利用真值表法求取主析取范式以及主合取范式的实现
本程序可以实现任意输入表达式，变元数最多可为3个，即可输出主析取式和主合取式。
规定符号：
! 否定 | 析取 & 合取
-> 条件 <->双条件
#include
#include
usingnamespace std;
stringorg; //原式
stringpcnf; //主合取范式
stringpdnf; //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。
intchoose;
classSeqStack
{
public:
SeqStack(int mSize);
~SeqStack();
bool Push(char x);
bool Pop();
char Top();
private:
int top;
char *st;
int maxtop;
};
SeqStack::SeqStack(intmSize)
{
maxtop = mSize - 1;
st = new char[mSize];
top = -1;
}
SeqStack::~SeqStack()
{
delete[]st;
}
boolSeqStack::Push(char x)
{
if(top == maxtop)
return false;
st[++top] = x;
return true;
}
boolSeqStack::Pop()
{
if(top == -1)
return false;
top--;
return true;
}
charSeqStack::Top()
{
return st[top];
}
voidAnd(); //合取
voidOr(); //析取
voidNot(); //否定
voidIf(); //条件
voidIif(); //双条件
boolCanIn(char out); //判断能否进栈
voidInfixToPostfix(); //求后缀表达式
voidCalculate(); //计算公式的值
void Print(); //输出真值表和范式
SeqStackstack(200);
intmain()
{
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 <= 3)" << 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; } 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; InfixToPostfix(); Print(); return 0; } voidAnd() //合取 { res = a * b; stack.Push(res); } voidOr() //析取 { res = a + b; res = res > 1 ? 1 : res; stack.Push(res); } voidNot() //否定 { a = stack.Top(); stack.Pop(); res = a == 1 ? 0 : 1; stack.Push(res); } voidIf() //条件,b->a { res = (b == 1 && a == 0) ? 0 : 1; stack.Push(res); } voidIif() //双条件 { res = (b == a) ? 1 : 0; stack.Push(res); } boolCanIn(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; } voidInfixToPostfix() //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 { 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; } voidCalculate() { if(choose == 3) { for(int i = 0; (unsigned)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 { 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; } } } } voidPrint() { 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; }