreeNode *pNodeA3 = CreateBinaryTreeNode(1);
TreeNode *pNodeA4 = CreateBinaryTreeNode(9);
TreeNode *pNodeA5 = CreateBinaryTreeNode(2);
TreeNode *pNodeA6 = CreateBinaryTreeNode(4);
TreeNode *pNodeA7 = CreateBinaryTreeNode(7);

ConnectTreeNodes(pNodeA1, pNodeA2, pNodeA3);
ConnectTreeNodes(pNodeA2, pNodeA4, pNodeA5);
ConnectTreeNodes(pNodeA5, pNodeA6, pNodeA7);

PrintTree(pNodeA1);

vector<int> ans = postorderTraversal(pNodeA1);

for (int i = 0; i < ans.size(); ++i)
{
cout << ans[i] << " ";
}
cout << endl;

DestroyTree(pNodeA1);
return 0;
}

9 4 7 2 6 1 8运行结果：

2.非递归实现

后序遍历的非递归实现是三种遍历方式中最难的一种。因为在后序遍历中，要保证左孩子和右孩子都已被访问并且左孩子在右孩子前访问才能访问根结点，这就为流程的控制带来了难题。下面介绍两种思路。

第一种思路：对于任一结点P，将其入栈，然后沿其左子树一直往下搜索，直到搜索到没有左孩子的结点，此时该结点出现在栈顶，但是此时不能将其出栈并访问， 因此其右孩子还为被访问。所以接下来按照相同的规则对其右子树进行相同的处理，当访问完其右孩子时，该结点又出现在栈顶，此时可以将其出栈并访问。这样就 保证了正确的访问顺序。可以看出，在这个过程中，每个结点都两次出现在栈顶，只有在第二次出现在栈顶时，才能访问它。因此需要多设置一个变量标识该结点是 否是第一次出现在栈顶。

test.cpp:

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#include <iostream>
#include <cstdio>
#include <stack>
#include <vector>
#include "BinaryTree.h"

using namespace std;

/**
* Definition for binary tree
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/

//中介节点
struct TempNode
{
TreeNode *btnode;
bool isFirst;
};

//非递归后序遍历-迭代
vector<int> postorderTraversal(TreeNode *root)
{
stack<TempNode *> s;
vector<int> path;
TreeNode *p = root;
TempNode *temp;
while(p != NULL || !s.empty())
{
while(p != NULL) //沿左子树一直往下搜索，直至出现没有左子树的结点
{
TempNode *tempNode = new TempNode;
tempNode->btnode = p;
tempNode->isFirst = true;
s.push(tempNode);
p = p->left;
}
if(!s.empty())
{
temp = s.top();
s.pop();
if(temp->isFirst == true) //表示是第一次出现在栈顶
{
temp->isFirst = false;
s.push(temp);
p = temp->btnode->right;
}
else //第二次出现在栈顶
{
path.push_back(temp->btnode->val);
p = NULL;
}
}
}
return path;
}

// 树中结点含有分叉，
// 8
// / \
// 6 1
// / \
// 9 2
// / \
// 4 7
int main()
{
TreeNode *pNodeA1 = CreateBinaryTreeNode(8);
TreeNode *pNodeA2 = CreateBinaryTreeNode(6);
TreeNode *pNodeA3 = CreateBinaryTreeNode(1);
TreeNode *pNodeA4 = CreateBinaryTreeNode(9);
TreeNode *pNodeA5 = CreateBinaryTreeNode(2);
TreeNode *pNodeA6 = CreateBinaryTreeNode(4);
TreeNode *pNodeA7 = CreateBinaryTreeNode(7);

ConnectTreeNodes(pNodeA1, pNodeA2, pNodeA3);
ConnectTreeNodes(pNodeA2, pNodeA4, pNodeA5);
ConnectTreeNodes(pNodeA5, pNodeA6, pNodeA7);

PrintTree(pNodeA1);

vector<int> ans = postorderTraversal(pNodeA1);

for (int i = 0; i < ans.size(); ++i)
{
cout << ans[i] << " ";
}
cout << endl;

DestroyTree(pNodeA1);
return 0;
}

输出结果：
9 4 7 2 6 1 8

BinaryTree.h:

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#ifndef _BINARY_TREE_H_
#define _BINARY_TREE_H_

struct TreeNode
{
int val;
TreeNode *left;
TreeNode *right;
TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};

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

#endif /*_BINARY_TREE_H_*/

BinaryTree.cpp:

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#include <iostream>
#include <cstdio>
#include "BinaryTree.h"

using namespace std;

/**
* Definition for binary tree
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/

//创建结点
TreeNode *CreateBinaryTreeNode(int value)
{
TreeNode *pNode = new TreeNode(value);

return pNode;
}

//连接结点
void ConnectTreeNodes(TreeNode *pParent, TreeNode *pLeft, TreeNode *pRight)
{
if(pParent != NULL)
{
pParent->left = pLeft;
pParent->right = pRight;
}
}

//打印节点内容以及左右子结点内容
void PrintTreeNode(TreeNode *pNode)
{
if(pNode != NULL)
{
printf("value of this node is: %d\n", pNode->val);

if(pNode->left != NULL)
printf("value of its left child is: %d.\n", pNode->left->val);
else
printf("left child is null.\n");

if(pNode->right != NULL)
printf("value of its right child is: %d.\n", pNode->right->val);
else
printf("right child is null.\n");
}
else
{
printf("this node is null.\n");
}

printf("\n");
}

//前序遍历递归方法打印结点内容
void PrintTree(TreeNode *pRoot)
{
PrintTreeNode(pRoot);

if(pRoot != NULL)
{
if(pRoot->left != NULL)
PrintTree(pRoot->left);

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

void DestroyTree(TreeNode *pRoot)
{
if(pRoot != NULL)
{
TreeNode *pLeft = pRoot->left;
TreeNode *pRight = pRoot->right;

delete pRoot;
pRoot = NULL;

DestroyTree(pLeft);
DestroyTree(pRight);
}
}

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