中缀表达式转二叉树

标准算法

#include
using namespace std;

using LL = long long;

class PBTNode {
public:
	PBTNode* l;
	PBTNode* r;

	char op; //保持操作符,操作符为x时，表示数字类型
	LL num;  //保存数字

	PBTNode() {
		l = NULL;
		r = NULL;
	}
};

class PrefixBinaryTree {
private:
	PBTNode* root;

	vector<PBTNode*> token_list;

	stack<PBTNode*>	 st; //符号栈
	vector<PBTNode*> ve; //后缀序列

	int pre_map[256];//符号优先级表

	//判断优先级
	int pre(char c) {
		return pre_map[c];
	}

	//字符串转整型
	LL string_to_num(string s) {
		stringstream ss(s);
		LL v;
		ss >> v;
		return v;
	}

	LL calc_dfs(PBTNode* p) {
		if(p->op == 'x') return p->num;
		
		LL a = calc_dfs(p->l);
		LL b = calc_dfs(p->r);

		if(p->op == '+') return a + b;
		if(p->op == '-') return a - b;
		if(p->op == '*') return a * b;
		if(p->op == '/') return a / b;

		return 0;
	}

public:
	PrefixBinaryTree() {
		memset(pre_map, 0, sizeof(pre_map));
		pre_map['+'] = 1;
		pre_map['-'] = 1;
		pre_map['*'] = 2;
		pre_map['/'] = 2;
	}

	//前缀表达式转换成token列表
	void to_token(string expr) {
		string str_t;
		int n = expr.length();
		int i = 0;

		while(i < n) {
			char x = expr[i];
			if(x == ' ') {
				i++;
			} else if(pre_map[x] > 0 || x == '(' || x == ')') {
				PBTNode* p = new PBTNode;
				p->op = x;
				token_list.push_back(p);
				i++;
			} else if(isdigit(x)) {
				string str_t;
				char y = expr[i];
				while(isdigit(y)) {
					str_t.push_back(y);
					i++;
					y = expr[i];
				}
				PBTNode* p = new PBTNode;
				p->op  = 'x';
				p->num = string_to_num(str_t);
				token_list.push_back(p);
			}
		}
	}

	//打印token列表
	void print_token_list() {
		for(auto p : token_list) {
			if(p->op == 'x') {
				printf("[%lld]", p->num);
			} else {
				printf("[%c]", p->op);
			}
		}
		printf("\n");
	}

	//前缀token列表转后缀序列
	void to_postfix() {
		for(auto p : token_list) {
			if(p->op == 'x') {
				ve.push_back(p);
			} else if(st.empty() || p->op == '(') {
				st.push(p);
			} else if(p->op == ')') {
				while(st.top()->op != '(') {
					ve.push_back(st.top());
					st.pop();
				}
				st.pop();//左括号出栈
			} else {
				//确保符号C比栈下一个优先级高
				while(!st.empty() && pre(p->op) <= pre(st.top()->op)) {
					ve.push_back(st.top());
					st.pop();
				}
				st.push(p);
			}
		}

		while(!st.empty()) {
			ve.push_back(st.top());
			st.pop();
		}
	}

	//得到后缀序列
	string get_postfix() {
		string buf;
		stringstream ss;
		for(auto p : ve) {
			if(p->op == 'x') {
				ss << "[" << p->num << "]";
			} else {
				ss << "[" << p->op << "]";
			}
		}
		ss >> buf;
		return buf;
	}

	//创建表达式二叉树
	void build_tree() {
		stack<PBTNode*> sts;
		for(auto p : ve) {
			if(p->op == 'x') {
				p->l = NULL;
				p->r = NULL;
				sts.push(p);
			} else if(pre_map[p->op] > 0) {
				p->r = sts.top();
				sts.pop();

				p->l = sts.top();
				sts.pop();
				sts.push(p);
			}
		}
		root = sts.top();
	}

	//先序遍历
	void preorder(PBTNode* p) {
		if(p == NULL) return;
		if(p->op == 'x') {
			cout << "[" << p->num << "]";
		} else {
			cout << "[" << p->op << "]";
		}
		preorder(p->l);
		preorder(p->r);
	}

	//先序遍历打印
	void print_preorder() {
		printf("preorder:");
		preorder(root);
		printf("\n");
	}

	int calc() {
		return calc_dfs(root);
	}
};

int main() {
	PrefixBinaryTree x;
	string expr = "2*(36+5)+17/1-4";
	x.to_token(expr);
	x.to_postfix();
	x.build_tree();
	LL v = x.calc();
	
	x.print_token_list();
	string expr_postfix = x.get_postfix();
	cout << expr_postfix << endl;
	x.print_preorder();
	cout << v << endl;
	
	return 0;
}