唯一的确定一棵二叉树

唯一的确定一棵二叉树

如果给出了遍历二叉树的前（后）序序列和中序序列，则可以构造出唯一的一棵二叉树。试编写实现上述功能的程序。

• 构造一棵二叉树
• 证明构造正确（即分别以前序和中序遍历该树，将得到的结果与给出的序列进行比较）
• 对该二叉树进行后序遍历，输出后序遍历序列
• 用凹入法输出该二叉树

BinTree.h

#include<iostream>
using namespace std;
struct BinTreeNode
{
	char data;
	BinTreeNode *leftChild, *rightChild;
	BinTreeNode() :leftChild(NULL), rightChild(NULL){}
	BinTreeNode(char x, BinTreeNode*l = NULL, BinTreeNode*r = NULL)
		:data(x),leftChild(l),rightChild(r){}
};
class BinTree
{
public:
	BinTreeNode * root;
	BinTree() :root(NULL) {};
	void InOrder(BinTreeNode*subtree);
	void PreOrder(BinTreeNode*subtree);
	void PosOrder(BinTreeNode*subtree);
	BinTreeNode*pre_mid_createBinTree(char* pre, char *ord, int n);
	BinTreeNode*pos_mid_createBinTree(char* pos, char *ord, int n);
	void PrintBinTree(BinTreeNode*&t, int level);
};
void BinTree::PrintBinTree(BinTreeNode*&t, int level)
{
	if (t == NULL)return;
	PrintBinTree(t->rightChild, level + 1);
	for (int i = 0; i < 4* (level - 1); i++)cout << " ";
	cout << t->data << endl;
	PrintBinTree(t->leftChild, level + 1);
}
void BinTree::PreOrder(BinTreeNode*subtree)
{
	if (subtree != NULL) {
		cout << subtree->data;
		PreOrder(subtree->leftChild);
		PreOrder(subtree->rightChild);
	}
}
void BinTree::InOrder(BinTreeNode*subtree)
{
	if (subtree != NULL) {
		InOrder(subtree->leftChild);
		cout << subtree->data;
		InOrder(subtree->rightChild);
	}
}
void BinTree::PosOrder(BinTreeNode*subtree)
{
	if (subtree != NULL) {
		PosOrder(subtree->leftChild);
		PosOrder(subtree->rightChild);
		cout << subtree->data;
	}
}
BinTreeNode* BinTree::pre_mid_createBinTree(char* pre, char *ord, int n)
{
	if (n<=0)return NULL;
	int k = 0;
	char ch = pre[0];
	while(ord[k]!=ch)k++;//寻找中序遍历的根结点
	BinTreeNode*t = new BinTreeNode(ch);
	//分隔左右孩子
	t->leftChild = pre_mid_createBinTree(pre + 1, ord, k);
	t->rightChild = pre_mid_createBinTree(pre + k + 1, ord + k + 1, n - k - 1);
	return t;
}
BinTreeNode* BinTree::pos_mid_createBinTree(char* pos, char *ord, int n)
{
	if (n <= 0)return NULL;
	char ch = pos[n - 1];
	int k = 0;
	while (ord[k]!=ch)
	{
		k++;
	}
	BinTreeNode*t = new BinTreeNode(ch);
	//分隔左右孩子
	t->leftChild = pos_mid_createBinTree(pos, ord, k);
	t->rightChild = pos_mid_createBinTree(pos+k, ord + k + 1, n - k - 1);
	return t;
}

cpp调用文件

#include<iostream>
#include<cstring>
#include"BinTree.h"
using namespace std;
char pre[100], ord[100], pos[100];
int main()
{
	cout << "依次输入前序遍历和中序遍历的序列：" << endl;
	cin >> pre >> ord;
	BinTree tree,tree1;
tree.root=tree.pre_mid_createBinTree(pre, ord, strlen(pre));
cout << "****************************************************" << endl;
cout << "建立之后的树的遍历如下：" << endl;
cout << "    前序遍历：" << endl;
	tree.PreOrder(tree.root);
	cout << endl;
	cout << "    中序遍历：" << endl;
	tree.InOrder(tree.root);
	cout << endl;
	cout << "    后序遍历：" << endl;
	tree.PosOrder(tree.root);
	cout << endl;
	cout << "打印二叉树：" << endl;
	tree.PrintBinTree(tree.root, 1);
cout << "****************************************************" << endl;
cout << "依次输入中序遍历和后序遍历的序列：" << endl;
cin >> ord >> pos;
tree1.root = tree1.pos_mid_createBinTree(pos, ord, strlen(pos));
cout << "****************************************************" << endl;
cout << "建立之后的树的遍历如下：" << endl;
cout << "    前序遍历：" << endl;
tree1.PreOrder(tree1.root);
cout << endl;
cout << "    中序遍历：" << endl;
tree1.InOrder(tree1.root);
cout << endl;
cout << "    后序遍历：" << endl;
tree1.PosOrder(tree1.root);
cout << endl;
cout << "打印二叉树：" << endl;
tree1.PrintBinTree(tree1.root, 1);
cout << "****************************************************" << endl;
	system("pause");
	return 0;
}