剑指Offer----面试题19：二叉树的镜像
2016-06-04 18:32
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题目：
请完成一个函数，输入一个二叉树，该函数输出它的镜像。方法一：
分析：镜像无非就是让二叉树每一个结点的左孩子和右孩子交换位置，显然，这要用到递归的知识。源代码如下：
#include"BinaryTree.h"
#include<iostream>
using std::cout;
using std::endl;
using namespace OrdinaryBinaryTreeSpace3;
BinaryTreeNode *Total(BinaryTreeNode *root);
void Change(BinaryTreeNode *root);
BinaryTreeNode *Total(BinaryTreeNode *root)
{
if (root == NULL)
{
cout << "二叉树为空,无法求其镜像" << endl;
return NULL;
}
if (root != NULL && (root)->left == NULL && (root)->right == NULL)
{
cout << "只有一个结点，不用求其镜像" << endl;
return NULL;
}
Change(root);
return root;
}
void Change(BinaryTreeNode *root)
{
if (root == NULL)
return;
if ((root)->left == NULL && (root)->right == NULL)
return;
BinaryTreeNode *left_temp = (root)->left;
BinaryTreeNode *right_temp = (root)->right;
(root)->left = right_temp;
(root)->right = left_temp;
Change((root)->left);
Change((root)->right);
}
/*
9 9
/ \ 转换之后 / \
8 2 2 8
*/
void test11()
{
cout << "===========简单满二叉树的镜像==============" << endl;
BinaryTreeNode *node1 = CreateBinaryTreeNode(8);
BinaryTreeNode *node2 = CreateBinaryTreeNode(9);
BinaryTreeNode *node3 = CreateBinaryTreeNode(2);
ConnectBinaryTreeNodes(node1, node2, node3);
ConnectBinaryTreeNodes(node2, NULL, NULL);
ConnectBinaryTreeNodes(node3, NULL, NULL);
cout << "Before change:";
PrintTreeMid(node1);
Total(node1);
cout << "\nAfter change:";
PrintTreeMid(node1);
cout << endl;
}
/*
8 8
/ \ / \
6 10 转换之后 10 6
/ \ / \ / \ / \
5 7 9 11 11 9 7 5
*/
void test12()
{
cout << "===========复杂满二叉树的镜像==============" << endl;
BinaryTreeNode *node1 = CreateBinaryTreeNode(8);
BinaryTreeNode *node2 = CreateBinaryTreeNode(6);
BinaryTreeNode *node3 = CreateBinaryTreeNode(10);
BinaryTreeNode *node4 = CreateBinaryTreeNode(5);
BinaryTreeNode *node5 = CreateBinaryTreeNode(7);
BinaryTreeNode *node6 = CreateBinaryTreeNode(9);
BinaryTreeNode *node7 = CreateBinaryTreeNode(11);
ConnectBinaryTreeNodes(node1, node2, node3);
ConnectBinaryTreeNodes(node2, node4, node5);
ConnectBinaryTreeNodes(node3, node6, node7);
ConnectBinaryTreeNodes(node4, NULL, NULL);
ConnectBinaryTreeNodes(node5, NULL, NULL);
ConnectBinaryTreeNodes(node6, NULL, NULL);
ConnectBinaryTreeNodes(node7, NULL, NULL);
cout << "Before change:";
PrintTreeMid(node1);
Total(node1);
cout << "\nAfter change:";
PrintTreeMid(node1);
cout << endl;
}
void test13()
{
cout << "===========空二叉树的镜像==============" << endl;
Total(NULL);
}
void test14()
{
cout << "===========只有一个父节点二叉树的镜像==============" << endl;
BinaryTreeNode *node1 = CreateBinaryTreeNode(8);
ConnectBinaryTreeNodes(node1, NULL, NULL);
cout << "Before change:";
PrintTreeMid(node1);
Total(node1);
cout << "\nAfter change:";
PrintTreeMid(node1);
cout << endl;
}
/*
1 1
/ \
2 2
/ \
3 3
/ \
4 转换之后 4
/ \
5 5
/ \
6 6
/ \
7 7
*/
void test15()
{
cout << "===========只有左孩子二叉树的镜像==============" << endl;
BinaryTreeNode *node1 = CreateBinaryTreeNode(1);
BinaryTreeNode *node2 = CreateBinaryTreeNode(2);
BinaryTreeNode *node3 = CreateBinaryTreeNode(3);
BinaryTreeNode *node4 = CreateBinaryTreeNode(4);
BinaryTreeNode *node5 = CreateBinaryTreeNode(5);
BinaryTreeNode *node6 = CreateBinaryTreeNode(6);
BinaryTreeNode *node7 = CreateBinaryTreeNode(7);
ConnectBinaryTreeNodes(node1, node2, NULL);
ConnectBinaryTreeNodes(node2, node3, NULL);
ConnectBinaryTreeNodes(node3, node4, NULL);
ConnectBinaryTreeNodes(node4, node5, NULL);
ConnectBinaryTreeNodes(node5, node6, NULL);
ConnectBinaryTreeNodes(node6, node7, NULL);
ConnectBinaryTreeNodes(node7, NULL, NULL);
cout << "Before change:";
PrintTreeMid(node1);
Total(node1);
cout << "\nAfter change:";
PrintTreeMid(node1);
cout << endl;
}
void test16()
{
cout << "===========只有右孩子二叉树的镜像==============" << endl;
BinaryTreeNode *node1 = CreateBinaryTreeNode(1);
BinaryTreeNode *node2 = CreateBinaryTreeNode(2);
BinaryTreeNode *node3 = CreateBinaryTreeNode(3);
BinaryTreeNode *node4 = CreateBinaryTreeNode(4);
BinaryTreeNode *node5 = CreateBinaryTreeNode(5);
BinaryTreeNode *node6 = CreateBinaryTreeNode(6);
BinaryTreeNode *node7 = CreateBinaryTreeNode(7);
ConnectBinaryTreeNodes(node1, NULL, node2);
ConnectBinaryTreeNodes(node2, NULL, node3);
ConnectBinaryTreeNodes(node3, NULL, node4);
ConnectBinaryTreeNodes(node4, NULL, node5);
ConnectBinaryTreeNodes(node5, NULL, node6);
ConnectBinaryTreeNodes(node6, NULL, node7);
ConnectBinaryTreeNodes(node7, NULL, NULL);
cout << "Before change:";
PrintTreeMid(node1);
Total(node1);
cout << "\nAfter change:";
PrintTreeMid(node1);
cout << endl;
}
int main()
{
test11();
cout << endl;
test12();
cout << endl;
test13();
cout << endl;
test14();
cout << endl;
test15();
cout << endl;
test16();
cout << endl;
system("pause");
return 0;
}运行结果：
===========简单满二叉树的镜像============== Before change:9 8 2 After change:2 8 9 ===========复杂满二叉树的镜像============== Before change:5 6 7 8 9 10 11 After change:11 10 9 8 7 6 5 ===========空二叉树的镜像============== 二叉树为空,无法求其镜像 ===========只有一个父节点二叉树的镜像============== Before change:8 只有一个结点，不用求其镜像 After change:8 ===========只有左孩子二叉树的镜像============== Before change:7 6 5 4 3 2 1 After change:1 2 3 4 5 6 7 ===========只有右孩子二叉树的镜像============== Before change:1 2 3 4 5 6 7 After change:7 6 5 4 3 2 1 请按任意键继续. . .
注意：题目中提到要用一个函数，而非两个函数。
方法二：
官方源代码：#include"BinaryTree.h"
#include<cstdlib>
#include<cstdio>
#include<stack>
using namespace OrdinaryBinaryTreeSpace3;
void MirrorRecursively(BinaryTreeNode *pNode)
{
if ((pNode == NULL) || (pNode->left == NULL && pNode->right == NULL))
return;
BinaryTreeNode *pTemp = pNode->left;
pNode->left = pNode->right;
pNode->right = pTemp;
if (pNode->left)
MirrorRecursively(pNode->left);
if (pNode->right)
MirrorRecursively(pNode->right);
}
void MirrorIteratively(BinaryTreeNode* pRoot)
{
if (pRoot == NULL)
return;
std::stack<BinaryTreeNode*> stackTreeNode;
stackTreeNode.push(pRoot);
while (stackTreeNode.size() > 0)
{
BinaryTreeNode *pNode = stackTreeNode.top();
stackTreeNode.pop();
BinaryTreeNode *pTemp = pNode->left;
pNode->left = pNode->right;
pNode->right = pTemp;
if (pNode->left)
stackTreeNode.push(pNode->left);
if (pNode->right)
stackTreeNode.push(pNode->right);
}
}
// ====================测试代码====================
// 测试完全二叉树：除了叶子节点，其他节点都有两个子节点
// 8
// 6 10
// 5 7 9 11
void Test1()
{
printf("=====Test1 starts:=====\n");
BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
BinaryTreeNode* pNode10 = CreateBinaryTreeNode(10);
BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
BinaryTreeNode* pNode9 = CreateBinaryTreeNode(9);
BinaryTreeNode* pNode11 = CreateBinaryTreeNode(11);
ConnectBinaryTreeNodes(pNode8, pNode6, pNode10);
ConnectBinaryTreeNodes(pNode6, pNode5, pNode7);
ConnectBinaryTreeNodes(pNode10, pNode9, pNode11);
PrintTreeMid(pNode8);
printf("=====Test1: MirrorRecursively=====\n");
MirrorRecursively(pNode8);
PrintTreeMid(pNode8);
printf("=====Test1: MirrorIteratively=====\n");
MirrorIteratively(pNode8);
PrintTreeMid(pNode8);
DestoryTree(pNode8);
}
// 测试二叉树：出叶子结点之外，左右的结点都有且只有一个左子结点
// 8
// 7
// 6
// 5
// 4
void Test2()
{
printf("=====Test2 starts:=====\n");
BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
ConnectBinaryTreeNodes(pNode8, pNode7, NULL);
ConnectBinaryTreeNodes(pNode7, pNode6, NULL);
ConnectBinaryTreeNodes(pNode6, pNode5, NULL);
ConnectBinaryTreeNodes(pNode5, pNode4, NULL);
PrintTreeMid(pNode8);
printf("=====Test2: MirrorRecursively=====\n");
MirrorRecursively(pNode8);
PrintTreeMid(pNode8);
printf("=====Test2: MirrorIteratively=====\n");
MirrorIteratively(pNode8);
PrintTreeMid(pNode8);
DestoryTree(pNode8);
}
// 测试二叉树：出叶子结点之外，左右的结点都有且只有一个右子结点
// 8
// 7
// 6
// 5
// 4
void Test3()
{
printf("=====Test3 starts:=====\n");
BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);
BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);
BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
ConnectBinaryTreeNodes(pNode8, NULL, pNode7);
ConnectBinaryTreeNodes(pNode7, NULL, pNode6);
ConnectBinaryTreeNodes(pNode6, NULL, pNode5);
ConnectBinaryTreeNodes(pNode5, NULL, pNode4);
PrintTreeMid(pNode8);
printf("=====Test3: MirrorRecursively=====\n");
MirrorRecursively(pNode8);
PrintTreeMid(pNode8);
printf("=====Test3: MirrorIteratively=====\n");
MirrorIteratively(pNode8);
PrintTreeMid(pNode8);
DestoryTree(pNode8);
}
// 测试空二叉树：根结点为空指针
void Test4()
{
printf("=====Test4 starts:=====\n");
BinaryTreeNode* pNode = NULL;
PrintTreeMid(pNode);
printf("=====Test4: MirrorRecursively=====\n");
MirrorRecursively(pNode);
PrintTreeMid(pNode);
printf("=====Test4: MirrorIteratively=====\n");
MirrorIteratively(pNode);
PrintTreeMid(pNode);
}
// 测试只有一个结点的二叉树
void Test5()
{
printf("=====Test5 starts:=====\n");
BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
PrintTreeMid(pNode8);
printf("=====Test4: MirrorRecursively=====\n");
MirrorRecursively(pNode8);
PrintTreeMid(pNode8);
printf("=====Test4: MirrorIteratively=====\n");
MirrorIteratively(pNode8);
PrintTreeMid(pNode8);
}
int main()
{
Test1();
putchar('\n');
Test2();
putchar('\n');
Test3();
putchar('\n');
Test4();
putchar('\n');
Test5();
putchar('\n');
system("pause");
return 0;
}运行结果：
=====Test1 starts:===== 5 6 7 8 9 10 11 =====Test1: MirrorRecursively===== 11 10 9 8 7 6 5 =====Test1: MirrorIteratively===== 5 6 7 8 9 10 11 =====Test2 starts:===== 4 5 6 7 8 =====Test2: MirrorRecursively===== 8 7 6 5 4 =====Test2: MirrorIteratively===== 4 5 6 7 8 =====Test3 starts:===== 8 7 6 5 4 =====Test3: MirrorRecursively===== 4 5 6 7 8 =====Test3: MirrorIteratively===== 8 7 6 5 4 =====Test4 starts:===== The tree is empty =====Test4: MirrorRecursively===== The tree is empty =====Test4: MirrorIteratively===== The tree is empty =====Test5 starts:===== 8 =====Test4: MirrorRecursively===== 8 =====Test4: MirrorIteratively===== 8 请按任意键继续. . .
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