练习12——二叉树与表达式

最新推荐文章于 2023-05-11 17:18:10 发布

原创最新推荐文章于 2023-05-11 17:18:10 发布 · 562 阅读

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该博客介绍如何使用二叉链表建立表达式二叉树，并通过先序遍历进行输出，同时计算表达式的结果。内容涵盖四种运算符：+,-,*,/，在输出时考虑括号的使用，解决优先级问题。通过递归求值策略，先计算子表达式，再结合根节点运算符得出最终结果。中序遍历序列转换为带括号的表达式，依据运算符优先级添加括号。" 9024929,1385070,理解Linux音频设备的ioctl调用,"['Linux驱动', '音频开发', '系统接口', '设备控制']

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将通过二叉链表实现的表达式二叉树进行输出，同时计算出结果。

要求：

1）二叉树建立时，使用先序建立；

2）四个运算符包括：+, -, *, /;

3 ) 在输出时，遇到优先级问题时，相应的括号也要输出。

提示：

1）递归执行下列步骤即可求值：先分别求出左子树和右子树表示的子表达式的值，最后根据根结点的运算符的要求，计算出表达式的最后结果。

2）二叉树的中序遍历序列与原算术表达式基本相同，但是需要将中序序列加上括号，即当根结点运算符优先级高于左子树（或右子树）根结点运算符时，就需要加括号。

#include <iostream>
using namespace std;
class BinaryTree;
class BinTreeNode {
	friend BinaryTree;
private:
	BinTreeNode * leftChild, *rightChild;
	char data;
public:
	BinTreeNode() {
		leftChild = NULL;
		rightChild = NULL;
	}
	BinTreeNode(char x, BinTreeNode *left = NULL, BinTreeNode *right = NULL) {
		data = x;
		leftChild = left;
		rightChild = right;
	}
	~BinTreeNode() {}
};
class BinaryTree {
private:
	char endTag;
	BinTreeNode *root;
	void create(BinTreeNode* &subTree);
	void destroy(BinTreeNode *&subTree);
	void preOrder(BinTreeNode *subTree);
	void inOrder(BinTreeNode *subTree);
	int getcount(BinTreeNode *subTree, int count = 0);
public:
	BinaryTree(char value) {
		endTag = value;
		root = NULL;
	}
	BinaryTree() {
		destroy(root);
	}
	void create() {
		create(root);
	}
	void preOrder() {
		preOrder(root);
	}
	void inOrder() {
		inOrder(root);
	}
	int getcount(int count=0) {
		return getcount(root, count);
	}
};
void BinaryTree::create(BinTreeNode *& subTree)
{
	char item;
	cin >> item;
	if (item != endTag) {
		subTree = new BinTreeNode(item);
		create(subTree->leftChild);
		create(subTree->rightChild);
	}
	else subTree = NULL;
}

void BinaryTree::destroy(BinTreeNode *& subTree)
{
	if (subTree != NULL) {
		destroy(subTree->leftChild);
		destroy(subTree->rightChild);
		delete subTree;
	}
}

void BinaryTree::preOrder(BinTreeNode * subTree)
{
	if (subTree != NULL) {
		cout << subTree->data;
		preOrder(subTree->leftChild);
		preOrder(subTree->rightChild);
	}
}

void BinaryTree::inOrder(BinTreeNode * subTree)
{
	if(subTree!=NULL){
    if ((subTree->data == '*' || subTree->data == '/') && (subTree->leftChild->data == '+' || subTree->leftChild->data == '-')&&(subTree->rightChild->data == '-' || subTree->rightChild->data == '+')) {

			int f = 1;
			cout << "(";
			inOrder(subTree->leftChild);
			cout << ")";
			cout << subTree->data;
			if (f == 1) {
				cout << "(";
				f = 0;
			}
			inOrder(subTree->rightChild);

			cout << ")";
     }
	else if ((subTree->data == '*' || subTree->data == '/') && (subTree->leftChild->data == '+' || subTree->leftChild->data == '-' || subTree->rightChild->data == '-'|| subTree->rightChild->data == '+')) {

			int f = 1;
			inOrder(subTree->leftChild);
			cout << subTree->data;
			if (f == 1) {
				cout << "(";
				f = 0;
			}
			inOrder(subTree->rightChild);

			cout << ")";
	}

	else {

			inOrder(subTree->leftChild);
			cout << subTree->data;
			inOrder(subTree->rightChild);
	}

	}
}

int BinaryTree::getcount(BinTreeNode * subTree, int count)
{
	if (subTree!=NULL) {
		if (subTree->data == '+') {
			return count+getcount(subTree->leftChild) + getcount(subTree->rightChild);
		}
		else if (subTree->data == '-') {
			return count + getcount(subTree->leftChild) - getcount(subTree->rightChild);
		}
		else if (subTree->data == '*') {
			return count + getcount(subTree->leftChild) * getcount(subTree->rightChild);
		}
		else if (subTree->data == '/') {
			return count + getcount(subTree->leftChild) / getcount(subTree->rightChild);
		}
		else {
			int tmp = subTree->data - '0';
			return tmp;
		}
	}
}
int main()
{
	BinaryTree b('@');
	b.create();
	b.inOrder();

	cout << "=" << b.getcount() << endl;;
    return 0;
}