Juicio de tabla discreta de matemáticas-verdad

Matemáticas discretas _ juicio de tabla de verdad

El algoritmo
es detallado y el código es relativamente largo,
principalmente usando la pila y una conversión binaria

Para el problema, el lugar a resolver debe ser la prioridad de los paréntesis,
todos saben que la pila es una buena forma de resolver la prioridad.

Entonces,
aparte de cualquier otra cosa, vaya al código
(escrito en C ++)

```cpp
#include<cstdio>
#include<iostream>
#include<cstring>
#include<string>
#include<cctype>
#include<stack>
#include<algorithm>
using namespace std;
char m[1005];//字母名称
stack<char>s, o;
string change(int n)
{
	string str1;
	int cnt = 0;
	string ans;
	while (n)
	{
		str1 += n % 2 + '0';
		n = n / 2;
	}
	string re;
	if (str1 == re)
	{
		str1 = '0';
	}
	reverse(str1.begin(), str1.end());
	return str1;
}//二进制转换
const char and_cal(char a, char b)
{
	if (a == '1' && b == '1')return '1';
	else return '0';
}
const char or_cal(char a, char b)
{
	if (a == '1' || b == '1')
		return '1';
	else return '0';
}
const char two_cal(char a, char b)
{
	if ((a == '1' && b == '1') || (a == '0' && b == '0'))return '1';
	else return '0';
}
const char no_cal(char a)
{
	if (a == '0')return '1';
	else return '0';
}
const char one_cal(char a, char b)
{
	if (a == '1' && b == '0')return '0';
	else return '1';
}//5个运算规则


int main()
{
	cout << "\t真值表判断\n";
	cout << "规则：\n";
	cout << "输入公式要由（ ）确定优先级\n";
	cout << "(1) 用 ! 代替 非 操作\n(2) 用 && 代替 ∧ 操作\n(3) 用 || 代替 ∨ 操作\n(4) 用 <> 代替 双条件 操作\n(5) 用 - 代替 → 操作\n";
	string str;
	string strre;//复制str在以后的每次改变中起到复原作用
	int cnt = 0;
	cin >> str;
	strre = str;
	int len = str.length();
	for (int i = 0; i < len; i++)
	{
		if (isalpha(str[i]))
		{
			for (int j = 0; j < cnt; j++)
			{
				if (str[i] == m[j])
					continue;
			}
			m[cnt++] = str[i];//字母种类
		}

	}//找到字母
	sort(m, m + cnt);
	for (int i = 0; i < cnt; i++)
		printf("%c\t", m[i]);
	cout << str << "\n";
	int d = pow(2, cnt);
	for (int a = 0; a < d; a++)
	{
		str = strre;//每一次替换都会改变原式，此处恢复原式
		while (!s.empty())s.pop();
		int go = 0;
		string num = change(a);//num为二进制表
		int aa = cnt;
		for (int i = 0; i < cnt; i++)
		{
			char rr = m[i];//记录当前准备替换的字母
			int re = num.length() - aa;
			if (re < 0)
			{
				cout << "0\t";
				for (int d = 0; d < str.length(); d++)
					if (str[d] == rr)str[d] = '0';
			}//二进制前导0处理
			else
			{
				char nn = num[num.length() - aa];
				cout << nn << "\t";
				for (int d = 0; d < str.length(); d++)
					if (str[d] == rr)str[d] = nn;
			}
			aa--;
		}//字母替换
		for (int i = 0; i < len; i++)
		{
			s.push(str[i]);
			if (str[i] == ')')
			{
				s.pop();//弹出右括号
				while (!o.empty())o.pop();
				while (s.top() != '(')
				{
					o.push(s.top());
					s.pop();
				}
				s.pop();//弹出前括号

				while (o.size() != 0)
				{
					char k = o.top();
					o.pop();
					if (o.top() == '&')
					{
						o.pop();
						o.pop();
						char c = and_cal(k, o.top());
						s.push(c);
						o.pop();
					}
					else if (o.top() == '|')
					{
						o.pop();
						o.pop();
						char c = or_cal(k, o.top());
						o.pop();
						s.push(c);
					}
					else if (o.top() == '<')
					{
						o.pop();
						o.pop();
						char c = two_cal(k, o.top());
						o.pop();
						s.push(c);
					}
					else if (k == '!')
					{
						char c = no_cal(o.top());
						s.push(c);
						o.pop();
					}
					else if (o.top() == '-')
					{
						o.pop();
						char c = one_cal(k, o.top());
						o.pop();
						s.push(c);
					}
				}

			}
		}//去除括号
		while (s.size() != 0)
		{
			if (s.size() == 1)
			{
				cout << s.top() << endl;
				break;
			}
			char k = s.top();
			s.pop();
			if (s.top() == '&')
			{
				s.pop();
				s.pop();
				char c = and_cal(k, s.top());
				s.pop();
				s.push(c);
			}
			else if (s.top() == '|')
			{
				s.pop();
				s.pop();
				char c = or_cal(k, s.top());
				s.pop();
				s.push(c);
			}
			else if (s.top() == '>' || s.top() == '<')
			{
				s.pop();
				s.pop();
				char c = two_cal(k, s.top());
				s.pop();
				s.push(c);
			}
			else if (s.top() == '!')
			{
				s.pop();
				char c = no_cal(k);
				s.push(c);
			}
			else if (s.top() == '-')
			{
				s.pop();
				char c = one_cal(s.top(), k);
				s.pop();
				s.push(c);
			}
		}
	}
}

上一张代码运行的图片(vs2019环境)
样例：((p&&Q)||R)<>(!S)
![在这里插入图片描述](https://img-blog.csdnimg.cn/20200413233222141.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FNb25zdGVyZQ==,size_16,color_FFFFFF,t_70#pic_center)[代码运行图片](https://img-blog.csdnimg.cn/20200413232255810.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FNb25zdGVyZQ==,size_16,color_FFFFFF,t_70#pic_center%29%20%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%E2%80%94%20%E7%89%88%E6%9D%83%E5%A3%B0%E6%98%8E%EF%BC%9A%E6%9C%AC%E6%96%87%E4%B8%BACSDN%E5%8D%9A%E4%B8%BB%E3%80%8CaMonstere%E3%80%8D%E7%9A%84%E5%8E%9F%E5%88%9B%E6%96%87%E7%AB%A0%EF%BC%8C%E9%81%B5%E5%BE%AA%20CC%204.0%20BY-SA%20%E7%89%88%E6%9D%83%E5%8D%8F%E8%AE%AE%EF%BC%8C%E8%BD%AC%E8%BD%BD%E8%AF%B7%E9%99%84%E4%B8%8A%E5%8E%9F%E6%96%87%E5%87%BA%E5%A4%84%E9%93%BE%E6%8E%A5%E5%8F%8A%E6%9C%AC%E5%A3%B0%E6%98%8E%E3%80%82%20%E5%8E%9F%E6%96%87%E9%93%BE%E6%8E%A5%EF%BC%9Ahttps://blog.csdn.net/aMonstere/article/details/105500694)
枯辽，图片只能通过链接去访问。。（有木有大佬知道怎么办emmm）
如果有小伙伴发现代码的bug欢迎骚扰，小菜鸡会在第一时间改正！