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【遍历二叉树】09判断二叉树是否关于自己镜像对称【Symmetric Tree】

2014-04-08 16:47 344 查看
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给定一个二叉树，判断是否他自己的镜像对称的。(以自身中间，为镜像对称的)

例如羡慕这个二叉树就是对称的：

1
/ \
2   2
/ \ / \
3  4 4  3

但是下面这个就不是对称的：

1
/ \
2   2
\   \
3    3

笔记：

如果你既能迭代的解决这个问题，又能递归的解决这个问题，那么将给你加分。

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Given a binary tree, check whether it is a mirror of itself (ie, symmetric around its center).

For example, this binary tree is symmetric:

1
/ \
2   2
/ \ / \
3  4 4  3

But the following is not:

1
/ \
2   2
\   \
3    3

Note:
Bonus points if you could solve it both recursively and iteratively.

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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) {}
* };
*/

bool isSymmetric(TreeNode *left, TreeNode *right)
{
if (!left && !right)
{
return true;
}
if (!left || !right)
{
return false;
}
return left->val == right->val && isSymmetric(left->left, right->right)
&& isSymmetric(left->right, right->left);
}

bool isSymmetric(TreeNode *root)
{
return root ? isSymmetric(root->left, root->right) : true;
}

// 树中结点含有分叉，
// 6
// / \
// 7 2
// / \
// 1 4
// / \
// 3 5
int main()
{
TreeNode *pNodeA1 = CreateBinaryTreeNode(6);
TreeNode *pNodeA2 = CreateBinaryTreeNode(7);
TreeNode *pNodeA3 = CreateBinaryTreeNode(2);
TreeNode *pNodeA4 = CreateBinaryTreeNode(1);
TreeNode *pNodeA5 = CreateBinaryTreeNode(4);
TreeNode *pNodeA6 = CreateBinaryTreeNode(3);
TreeNode *pNodeA7 = CreateBinaryTreeNode(5);

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

// 树中结点含有分叉，
// 1
// / \
// 2 2
// / \ / \
// 3 4 4 3

TreeNode *pNodeB1 = CreateBinaryTreeNode(1);
TreeNode *pNodeB2 = CreateBinaryTreeNode(2);
TreeNode *pNodeB3 = CreateBinaryTreeNode(2);
TreeNode *pNodeB4 = CreateBinaryTreeNode(3);
TreeNode *pNodeB5 = CreateBinaryTreeNode(4);
TreeNode *pNodeB6 = CreateBinaryTreeNode(4);
TreeNode *pNodeB7 = CreateBinaryTreeNode(3);

ConnectTreeNodes(pNodeB1, pNodeB2, pNodeB3);
ConnectTreeNodes(pNodeB2, pNodeB4, pNodeB5);
ConnectTreeNodes(pNodeB3, pNodeB6, pNodeB7);

bool ans = isSymmetric(pNodeA1);

if (ans == true)
{
cout << "Symmetric Tree!" << endl;
}
else
{
cout << "Not Symmetric Tree!" << endl;
}

bool ans1 = isSymmetric(pNodeB1);

if (ans1 == true)
{
cout << "Symmetric Tree!" << endl;
}
else
{
cout << "Not Symmetric Tree!" << endl;
}
DestroyTree(pNodeA1);
DestroyTree(pNodeB1);
return 0;
}

结果输出：
Not Symmetric Tree!

Symmetric Tree!

迭代版本：

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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) {}
* };
*/
bool isSymmetric(TreeNode *root)
{
if (!root)
{
return true;
}
stack<TreeNode *> s;
s.push(root->left);
s.push(root->right);

TreeNode *p, *q;
while (!s.empty())
{
p = s.top();
s.pop();
q = s.top();
s.pop();

if (!p && !q)
{
continue;
}
if (!p || !q)
{
return false;
}
if (p->val != q->val)
{
return false;
}

s.push(p->left);
s.push(q->right);

s.push(p->right);
s.push(q->left);
}
return true;
}

// 树中结点含有分叉，
// 6
// / \
// 7 2
// / \
// 1 4
// / \
// 3 5
int main()
{
TreeNode *pNodeA1 = CreateBinaryTreeNode(6);
TreeNode *pNodeA2 = CreateBinaryTreeNode(7);
TreeNode *pNodeA3 = CreateBinaryTreeNode(2);
TreeNode *pNodeA4 = CreateBinaryTreeNode(1);
TreeNode *pNodeA5 = CreateBinaryTreeNode(4);
TreeNode *pNodeA6 = CreateBinaryTreeNode(3);
TreeNode *pNodeA7 = CreateBinaryTreeNode(5);

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

// 树中结点含有分叉，
// 1
// / \
// 2 2
// / \ / \
// 3 4 4 3

TreeNode *pNodeB1 = CreateBinaryTreeNode(1);
TreeNode *pNodeB2 = CreateBinaryTreeNode(2);
TreeNode *pNodeB3 = CreateBinaryTreeNode(2);
TreeNode *pNodeB4 = CreateBinaryTreeNode(3);
TreeNode *pNodeB5 = CreateBinaryTreeNode(4);
TreeNode *pNodeB6 = CreateBinaryTreeNode(4);
TreeNode *pNodeB7 = CreateBinaryTreeNode(3);

ConnectTreeNodes(pNodeB1, pNodeB2, pNodeB3);
ConnectTreeNodes(pNodeB2, pNodeB4, pNodeB5);
ConnectTreeNodes(pNodeB3, pNodeB6, pNodeB7);

bool ans = isSymmetric(pNodeA1);

if (ans == true)
{
cout << "Symmetric Tree!" << endl;
}
else
{
cout << "Not Symmetric Tree!" << endl;
}

bool ans1 = isSymmetric(pNodeB1);

if (ans1 == true)
{
cout << "Symmetric Tree!" << endl;
}
else
{
cout << "Not Symmetric Tree!" << endl;
}
DestroyTree(pNodeA1);
DestroyTree(pNodeB1);
return 0;
}

结果输出：
Not Symmetric Tree!

Symmetric Tree!

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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bool isSymmetric(TreeNode *root)
{

if(root == NULL)
{
return true;
}
queue<TreeNode *> lt, rt;
if(root->left != NULL)
{
lt.push(root->left);
}
if(root->right != NULL)
{
rt.push(root->right);
}
TreeNode *l;
TreeNode *r;
while(!lt.empty() && !rt.empty())
{
l = lt.front();
lt.pop();
r = rt.front();
rt.pop();

if(l == NULL && r == NULL)
{
continue;
}
if( (l != NULL && r == NULL) || (l == NULL && r != NULL) )
{
return false;
}
if(l->val != r->val)
{
return false;
}
/*这个入队列的顺序很重要*/
lt.push(l->left);
lt.push(l->right);
rt.push(r->right);
rt.push(r->left);
}
if(lt.empty() && rt.empty())
{
return true;
}
else
{
return false;
}

}

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bool isSameTree(TreeNode *p, TreeNode *q)
{

if(p == NULL)
{
return q == NULL;
}
else if(q == NULL)
{
return false;
}
else if(p->val == q->val)
{
return isSameTree(p->left, q->left) && isSameTree(p->right, q->right);
}
else
{
return false;
}
}

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