Title: and enter the result in a preorder traversal of a binary tree in preorder traversal of the binary tree rebuild. Suppose Results preorder traversal order and input of duplicate numbers are free. For example, the input preorder traversal sequence {1, 2, 4, 7, 3, 5, 6, 8}, and preorder sequence {4, 7, 2, 1, 53, 8, 6}, the reconstruction below and outputting the binary tree shown in its head node. Node binary tree defined as follows:
struct BinaryTreeNode{
int m_nValue;
BinaryTreeNode* m_pLeft;
BinaryTreeNode* m_pRight;
};
// 1
// / \
// 2 3
// / / \
// 4 5 6
// \ /
// 7 8
Test Case:
- Ordinary binary tree (complete binary tree, not a complete binary tree).
- Special binary tree (all nodes have no right child of a binary tree; all nodes are not left child node of a binary tree; only one node of a binary tree).
- Special test input (nullptr a binary tree root pointer; input preamble sequence preorder traversal sequence does not match).
Test code:
void Test(char* testName, int* preorder, int* inorder, int length)
{
if(testName != nullptr)
printf("%s begins:\n", testName);
printf("The preorder sequence is: ");
for(int i = 0; i < length; ++ i)
printf("%d ", preorder[i]);
printf("\n");
printf("The inorder sequence is: ");
for(int i = 0; i < length; ++ i)
printf("%d ", inorder[i]);
printf("\n");
try
{
BinaryTreeNode* root = Construct(preorder, inorder, length);
PrintTree(root);
DestroyTree(root);
}
catch(std::exception& exception)
{
printf("Invalid Input.\n");
}
}
// 普通二叉树
// 1
// / \
// 2 3
// / / \
// 4 5 6
// \ /
// 7 8
void Test1()
{
const int length = 8;
int preorder[length] = {1, 2, 4, 7, 3, 5, 6, 8};
int inorder[length] = {4, 7, 2, 1, 5, 3, 8, 6};
Test("Test1", preorder, inorder, length);
}
// 所有结点都没有右子结点
// 1
// /
// 2
// /
// 3
// /
// 4
// /
// 5
void Test2()
{
const int length = 5;
int preorder[length] = {1, 2, 3, 4, 5};
int inorder[length] = {5, 4, 3, 2, 1};
Test("Test2", preorder, inorder, length);
}
// 所有结点都没有左子结点
// 1
// \
// 2
// \
// 3
// \
// 4
// \
// 5
void Test3()
{
const int length = 5;
int preorder[length] = {1, 2, 3, 4, 5};
int inorder[length] = {1, 2, 3, 4, 5};
Test("Test3", preorder, inorder, length);
}
// 树中只有一个结点
void Test4()
{
const int length = 1;
int preorder[length] = {1};
int inorder[length] = {1};
Test("Test4", preorder, inorder, length);
}
// 完全二叉树
// 1
// / \
// 2 3
// / \ / \
// 4 5 6 7
void Test5()
{
const int length = 7;
int preorder[length] = {1, 2, 4, 5, 3, 6, 7};
int inorder[length] = {4, 2, 5, 1, 6, 3, 7};
Test("Test5", preorder, inorder, length);
}
// 输入空指针
void Test6()
{
Test("Test6", nullptr, nullptr, 0);
}
// 输入的两个序列不匹配
void Test7()
{
const int length = 7;
int preorder[length] = {1, 2, 4, 5, 3, 6, 7};
int inorder[length] = {4, 2, 8, 1, 6, 3, 7};
Test("Test7: for unmatched input", preorder, inorder, length);
}
This question test sites:
- Comprehension test candidates of the binary tree in preorder traversal and traversing. Only different binary tree traversal algorithm to have a deep understanding of possible candidates left in the divided traversal sequence, the sequence corresponding to the right child.
- The ability to examine the complex issues of the candidates analysis. We build big problem is broken down into binary construct two small problems left and right sub-tree. We found a small problem and a big problem in essence is the same, and therefore can be solved with a recursive manner.
Implementation code:
/*********************************BinaryTree.h************************************/
struct BinaryTreeNode
{
int m_nValue;
BinaryTreeNode* m_pLeft;
BinaryTreeNode* m_pRight;
};
BinaryTreeNode* CreateBinaryTreeNode(int value);
void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight);
void PrintTreeNode(const BinaryTreeNode* pNode);
void PrintTree(const BinaryTreeNode* pRoot);
void DestroyTree(BinaryTreeNode* pRoot);
/*********************************BinaryTree.cpp************************************/
#include <cstdio>
#include "BinaryTree.h"
BinaryTreeNode* CreateBinaryTreeNode(int value)
{
BinaryTreeNode* pNode = new BinaryTreeNode();
pNode->m_nValue = value;
pNode->m_pLeft = nullptr;
pNode->m_pRight = nullptr;
return pNode;
}
void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight)
{
if(pParent != nullptr)
{
pParent->m_pLeft = pLeft;
pParent->m_pRight = pRight;
}
}
void PrintTreeNode(const BinaryTreeNode* pNode)
{
if(pNode != nullptr)
{
printf("value of this node is: %d\n", pNode->m_nValue);
if(pNode->m_pLeft != nullptr)
printf("value of its left child is: %d.\n", pNode->m_pLeft->m_nValue);
else
printf("left child is nullptr.\n");
if(pNode->m_pRight != nullptr)
printf("value of its right child is: %d.\n", pNode->m_pRight->m_nValue);
else
printf("right child is nullptr.\n");
}
else
{
printf("this node is nullptr.\n");
}
printf("\n");
}
void PrintTree(const BinaryTreeNode* pRoot)
{
PrintTreeNode(pRoot);
if(pRoot != nullptr)
{
if(pRoot->m_pLeft != nullptr)
PrintTree(pRoot->m_pLeft);
if(pRoot->m_pRight != nullptr)
PrintTree(pRoot->m_pRight);
}
}
void DestroyTree(BinaryTreeNode* pRoot)
{
if(pRoot != nullptr)
{
BinaryTreeNode* pLeft = pRoot->m_pLeft;
BinaryTreeNode* pRight = pRoot->m_pRight;
delete pRoot;
pRoot = nullptr;
DestroyTree(pLeft);
DestroyTree(pRight);
}
}
/*********************************ConstructBinaryTree.cpp************************************/
#include "..\Utilities\BinaryTree.h"
#include <exception>
#include <cstdio>
BinaryTreeNode* ConstructCore(int* startPreorder, int* endPreorder, int* startInorder, int* endInorder);
BinaryTreeNode* Construct(int* preorder, int* inorder, int length)
{
if(preorder == nullptr || inorder == nullptr || length <= 0)
return nullptr;
return ConstructCore(preorder, preorder + length - 1,
inorder, inorder + length - 1);
}
BinaryTreeNode* ConstructCore
(
int* startPreorder, int* endPreorder,
int* startInorder, int* endInorder
)
{
// 前序遍历序列的第一个数字是根结点的值
int rootValue = startPreorder[0];
BinaryTreeNode* root = new BinaryTreeNode();
root->m_nValue = rootValue;
root->m_pLeft = root->m_pRight = nullptr;
if(startPreorder == endPreorder)
{
if(startInorder == endInorder && *startPreorder == *startInorder)
return root;
else
throw std::exception("Invalid input.");
}
// 在中序遍历中找到根结点的值
int* rootInorder = startInorder;
while(rootInorder <= endInorder && *rootInorder != rootValue)
++ rootInorder;
if(rootInorder == endInorder && *rootInorder != rootValue)
throw std::exception("Invalid input.");
int leftLength = rootInorder - startInorder;
int* leftPreorderEnd = startPreorder + leftLength;
if(leftLength > 0)
{
// 构建左子树
root->m_pLeft = ConstructCore(startPreorder + 1, leftPreorderEnd,
startInorder, rootInorder - 1);
}
if(leftLength < endPreorder - startPreorder)
{
// 构建右子树
root->m_pRight = ConstructCore(leftPreorderEnd + 1, endPreorder,
rootInorder + 1, endInorder);
}
return root;
}
int main(int argc, char* argv[])
{
Test1();
Test2();
Test3();
Test4();
Test5();
Test6();
Test7();
int a;
scanf("%d", &a);
return 0;
}