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超级改进版

#include <bits/stdc++.h>

using namespace std;

// 有理数（分数）类
struct Rational {
    long long numerator;
    long long denominator;
    
    Rational(long long num = 0, long long denom = 1) : numerator(num), denominator(denom) {
        simplify();
    }
    
    void simplify() {
        if (denominator < 0) {
            numerator = -numerator;
            denominator = -denominator;
        }
        long long gcd_val = gcd(abs(numerator), abs(denominator));
        numerator /= gcd_val;
        denominator /= gcd_val;
    }
    
    static long long gcd(long long a, long long b) {
        return b == 0 ? a : gcd(b, a % b);
    }
    
    Rational operator+(const Rational& other) const {
        return Rational(numerator * other.denominator + other.numerator * denominator, 
                       denominator * other.denominator);
    }
    
    Rational operator-(const Rational& other) const {
        return Rational(numerator * other.denominator - other.numerator * denominator, 
                       denominator * other.denominator);
    }
    
    Rational operator*(const Rational& other) const {
        return Rational(numerator * other.numerator, denominator * other.denominator);
    }
    
    Rational operator/(const Rational& other) const {
        return Rational(numerator * other.denominator, denominator * other.numerator);
    }
    
    bool operator==(const Rational& other) const {
        return numerator == other.numerator && denominator == other.denominator;
    }
    
    string toString() const {
        if (denominator == 1) return to_string(numerator);
        return to_string(numerator) + "/" + to_string(denominator);
    }
    
    string toExpressionString() const {
        if (denominator == 1) return to_string(numerator);
        return "(" + to_string(numerator) + "/" + to_string(denominator) + ")";
    }
};

const Rational TARGET(24, 1);
set<string> unique_solutions; // 用于存储唯一解

// 表达式类，用于构建运算过程
struct Expression {
    Rational value;
    string expr;
    
    Expression(Rational v, const string& e) : value(v), expr(e) {}
};

// 递归计算所有可能的组合
void calculate24(vector<Expression>& numbers) {
    if (numbers.size() == 1) {
        if (numbers[0].value == TARGET) {
            unique_solutions.insert(numbers[0].expr);
        }
        return;
    }

    for (size_t i = 0; i < numbers.size(); ++i) {
        for (size_t j = i + 1; j < numbers.size(); ++j) {
            Expression a = numbers[i];
            Expression b = numbers[j];
            
            // 生成剩余数字
            vector<Expression> nextNumbers;
            for (size_t k = 0; k < numbers.size(); ++k) {
                if (k != i && k != j) {
                    nextNumbers.push_back(numbers[k]);
                }
            }
            
            // 加法
            nextNumbers.push_back(Expression(a.value + b.value, 
                "(" + a.expr + " + " + b.expr + ")"));
            calculate24(nextNumbers);
            nextNumbers.pop_back();
            
            // 减法 (a - b)
            nextNumbers.push_back(Expression(a.value - b.value, 
                "(" + a.expr + " - " + b.expr + ")"));
            calculate24(nextNumbers);
            nextNumbers.pop_back();
            
            // 减法 (b - a)
            nextNumbers.push_back(Expression(b.value - a.value, 
                "(" + b.expr + " - " + a.expr + ")"));
            calculate24(nextNumbers);
            nextNumbers.pop_back();
            
            // 乘法
            nextNumbers.push_back(Expression(a.value * b.value, 
                "(" + a.expr + " * " + b.expr + ")"));
            calculate24(nextNumbers);
            nextNumbers.pop_back();
            
            // 除法 (a / b)
            if (b.value.numerator != 0) {
                nextNumbers.push_back(Expression(a.value / b.value, 
                    "(" + a.expr + " / " + b.expr + ")"));
                calculate24(nextNumbers);
                nextNumbers.pop_back();
            }
            
            // 除法 (b / a)
            if (a.value.numerator != 0) {
                nextNumbers.push_back(Expression(b.value / a.value, 
                    "(" + b.expr + " / " + a.expr + ")"));
                calculate24(nextNumbers);
                nextNumbers.pop_back();
            }
        }
    }
}

// 打印解决方案
void printSolutions() {
    if (unique_solutions.empty()) {
        cout << "无法用这些数字计算出24点。" << endl;
        return;
    }
    
    cout << "找到 " << unique_solutions.size() << " 种解决方案:" << endl;
    for (const auto& solution : unique_solutions) {
        cout << solution << " = 24" << endl;
    }
}

int main() {
    vector<Expression> numbers;
    int input;
    
    cout << "高精度24点计算器" << endl;
    cout << "请输入4个数字(用空格分隔): ";
    
    for (int i = 0; i < 4; ++i) {
        cin >> input;
        numbers.emplace_back(Rational(input, 1), to_string(input));
    }
    
    calculate24(numbers);
    printSolutions();
    
    return 0;
}

10*11=110 110+10=120 120/5=24