面试题8:二叉树的下一个结点
1、题目
2、分析
3、测试代码
4、测试结果如下
1、 题目:
给定一棵二叉树和其中的一个结点,如何找出中序遍历顺序的下一个结点?
树中的结点除了有两个分别指向左右子结点的指针以外,还有一个指向父结点的指针,如下所示:
typedef struct BinTreeNode
{
int _value;
BinTreeNode* _pLeft;
BinTreeNode* _pRight;
BinTreeNode* _pParent;
};
2、分析:
分为两个大的方面来求解:
【1】、该节点没有右孩子节点
<1>该节点是其父节点的左节点
那么,所求的下一个节点就是其父节点
<2>该节点是其父节点的右节点
那么,所求的节点就是从该节点向上遍历,直到它的某个父节点为左子节点为止
【2】、该节点存在右孩子节点
那么,所求的节点沿着右孩子节点的左孩子节点一直向下遍历,直到遍历成叶子节点为止
3、测试代码:
#include<iostream>
using namespace std;
typedef struct BinTreeNode
{
int _value;
BinTreeNode* _pLeft;
BinTreeNode* _pRight;
BinTreeNode* _pParent;
};
BinTreeNode* GetNext(BinTreeNode* pNode)
{
if(pNode == NULL)
{
return NULL;
}
BinTreeNode* pNext = NULL;
if(pNode->_pRight != NULL)
{
BinTreeNode* right = pNode->_pRight ;
while(right->_pLeft != NULL)
{
right =right->_pLeft;
}
pNext= right;
}
else
{
if(pNode->_pParent != NULL)
{
BinTreeNode* pCur = pNode;
BinTreeNode* pParent =pNode->_pParent ;
while(pParent != NULL && pCur == pParent->_pRight )
{
pCur = pCur->_pParent ;
pParent = pParent->_pParent;
}
pNext = pParent;
}
}
return pNext;
}
// ==================== 辅助代码用来构建二叉树 ====================
BinTreeNode* CreateBinaryTreeNode(int value)
{
BinTreeNode* pNode = new BinTreeNode();
pNode->_value = value;
pNode->_pLeft = NULL;
pNode->_pRight = NULL;
pNode->_pParent = NULL;
return pNode;
}
void ConnectTreeNodes(BinTreeNode* pParent, BinTreeNode* pLeft, BinTreeNode* pRight)
{
if(pParent != NULL)
{
pParent->_pLeft = pLeft;
pParent->_pRight = pRight;
if(pLeft != NULL)
pLeft->_pParent = pParent;
if(pRight != NULL)
pRight->_pParent = pParent;
}
}
void PrintTreeNode(BinTreeNode* pNode)
{
if(pNode != NULL)
{
printf("value of this node is: %d\n", pNode->_value);
if(pNode->_pLeft != NULL)
printf("value of its left child is: %d.\n", pNode->_pLeft->_value);
else
printf("left child is null.\n");
if(pNode->_pRight != NULL)
printf("value of its right child is: %d.\n", pNode->_pRight->_value);
else
printf("right child is null.\n");
}
else
{
printf("this node is null.\n");
}
printf("\n");
}
void PrintTree(BinTreeNode* pRoot)
{
PrintTreeNode(pRoot);
if(pRoot != NULL)
{
if(pRoot->_pLeft != NULL)
PrintTree(pRoot->_pLeft);
if(pRoot->_pRight != NULL)
PrintTree(pRoot->_pRight);
}
}
void DestroyTree(BinTreeNode* pRoot)
{
if(pRoot != NULL)
{
BinTreeNode* pLeft = pRoot->_pLeft;
BinTreeNode* pRight = pRoot->_pRight;
delete pRoot;
pRoot = NULL;
DestroyTree(pLeft);
DestroyTree(pRight);
}
}
// ====================测试代码====================
void Test(char* testName, BinTreeNode* pNode, BinTreeNode* expected)
{
if(testName != NULL)
printf("%s 开始: ", testName);
BinTreeNode* pNext = GetNext(pNode);
if(pNext == expected)
printf("测试成功.\n");
else
printf("测试失败.\n");
}
// 8
// 6 10
// 5 7 9 11
void Test1_7()
{
BinTreeNode* pNode8 = CreateBinaryTreeNode(8);
BinTreeNode* pNode6 = CreateBinaryTreeNode(6);
BinTreeNode* pNode10 = CreateBinaryTreeNode(10);
BinTreeNode* pNode5 = CreateBinaryTreeNode(5);
BinTreeNode* pNode7 = CreateBinaryTreeNode(7);
BinTreeNode* pNode9 = CreateBinaryTreeNode(9);
BinTreeNode* pNode11 = CreateBinaryTreeNode(11);
ConnectTreeNodes(pNode8, pNode6, pNode10);
ConnectTreeNodes(pNode6, pNode5, pNode7);
ConnectTreeNodes(pNode10, pNode9, pNode11);
Test("Test1", pNode8, pNode9);
Test("Test2", pNode6, pNode7);
Test("Test3", pNode10, pNode11);
Test("Test4", pNode5, pNode6);
Test("Test5", pNode7, pNode8);
Test("Test6", pNode9, pNode10);
Test("Test7", pNode11, NULL);
printf("\n");
DestroyTree(pNode8);
}
// 5
// 4
// 3
// 2
void Test8_11()
{
BinTreeNode* pNode5 = CreateBinaryTreeNode(5);
BinTreeNode* pNode4 = CreateBinaryTreeNode(4);
BinTreeNode* pNode3 = CreateBinaryTreeNode(3);
BinTreeNode* pNode2 = CreateBinaryTreeNode(2);
ConnectTreeNodes(pNode5, pNode4, NULL);
ConnectTreeNodes(pNode4, pNode3, NULL);
ConnectTreeNodes(pNode3, pNode2, NULL);
Test("Test8", pNode5, NULL);
Test("Test9", pNode4, pNode5);
Test("Test10", pNode3, pNode4);
Test("Test11", pNode2, pNode3);
printf("\n");
DestroyTree(pNode5);
}
// 2
// 3
// 4
// 5
void Test12_15()
{
BinTreeNode* pNode2 = CreateBinaryTreeNode(2);
BinTreeNode* pNode3 = CreateBinaryTreeNode(3);
BinTreeNode* pNode4 = CreateBinaryTreeNode(4);
BinTreeNode* pNode5 = CreateBinaryTreeNode(5);
ConnectTreeNodes(pNode2, NULL, pNode3);
ConnectTreeNodes(pNode3, NULL, pNode4);
ConnectTreeNodes(pNode4, NULL, pNode5);
Test("Test12", pNode5, NULL);
Test("Test13", pNode4, pNode5);
Test("Test14", pNode3, pNode4);
Test("Test15", pNode2, pNode3);
printf("\n");
DestroyTree(pNode2);
}
void Test16()
{
BinTreeNode* pNode5 = CreateBinaryTreeNode(5);
Test("Test16", pNode5, NULL);
printf("\n");
DestroyTree(pNode5);
}
int main(int argc, char* argv[])
{
Test1_7();
Test8_11();
Test12_15();
Test16();
}