【C++】二叉树——表达式求值

只支持整数运算
浮点数运算之后更新

#include
#include
#include
#include
#include
#include
#include
using namespace std;
const int N = 1010;
int lch[N], rch[N]; //存储结点i的左、右孩子结点编号
string op[N];
int cnt = 0;// 结点个数
//字符串有效区间[x,y)

int getSum(int u)
{
	
	if (op[u] == "+") return getSum(lch[u]) + getSum(rch[u]);
	if (op[u] == "-") return getSum(lch[u]) - getSum(rch[u]);
	if (op[u] == "*") return getSum(lch[u]) * getSum(rch[u]);
	if (op[u] == "/") return getSum(lch[u]) / getSum(rch[u]);
	int sum = 0;
	for (int i = 0; i < op[u].size(); i++)
	{
		sum = sum * 10 + op[u][i] - '0';
	}
	return sum;
}
int BuildTree(string s, int x, int y)
{
	int c1 = -1, c2 = -1, p = 0; //c1记录"最右"出现的+或-的位置， c2记录"最右"出现的*或/的位置
	int u;
	int num = 0; //数字字符个数
	string temp;
	for (int i = x; i < y; i++)
	{
		if (s[i] >= '0'&&s[i] <= '9') num++;
		temp += s[i];
	}
	if (num == y - x) //区间内全是数字字符
	{
		u = ++cnt;
		lch[u] = -1;
		rch[u] = -1;
		op[u] = temp;
		return u;
	}
	for (int i = x; i < y; i++) //找到当前区间内表达式优先级最低的运算符，c1记录优先级最低的运算符所在位置
	{
		switch (s[i])
		{
		case '(':
			p++;
			break;
		case ')':
			p--;
			break;
		case '+':case '-':
			if (p == 0) c1 = i; //p==0时，在括号外面，优先级较低
			break;
		case '*':case '/':
			if (p == 0) c2 = i;
			break;
		default:
			break;
		}
	}
	if (c1 < 0) c1 = c2; //括号外不存在+或-，则*或/所在位置优先级最低，c1记录优先级最低的运算符所在位置
	if (c1 < 0) //括号外也没有*或/，说明整个表达式最外面是一个括号
	{
		if (y - 1 > x + 1)
			return BuildTree(s, x + 1, y - 1);
	}
	u = ++cnt;
	lch[u] = BuildTree(s, x, c1); //左边为左子树，递归建树
	rch[u] = BuildTree(s, c1 + 1, y); //右边为右子树
	op[u] = s[c1];
	return u;
}
void preOrder(int u) //前序遍历
{
	if (u == -1) return;
	cout << op[u] << " ";
	preOrder(lch[u]);
	preOrder(rch[u]);
}
void inOrder(int u) //中序遍历
{
	if (u == -1) return;
	inOrder(lch[u]);
	cout << op[u] << " ";
	inOrder(rch[u]);
}
void postOrder(int u) //后序遍历
{
	if (u == -1) return;
	postOrder(lch[u]);
	postOrder(rch[u]);
	cout << op[u] << " ";
}
int main()
{
	cout << "输入中缀表达式：" << endl;
	string s;
	cin >> s;
	BuildTree(s, 0, s.size());
	cout << "前序遍历结果为：";
	preOrder(1);
	cout << endl;
	cout << "中序遍历结果为：";
	inOrder(1);
	cout << endl;
	cout << "后序遍历结果为：";
	postOrder(1);
	cout << endl;
	cout << "表达式的结果为：" << getSum(1);
}