南邮离散数学实验1 （栈版） 根据表达式求真值表和主范式
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#include <iostream>#include <string>using namespace std;string org; //原式string pcnf; //主合取范式string pdnf; //主析取范式int p, q, r, s, t, u; //变量 P、Q、R、S、T、U的值int a, b, res; //a、b保存出栈的两个元素的值，res保存计算结果int v = 0; //保存进栈的值，0或者1 。计算的时候是先识别变量，然后进栈的是变量的值，用v保存。int choose;class SeqStack {public: SeqStack(int mSize); ~SeqStack(); bool Push(char x); bool Pop(); char Top(); private: int top; char *st; int maxtop;};SeqStack::SeqStack(int mSize){ maxtop = mSize - 1; st = new char[mSize]; top = -1;}SeqStack::~SeqStack(){ delete[]st;}bool SeqStack::Push(char x) { if(top == maxtop) return false; st[++top] = x; return true;}bool SeqStack::Pop() { if(top == -1) return false; top--; return true;}char SeqStack::Top() { return st[top];}void And(); //合取void Or(); //析取void Not(); //否定void If(); //条件void Iif(); //双条件bool CanIn(char out); //判断能否进栈void Suffix(); //求后缀表达式void Calculate(); //计算公式的值void Print(); //输出真值表和范式SeqStack stack(200); int main(){ cout << "! 否定" << endl << "| 析取" << endl <<"& 合取" << endl << "-> 条件" << endl << "<-> 双条件" << endl << endl; cout << "输入变元数量 (2 <= n <= 6)" << endl << endl; cin >> choose; switch(choose) { case 2:cout << endl << "变元请用P、Q表示" << endl << endl; break; case 3:cout << endl << "变元请用P、Q、R表示" << endl << endl; break; case 4:cout << endl << "变元请用P、Q、R、S表示" << endl << endl; break; case 5:cout << endl << "变元请用P、Q、R、S、T表示" << endl << endl; break; case 6:cout << endl << "变元请用P、Q、R、S、T、U表示" << endl << endl; break; } char str[100]; char ch[100]; cin >> str; int cnt = 0; for(int i = 0; i < strlen(str);) { if(str[i] == '-') { ch[cnt++] = '>'; i += 2; } else if(str[i] == '<') { ch[cnt++] = '~'; i += 3; } else { ch[cnt++] = str[i]; i++; } } ch[cnt++] = '\0'; org = ch; Suffix(); Print(); return 0;}void And() //合取{ res = a * b; stack.Push(res);}void Or() //析取{ res = a + b; res = res > 1 ? 1 : res; stack.Push(res);}void Not() //否定{ a = stack.Top(); stack.Pop(); res = a == 1 ? 0 : 1; stack.Push(res);}void If() //条件,b->a{ res = (b == 1 && a == 0) ? 0 : 1; stack.Push(res);}void Iif() //双条件{ res = (b == a) ? 1 : 0; stack.Push(res);}bool CanIn(char out) //先计算优先级，然后判断能否进栈{ char in = stack.Top(); int i, o; //分别表示栈内外运算符的优先级 switch(in) { case '#':i = 0; break; case '(':i = 1; break; case '~':i = 3; break; case '>':i = 5; break; case '|':i = 7; break; case '&':i = 9; break; case '!':i = 11; break; case ')':i = 12; break; } switch(out) { case '#':o = 0; break; case '(':o = 12; break; case '~':o = 2; break; case '>':o = 4; break; case '|':o = 6; break; case '&':o = 8; break; case '!':o = 10; break; case ')':o = 1; break; } if(i < o) //如果栈外的优先级比栈内的高，就可以进栈，因为离栈顶越近，就越先出栈 return true; else return false;}void Suffix() //转换为后缀表达式{ string tmp = ""; //保存后缀表达式 stack.Push('#'); //栈底 for(int i = 0; (unsigned)i < org.length(); i++) { if(org[i] == 'P' || org[i] == 'Q' || org[i] == 'R' || org[i] == 'S' || org[i] == 'T' || org[i] == 'U') //如果是P、Q、R 就保存到字符串tmp中 { tmp = tmp + org[i]; continue; } if(CanIn(org[i])) stack.Push(org[i]); else if(org[i] == ')') { while(stack.Top() != '(') { tmp = tmp + stack.Top(); stack.Pop(); } stack.Pop(); } else { do { tmp = tmp + stack.Top(); stack.Pop(); } while(!CanIn(org[i])); stack.Push(org[i]); } } while(stack.Top() != '#') { tmp = tmp + stack.Top(); stack.Pop(); } stack.Pop(); // '#' 出栈 org = tmp; }void Calculate() { if(choose == 6) { for(int i = 0; (unsigned)i < org.length(); i++) { if(org[i] == 'P' || org[i] == 'Q' || org[i] == 'R' || org[i] == 'S' || org[i] == 'T' || org[i] == 'U') { v = org[i] == 'P' ? p : org[i] == 'Q' ? q : org[i] == 'S' ? r : org[i] == 'T' ? s : org[i] == 'U' ? t : u; stack.Push(v); continue; } if(org[i] != '!') { a = stack.Top(); stack.Pop(); b = stack.Top(); stack.Pop(); } switch(org[i]) { case '~':Iif(); break; case '>':If(); break; case '|':Or(); break; case '&':And(); break; case '!':Not(); break; } } } if(choose == 5) { for(int i = 0; (unsigned)i < org.length(); i++) { if(org[i] == 'P' || org[i] == 'Q' || org[i] == 'R' || org[i] == 'S' || org[i] == 'T') { v = org[i] == 'P' ? p : org[i] == 'Q' ? q : org[i] == 'S' ? r : org[i] == 'T' ? s : t; stack.Push(v); continue; } if(org[i] != '!') { a = stack.Top(); stack.Pop(); b = stack.Top(); stack.Pop(); } switch(org[i]) { case '~':Iif(); break; case '>':If(); break; case '|':Or(); break; case '&':And(); break; case '!':Not(); break; } } } if(choose == 4) { for(int i = 0; (unsigned)i < org.length(); i++) { if(org[i] == 'P' || org[i] == 'Q' || org[i] == 'R' || org[i] == 'S') { v = org[i] == 'P' ? p : org[i] == 'Q' ? q : org[i] == 'S' ? r : s; stack.Push(v); continue; } if(org[i] != '!') { a = stack.Top(); stack.Pop(); b = stack.Top(); stack.Pop(); } switch(org[i]) { case '~':Iif(); break; case '>':If(); break; case '|':Or(); break; case '&':And(); break; case '!':Not(); break; } } } if(choose == 3) { for(int i = 0; (unsigned)i < org.length(); i++) { if(org[i] == 'P' || org[i] == 'Q' || org[i] == 'R') { v = org[i] == 'P' ? p : org[i] == 'Q' ? q : r; stack.Push(v); continue; } if(org[i] != '!') { a = stack.Top(); stack.Pop(); b = stack.Top(); stack.Pop(); } switch(org[i]) { case '~':Iif(); break; case '>':If(); break; case '|':Or(); break; case '&':And(); break; case '!':Not(); break; } } } if(choose == 2) { for(int i = 0; (unsigned)i < org.length(); i++) { if(org[i] == 'P' || org[i] == 'Q') { v = org[i] == 'P' ? p : q; stack.Push(v); continue; } if(org[i] != '!') { a = stack.Top(); stack.Pop(); b = stack.Top(); stack.Pop(); } switch(org[i]) { case '~':Iif(); break; case '>':If(); break; case '|':Or(); break; case '&':And(); break; case '!':Not(); break; } } }}void Print() { if(choose == 6) { cout << "P\t" << "Q\t" << "R\t" << "S\t" << "T\t" << "U\t" << "Z" << endl; for(p = 1; p >= 0; p--) { for(q = 1; q >= 0; q--) { for(r = 1; r >= 0; r--) { for(s = 1; s >= 0; s--) { for(t = 1; t >= 0; t--) { for(u = 1; u >= 0; u--) { Calculate(); if(res == 1) pdnf = pdnf + "(" + (p == 1 ? "P" : "!P") + "&" + (q == 1 ? "Q" : "!Q") + "&" + (r == 1 ? "R" : "!R") + "&" + (s == 1 ? "S" : "!S") + "&" + (t == 1 ? "T" : "!T") + "&" + (u == 1 ? "U" : "!U") + ")" + " | "; else pcnf = pcnf + "(" + (p == 0 ? "P" : "!P") + "|" + (q == 0 ? "Q" : "!Q") + "|" + (r == 0 ? "R" : "!R") + "|" + (s == 0 ? "S" : "!S") + "|" + (t == 0 ? "T" : "!T") + "|" + (u == 0 ? "U" : "!U") + ")" + " & "; cout << p << "\t" << q << "\t" << r << "\t" << s << "\t" << t << "\t" << u << "\t" << res << endl; } } } } } } } if(choose == 5) { cout << "P\t" << "Q\t" << "R\t" << "S\t" << "T\t" << "Z" << endl; for(p = 1; p >= 0; p--) { for(q = 1; q >= 0; q--) { for(r = 1; r >= 0; r--) { for(s = 1; s >= 0; s--) { for(t = 1; t >= 0; t--) { Calculate(); if(res == 1) pdnf = pdnf + "(" + (p == 1 ? "P" : "!P") + "&" + (q == 1 ? "Q" : "!Q") + "&" + (r == 1 ? "R" : "!R") + "&" + (s == 1 ? "S" : "!S") + "&" + (t == 1 ? "T" : "!T") + ")" + " | "; else pcnf = pcnf + "(" + (p == 0 ? "P" : "!P") + "|" + (q == 0 ? "Q" : "!Q") + "|" + (r == 0 ? "R" : "!R") + "|" + (s == 0 ? "S" : "!S") + "|" + (t == 0 ? "T" : "!T") + ")" + " & "; cout << p << "\t" << q << "\t" << r << "\t" << s << "\t" << t << "\t" << res << endl; } } } } } } if(choose == 4) { cout << "P\t" << "Q\t" << "R\t" << "S\t" << "Z" << endl; for(p = 1; p >= 0; p--) { for(q = 1; q >= 0; q--) { for(r = 1; r >= 0; r--) { for(s = 1; s >= 0; s--) { Calculate(); if(res == 1) pdnf = pdnf + "(" + (p == 1 ? "P" : "!P") + "&" + (q == 1 ? "Q" : "!Q") + "&" + (r == 1 ? "R" : "!R") + "&" + (s == 1 ? "S" : "!S") + ")" + " | "; else pcnf = pcnf + "(" + (p == 0 ? "P" : "!P") + "|" + (q == 0 ? "Q" : "!Q") + "|" + (r == 0 ? "R" : "!R") + "|" + (s == 0 ? "S" : "!S") + ")" + " & "; cout << p << "\t" << q << "\t" << r << "\t" << s << "\t" << res << endl; } } } } } if(choose == 3) { cout << "P\t" << "Q\t" << "R\t" << "Z" << endl; for(p = 1; p >= 0; p--) { for(q = 1; q >= 0; q--) { for(r = 1; r >= 0; r--) { Calculate(); if(res == 1) pdnf = pdnf + "(" + (p == 1 ? "P" : "!P") + "&" + (q == 1 ? "Q" : "!Q") + "&" + (r == 1 ? "R" : "!R") + ")" + " | "; else pcnf = pcnf + "(" + (p == 0 ? "P" : "!P") + "|" + (q == 0 ? "Q" : "!Q") + "|" + (r == 0 ? "R" : "!R") + ")" + " & "; cout << p << "\t" << q << "\t" << r << "\t" << res << endl; } } } } if(choose == 2) { cout << "P\t" << "Q\t" << "Z" << endl; for(p = 1; p >= 0; p--) { for(q = 1; q >= 0; q--) { Calculate(); if(res == 1) pdnf = pdnf + "(" + (p == 1 ? "P" : "!P") + "&" + (q == 1 ? "Q" : "!Q") + ")" + " | "; else pcnf = pcnf + "(" + (p == 0 ? "P" : "!P") + "|" + (q == 0 ? "Q" : "!Q") + ")" + " & "; cout << p << "\t" << q << "\t" << res << endl; } } } cout << pdnf.length() << endl; cout << pcnf.length() << endl; //考虑永真和永假的情况 if(pdnf.length() != 0) pdnf.erase(pdnf.length() - 2); if(pcnf.length() != 0) pcnf.erase(pcnf.length() - 2); cout << "主析取范式：" << pdnf << endl << endl; cout << "主合取范式：" << pcnf << endl << endl;} 0 0
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