Discrete mathematics _ truth table judgment
The algorithm
is verbose and the code is relatively long,
mainly using the stack and a binary conversion
For the problem, the place to be solved should be the priority of the brackets.
Everyone knows that the stack is a good way to solve the priority.
So
aside from anything else, the code
(written in 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)
[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！