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【遍历二叉树】01二叉树的前序遍历【Binary Tree Preorder Traversal】

2014-04-08 16:15 134 查看
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给定一个二叉树，返回他的前序遍历的节点的values。

例如：

给定一个二叉树 
{1,#,2,3}
,

1
\
2
/
3

返回 
[1,2,3].


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 preorder traversal of its nodes' values.

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

1
\
2
/
3

return 
[1,2,3]
.

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

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1.递归实现
test.cpp:

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

using namespace std;

void preorder(TreeNode *root, vector<int> &path)
{
if(root != NULL)
{
path.push_back(root->val);
preorder(root->left, path);
preorder(root->right, path);
}
}
vector<int> preorderTraversal(TreeNode *root)
{
vector<int> path;
preorder(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 = preorderTraversal(pNodeA1);

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

DestroyTree(pNodeA1);
return 0;
}

输出结果：
8 6 9 2 4 7 1

2.非递归实现（迭代实现）

根据前序遍历访问的顺序，优先访问根结点，然后再分别访问左孩子和右孩子。即对于任一结点，其可看做是根结点，因此可以直接访问，访问完之后，若其左孩子不为空，按相同规则访问它的左子树；当访问其左子树时，再访问它的右子树。因此其处理过程如下：

对于任一结点P：

1)访问结点P，并将结点P入栈;

2)判断结点P的左孩子是否为空，若为空，则取栈顶结点并进行出栈操作，并将栈顶结点的右孩子置为当前的结点P，循环至1);若不为空，则将P的左孩子置为当前的结点P;

3)直到P为NULL并且栈为空，则遍历结束。

test.cpp:

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

using namespace std;

//非递归前序遍历
vector<int> preorderTraversal(TreeNode *root)
{
stack<TreeNode *> s;
vector<int> path;
TreeNode *p = root;
while(p != NULL || !s.empty())
{
while(p != NULL)
{
path.push_back(p->val);
s.push(p);
p = p->left;
}
if(!s.empty())
{
p = s.top();
s.pop();
p = p->right;
}
}
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 = preorderTraversal(pNodeA1);

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

DestroyTree(pNodeA1);
return 0;
}

输出结果：
8 6 9 2 4 7 1

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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