Data-Structure/Exercise/Homework3/Q1.cpp

#include <iostream>
#include <string>
using namespace std;
//想法：构建表达式树，进行计算（从右往左） 
//当然也可以用两个栈，一个存符号一个存数字（从左往右） 

//辅助
long long fastpow(long long d, long long u){
	//d^u，用快速幂 
	long long result = 1, base = d, b = u;
	while(b > 0){
		if(b & 1) result *= base; 
		base *= base;
		b >>= 1;
	} 
	return result; 
}
int level(char c){
	switch(c){
		case '+':
		case '-': {
			return 1; 
			break;
		} 
		case '*':
		case '/': {
			return 2;
			break;
		}
		case '^': {
			return 3;
			break;
		}
		default: {
			return 0;
			break;
		}
	}
}

int findexp(const string& s, int l, int r) {
    int pos = -1;
    int min_level = 114514;
    int js = 0;
    for (int i = r; i >= l; i--) {
        if (s[i] == ')') js--; 
        else if (s[i] == '(') js++;
        
        if (js == 0 && level(s[i])) {
            // 对于右结合的^，使用<而不是<=
            if ((s[i] == '^' && level(s[i]) < min_level) || 
                (s[i] != '^' && level(s[i]) <= min_level)) {
                min_level = level(s[i]);
                pos = i;
            }
        }
    }
    return pos;	
}

long long toNum(const string& s, int l, int r) {
    long long tmp = 0;
    
    // 跳过空格
    while (l <= r && s[l] == ' ') l++;
    while (l <= r && s[r] == ' ') r--;
    
    if (l > r) return 0;
    
    // 从左到右处理数字
    for (int i = l; i <= r; i++) {
        if (isdigit(s[i])) {
            tmp = tmp * 10 + (s[i] - '0');
        } else {
            return 0; // 非法字符
        }
    }
    
    return tmp; 
}
/*
带符号的版本 
long long toNum(const string& s, int l, int r){
	long long tmp = 0;
	bool neg = false;
	if (s[l] == '-') { neg = true; l++; }
	for(int i = l; i <= r; i++){
		if(isdigit(s[i])) tmp = tmp * 10 + (s[i] - '0');
	}
	return neg ? -tmp : tmp;
} 
*/

struct Node{
	char sign;
	long long num;
	Node* left;
	Node* right;
	
	Node(): sign('?'), num(-1), left(nullptr), right(nullptr) {}
	Node(char s): sign(s), num(-1), left(nullptr), right(nullptr) {}
	Node(long long n): sign('?'), num(n), left(nullptr), right(nullptr) {}
};

class Expression{
public:
	string exp;
	Node* root;
	long long result;
	bool isValid; 
	
	Expression(const string& s): exp(s), root(nullptr), result(-1), isValid(true) {}
	
	void inorder(Node* r){
		if(!r) return;
		inorder(r->left);
        if (r->sign == '?') cout << r->num;
        else cout << r->sign;
		inorder(r->right);
	}
	
	Node* build(const string& s, int l, int r){
		//[l, r]
		//处理空格 
		while(l <= r && s[l] == ' ') l++;
		while(l <= r && s[r] == ' ') r--;
		if(l > r) return nullptr;
		//处理外部括号 
		if(s[l] == '(' && s[r] == ')'){
			bool hasQuote = true; 
			int js = 0;
			for(int i = l; i <= r; i++){
				if(s[i] == '(') js++;
				else if(s[i] == ')') js--;
				
				if(js == 0 && i != r){
					hasQuote = false;
					break;	
				}
			}
			if (hasQuote) return build(s, l + 1, r - 1);
		}
		
		int pos = findexp(s, l, r);
		//处理纯数字
		if(pos == -1) {
			long long x = toNum(s, l, r);
			//cout << "*" << r << endl; ？为什么输出0 
			return new Node(x);
			//无下方节点 
		}
		Node* tmp = new Node(s[pos]);
		tmp->left = build(s, l, pos - 1);
		tmp->right = build(s, pos + 1, r); 
		return tmp;
	}
	
	long long calc(Node* r, bool& isValid){
		if(!r) return 0; 
		//数字
		if(r->sign == '?') return r->num;
		
		//符号
		long long left = calc(r->left, isValid);
		long long right = calc(r->right, isValid); 
		if(r->num == -1){
			char c = r->sign;
			switch(c){
				case '+': return left + right;
				case '-': return left - right;
				case '*': return left * right;
				case '/': {
					if(right == 0) {
						isValid = false;
						return 0;
					}
					else return left / right;
				} 
				case '^': {
					if(left == 0 && right == 0) { isValid = false; return 0; }
    				return fastpow(left, right);
					break;
				}
				default: return 0;
			}
		}
	}
	void print(){
		inorder(root);
	}
}; 



int main(){
	/*
	string s;
	getline(cin, s);
	Expression tree(s);
	tree.root = tree.build(s, 0, s.length() - 1);
	//tree.print();
	cout << tree.calc(tree.root, tree.isValid) << endl;
	//if(!tree.isValid && result != -1) cout << result <<endl;
	//else cout << "Invalid" << endl; */
	string s;
	while(getline(cin, s)){
    	Expression tree(s);
    	tree.root = tree.build(s, 0, s.length()-1);
    	long long result = tree.calc(tree.root, tree.isValid);
    	if(tree.isValid) cout << result << endl;
    	else cout << "INVALID" << endl;
	}
	return 0;
}