利用真值表法求取主析取范式以及主合取范式的实现

#include <iostream>#include <cmath>#include <cassert>#include <cctype>using namespace std;char str[100]; //输入的命题公式int tv[20] = {0}; //真值指派的数组int length; //命题公式长度char expression[100]; //将命题公式中的命题变元变为真值后的数组int icp(const char c) //联结词的栈外优先级{int result = -1;switch(c){case '#': result = 0; break;case '(': result = 10; break;case '!': result = 9; break;case '&': result = 6; break;case '|': result = 4; break;case '>': result = 2; break;case ')': result = 1;}return result;}int isp(const char c) //联结词的栈内优先级{int result = -1;switch(c){case '#': result = 0; break;case '(': result = 1; break;case '!': result = 8; break;case '&': result = 7; break;case '|': result = 5; break;case '>': result = 3; break;case ')': result = 10;}return result;}void Plus(int a[],int q) //二进制加法指派真值{a[q]=a[q]+1;for (int i = q; a[i] == 2; i--){a[i]=0;a[i-1]=a[i-1]+1;}}template<class T>class Stack{public:virtual bool IsEmpty() const = 0;virtual bool IsFull() const = 0;virtual bool Top(T& x) const = 0;virtual bool Push(T x) = 0;virtual bool Pop() = 0;virtual void Clear() = 0;};template<class T>class SeqStack: public Stack<T> //顺序栈类{public:SeqStack(int mSize = 30);~SeqStack() { delete []s; }bool IsEmpty() const { return top == -1; }bool IsFull() const { return top == maxTop; } bool Top(T& x) const;bool Push(T x);bool Pop();void Clear() { top = -1; }private:int top;int maxTop;T* s;};template<class T>SeqStack<T>::SeqStack(int mSize){maxTop = mSize - 1;s = new T[mSize];top = -1;}template<class T>bool SeqStack<T>::Top(T& x) const{if (IsEmpty()){cout << "Empty" << endl;return false;}x = s[top];return true;}template<class T>bool SeqStack<T>::Push(T x){if (IsFull()){cout << "Overflow" << endl;return false;}s[++top]=x;return true;}template<class T>bool SeqStack<T>::Pop(){if(IsEmpty()){cout << "Underflow" << endl;}top--;return true;}class Calculator{public:Calculator(int maxSize):s(maxSize){}void Change();int Run();void Solve();void Clear() { s.Clear(); }private:SeqStack<bool> s; //运算栈void PushOperand(bool);bool GetOperands(bool &, bool &);void DoOperator(char);};void Calculator::PushOperand(bool op){s.Push(op);}bool Calculator::GetOperands(bool & op1, bool & op2) //获取栈顶两个元素{if (!s.Top(op1)){cerr << "Missing operand!" << endl;return false;}s.Pop();if (!s.Top(op2)){cerr << "Missing operand!" << endl;return false;}s.Pop();return true;}void Calculator::DoOperator(char oper) //联结词运算{bool left, right;bool result = GetOperands(left, right);if (result)switch(oper){case '!': s.Push(!left && right); break; //not运算case '&': s.Push(left && right); break; //and运算case '|': s.Push(left || right); break; //or运算case '>': s.Push(!right || left); break; //条件运算}elseClear();}void Calculator::Change() //将输入的字符串转化为可计算的表达式{int k = 0, t = 0;int flag = 1; //标记，防止相同的命题变元赋入不同的值int count = 0;for (int i = 0; i < pow(2,count); i++){k=1;for (int m = 0; m < length; m++){if (isalpha(str[m])) //将原来的命题变元修改为真值{if (flag == 1){if(tv[k] == 0)expression[m] = '0';elseexpression[m] = '1';k++;}elseexpression[m] = '0';flag = 1;for (t = m; t >= 0; t--)if ((str[m+1] == str[t]) && isalpha(str[m+1]) && isalpha(str[t]))flag = 0;}else{expression[m] = str[m]; //逻辑联结词不变for (t = m; t >= 0; t--)if ((str[m+1] == str[t]) && isalpha(str[m+1]) && isalpha(str[t]))flag = 0;}}for (int t = 0; t < length; t++)for (int j = t; j < length; j++)if (str[t] == str[j])expression[j] = expression[t]; //相同的命题变元复制赋值}}int Calculator::Run(){SeqStack<char> s1; //联结词栈char ch, y;char p[100];int i = 0;s1.Push('#');for (int temp=0; temp < length ; temp++){ch = expression[temp];if (isdigit(ch)){p[i++] = ch;}else if(ch == ')')for(s1.Top(y), s1.Pop(); y != '('; s1.Top(y), s1.Pop())p[i++] = y;else{if(ch == '!') p[i++] = '1'; //非运算，在!前加1，将!视作双目操作符for(s1.Top(y), s1.Pop(); icp(ch) <= isp(y); s1.Top(y), s1.Pop())p[i++] = y;s1.Push(y);s1.Push(ch);}}while(!s1.IsEmpty()){s1.Top(y);s1.Pop();if(y != '#')p[i++] = y;}p[i++] = '#';/* ------↑中缀表达式转化为后缀表达式-----------↓计算后缀表达式结果------------- */bool newop;for (i = 0; p[i] !='#'; i++){switch(p[i]){case '!':case '&':case '|':case '>': DoOperator(p[i]); break;default:cin.putback(p[i]);cin >> newop;PushOperand(newop);break;}}if (s.Top(newop)){cout << (int)newop << endl;return (int)newop; //输出并返回最终结果}}void Calculator::Solve(){cout << "***************************************" << endl;//标语cout << "** 欢迎进入逻辑运算软件**" << endl;cout << "** (可运算真值表，主范式，支持括号) **" << endl;cout << "** **" << endl;cout << "** 用!表示not 用&表示and **" << endl;cout << "** 用|表示or 用>表示蕴含**" << endl;cout << "** **" << endl;cout << "***************************************" << endl;cout << "请输入合法的命题公式(以#结尾): ";int flag = 1; //标记，防止重复添加命题变元int count = 0; //命题变元的数目cin >> str; //输入命题公式length = strlen(str) - 1;char index[10]; //命题变元数组for (int i = 0; i < length; i++) //逐次添加命题变元{if (isalpha(str[i]) && (flag == 1))index[count++] = str[i];flag=1;for (int k = 0; k < count; k++)if (index[k] == str[i+1])flag=0;}if (!count){cout << "无命题变元,重新输入!" << endl;system("pause");system("cls");Solve();}cout << "真值表:" << endl;for (int w = 0; w < count; w++)cout << index[w] << ' ';for (w = 0; w < length; w++)cout << str[w];cout << endl;int *truth = new int[pow(2,count)];int xx = 0, dx = 0; //小项，大项for (int r = 0; r < pow(2,count); r++) //输出真值表{for (int j = 1; j <= count; j++)cout << tv[j] << ' ';Change();truth[r] = Run();if (truth[r]) //记录小项和大项的个数xx++;elsedx++;Plus(tv,count);}if(xx > 1) //输出主析取范式{int flag_xx = 0;cout << "主析取范式为";for(r = 0; r < pow(2,count); r++){if (truth[r]){if (flag_xx) cout << " \\/ ";cout << "m" << r;flag_xx = 1;}}cout << endl;}elsecout << "没有主析取范式!" << endl;if(dx > 1) //输出主合取范式{int flag_dx = 0;cout << "主合取范式为";for(r = 0; r < pow(2,count); r++){if (!truth[r]){if (flag_dx) cout << " /\\ ";cout << "M" << r;flag_dx = 1;}}cout << endl;}elsecout << "没有主合取范式!" << endl;cout << "是否继续运算?(Y/N)" << endl;char goon;cin >> goon;if (goon=='y' || goon=='Y'){system("cls");Solve(); //递归调用Solve，重新计算}elseexit(0);}int main(){Calculator Cal(100);Cal.Solve();return 0;}。