本程序可以實現任意輸入表達式，變元數最多可爲3個，即可輸出主析取式和主合取式。
規定符號：
! 否定 | 析取 & 合取
-> 條件 <->雙條件
#include<iostream>
#include<string.h>
usingnamespace std;
stringorg; //原式
stringpcnf; //主合取範式
stringpdnf; //主析取範式
int p,q, r, s, t, u; //變量 P、Q、R、S、T、U的值
int a,b, res; //a、b保存出棧的兩個元素的值，res保存計算結果
int v =0; //保存進棧的值，0或者1 。計算的時候是先識別變量，然後進棧的是變量的值，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(); //條件
voidIif(); //雙條件
boolCanIn(char out); //判斷能否進棧
voidInfixToPostfix(); //求後綴表達式
voidCalculate(); //計算公式的值
void Print(); //輸出真值表和範式
SeqStackstack(200);
intmain()
{
cout << "! 否定" << endl << "| 析取" << endl <<"& 合取" << endl << "-> 條件" << endl << "<-> 雙條件" << endl << endl;
cout << "輸入變元數量 (2 <= n <= 3)" << endl <<endl;
cin >> choose;
switch(choose)
{
case 2:cout << endl <<"變元請用P、Q表示" << endl << endl; break;
case 3:cout << endl <<"變元請用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() //條件,b->a
{
res = (b == 1 && a == 0) ? 0 : 1;
stack.Push(res);
}
voidIif() //雙條件
{
res = (b == a) ? 1 : 0;
stack.Push(res);
}
boolCanIn(char out) //先計算優先級，然後判斷能否進棧
{
char in = stack.Top();
int i, o; //分別表示棧內外運算符的優先級
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) //如果棧外的優先級比棧內的高，就可以進棧，因爲離棧頂越近，就越先出棧
return true;
else
return false;
}
voidInfixToPostfix() //轉換爲後綴表達式
{
string tmp = ""; //保存後綴表達式
stack.Push('#'); //棧底
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(); // '#' 出棧
org = tmp;
}
voidCalculate()
{
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;
}
}
}
}
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;
//考慮永真和永假的情況
if(pdnf.length() != 0)
pdnf.erase(pdnf.length() - 2);
if(pcnf.length() != 0)
pcnf.erase(pcnf.length() - 2);
cout << "主析取範式：" << pdnf << endl << endl;
cout << "主合取範式：" << pcnf << endl << endl;
}