试题:用123456789和+-*/组合出100

最新推荐文章于 2023-11-24 13:17:01 发布

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本文展示了如何通过组合数字1到9或9到1和基本运算符（加、减、乘、除），在特定约束下达到目标数值100。包括了算法实现和实例演示。

#include <iostream>
using namespace std;

struct MyException
{

};

double Plus(double first, double second)
{
    return (first + second);
}

double Minus(double first, double second)
{
    return (first - second);
}

double Multiply(double first, double second)
{
    return (first * second);
}

double Divide(double first, double second)
{
    return (first / second);
}

typedef double (*Calculate) (double, double);

Calculate Symbol2Calculate(char symbol)
{
    switch (symbol)
    {
        case '+':
        {
            return Plus;
        }
        case '-':
        {
            return Minus;
        }
        case '*':
        {
            return Multiply;
        }
        case '/':
        {
            return Divide;
        }
        default:
        {
            throw MyException();
            return NULL;
        }
    }
}


void have_a_try(double numbers[], char symbols[], int & symbols_max_index,
                double prev_lvalue, char prev_oper, double prev_rvalue,
                int array[], int start, int end, int & solve_num, int need)
{
	if (start == end)
	{
		double result = (Symbol2Calculate(prev_oper))(prev_lvalue, prev_rvalue) - need;
		if (result > -0.000001 && result < 0.000001)
		{
			++solve_num;
			cout << "solve " << solve_num << " :  ";
			for (int i = 0; i < symbols_max_index; ++i)
			{
				cout << numbers[i] << ' ' << symbols[i] << ' ';
			}
			cout << numbers[symbols_max_index] << " = " << 100 << endl;
		}
	}
	else
	{
		long value = 0;
		for (int i = start; i < end; ++i)
		{
			value = 10 * value + array[i];
			numbers[symbols_max_index + 1] = value;

			static char oper[] = { '+', '-', '*', '/' };
			static Calculate calculate[] = { Plus, Minus, Multiply, Divide };

			for (int j = 0; j < 4; ++j)
			{
                symbols[symbols_max_index] = oper[j];
                ++symbols_max_index;

                double lvalue = 0.0;
                double rvalue = 0.0;
                char next_oper = '\0';
                if (j < 2)
                {
                    lvalue = (Symbol2Calculate(prev_oper))(prev_lvalue, prev_rvalue);
                    rvalue = value;
                    next_oper = oper[j];
                }
                else
                {
                    if ('*' == prev_oper || '/' == prev_oper)
                    {
                        lvalue = (Symbol2Calculate(prev_oper))(prev_lvalue, prev_rvalue);
                        rvalue = value;
                        next_oper = oper[j];
                    }
                    else
                    {
                        lvalue = prev_lvalue;
                        rvalue = (Symbol2Calculate(oper[j]))(prev_rvalue, value);
                        next_oper = prev_oper;
                    }
                }

                have_a_try(
                    numbers, symbols, symbols_max_index, lvalue,
                    next_oper, rvalue, array, i + 1, end, solve_num, need
                );
                
                --symbols_max_index;
			}
		}
	}
}

void get_expression(int array[], int length, int need)
{
	double * numbers = new double[length];
	char * symbols = new char[length - 1];
	int symbols_max_index = 0;
	int solve_num = 0;

	long value = 0;
	for (int i = 0; i < length; ++i)
	{
		value = 10 * value + array[i];
		numbers[0] = value;

		have_a_try(
            numbers, symbols, symbols_max_index, 1, '*', value,
            array, i + 1, length, solve_num, need
        );
	}

	if (0 == solve_num)
	{
		cout << "no answer!" << endl;
	}
	else
	{
		cout << "there are " << solve_num << " solves!" << endl;
	}

	delete [] numbers;
	delete [] symbols;
}

int main()
{
	cout << " using 1,2,3,4,5,6,7,8,9 with +,-,*,/ to get 100 " << endl;
	int array1[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
	int length1 = sizeof(array1) / sizeof(array1[0]);
	int need1 = 100;
	try
	{
        get_expression(array1, length1, need1);
	}
	catch (MyException & e)
	{
	    cout << "exception" << endl;
	}

	cin.get();

	cout << " using 9,8,7,6,5,4,3,2,1 with +,-,*,/ to get 100 " << endl;
	int array2[] = { 9, 8, 7, 6, 5, 4, 3, 2, 1 };
	int length2 = sizeof(array2) / sizeof(array2[0]);
	int need2 = 100;
    try
	{
        get_expression(array2, length2, need2);
	}
	catch (MyException & e)
	{
	    cout << "exception" << endl;
	}

	return 0;
}