用c语言编程求主析取范式,求主析取范式.cpp · wangzhankun/C-Programming-Learn - Gitee.com...
/*
實(shí)現(xiàn)功能：輸入命題公式的合式公式，求出公式的真值表，并輸出該公式的主合取范式和主析取范式。
輸入：命題公式的合式公式
輸出：公式的主析取范式和主析取范式，輸出形式為：“ mi ∨ mj ; Mi ∧ Mj” ，極小項(xiàng)和 ∨ 符號(hào)之間有一個(gè)空格，極大項(xiàng)和 ∧ 符號(hào)之間有一個(gè)空格；
主析取范式和主合取范式之間用“ ; ”隔開，“ ; ”前后各有一個(gè)空格。 永真式的主合取范式為 1 ，永假式的主析取范式為 0 。
輸入公式的符號(hào)說明：
! 非，相當(dāng)于書面符號(hào)中的 “ ? ”
& 與，相當(dāng)于書面符號(hào)中的 “ ∧ ”
| 或，相當(dāng)于書面符號(hào)中的 “ ∨ ”
- 蘊(yùn)含聯(lián)結(jié)詞，相當(dāng)于書面符號(hào)中的 “ → ”
+ 等價(jià)聯(lián)結(jié)詞，相當(dāng)于書面符號(hào)中的 “ ? ”
( 前括號(hào)
) 后括號(hào)
輸入：
a&b
輸出：
m3 ; M0 ∧ M1 ∧ M2
//*/
#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
class Calculate
{
map optPriority;
string expression;
string expression_tmp;
int num_of_variables;
vector variables;
map dict; //存儲(chǔ)變量以及其所代表的值
int error; //error == 1, divided by 0; error == 2, expression is wrong
stack numStack;
stack optStack;
int sTOi(int firstindex, int lastindex); //transport expression to number
string iTOs(int num); //translate number to string
void changeMinus(); //find '-' and judge if it means minus, if so, change it into '#'
void pushINTOstack();
void pushOPT(int index); //push the operation at index into optStack and calculate value if necessary
void computeAB(char opt); //comput 'a opt b'
void Error(); //do when error occurs
int cal();
void countVariable();
void assigement(string input);
void dfs(int level);
void kernel(string inpug);
public:
vector output;
Calculate();
int start(string expression);
};
Calculate::Calculate()
{
//this->expression = expression;
//value = 0;
error = 0;
optPriority['('] = 0;
optPriority['&'] = 1;
optPriority['|'] = 2;
optPriority['-'] = 3;
optPriority['+'] = 4;
optPriority['!'] = 5;
}
int Calculate::sTOi(int firstindex, int lastindex)
{
string tmp = expression.substr(firstindex, lastindex - firstindex);
int num_tmp = 0;
for (int i = 0; i < (int)tmp.size(); i++)
{
num_tmp *= 10;
num_tmp += tmp[i] - '0';
}
return num_tmp;
}
string Calculate::iTOs(int num)
{
ostringstream s;
s << num;
string tmp = s.str();
return tmp;
}
void Calculate::changeMinus()
{
if (expression[0] == '-')
expression[0] = '#';
for (int i = 1; i < (int)expression.size(); ++i)
{
if (expression[i] == '-')
{
if (expression[i - 1] == ')')
continue;
if (expression[i - 1] >= '0' && expression[i - 1] <= '9')
continue;
expression[i] = '#';
}
}
return;
}
void Calculate::computeAB(char opt)
{
if (numStack.empty()) //not enough number
{
if (!error)
error = 2;
return;
}
if (opt == '!')
{
int b = numStack.top();
numStack.pop();
if (b == 0)
b = 1;
else
b = 0;
numStack.push(b);
return;
}
int b = numStack.top();
numStack.pop();
if (numStack.empty()) //not enough number
{
if (!error)
error = 2;
return;
}
int a = numStack.top();
numStack.pop();
int c = 0;
switch (opt)
{
case '&':
c = a * b;
break;
case '|':
c = a + b;
if (c > 1)
c = 1;
break;
case '-':
if (a == 1 && b == 0)
c = 0;
else
c = 1;
break;
case '+':
if (a == b)
c = 1;
else
{
c = 0;
}
break;
}
numStack.push(c);
return;
}
void Calculate::Error()
{
if (error == 1)
{
cout << "Divide 0.\n";
}
else
{
cout << "error.\n";
}
return;
}
void Calculate::pushOPT(int index)
{
char opt = expression[index];
if (opt == '(' || opt == '!')
{
optStack.push(opt);
return;
}
else
{
if (opt == ')')
{
int flag = 1; //mark expression is wrong for there is no '('
while (!optStack.empty())
{
char opt_tmp = optStack.top();
optStack.pop();
if (opt_tmp == '(')
{
flag = 0;
break;
}
computeAB(opt_tmp);
if (error)
return;
}
if (flag) //there is no '('
{
if (!error)
error = 2;
return;
}
}
else
{
if (index)
{
if (expression[index - 1] == '(')
{
error = 2;
return;
}
}
while (!optStack.empty())
{
char opt_tmp = optStack.top();
optStack.pop();
if (optPriority[opt] >= optPriority[opt_tmp])
{
if (opt == '^')
{
optStack.push(opt_tmp);
break;
}
else
{
if (optPriority[opt] > optPriority[opt_tmp])
{
optStack.push(opt_tmp);
break;
}
}
}
computeAB(opt_tmp);
if (error)
{
return;
}
}
optStack.push(opt);
}
}
return;
}
void Calculate::pushINTOstack()
{
for (int i = 0; i < (int)expression.size(); ++i)
{
if (expression[i] >= '0' && expression[i] <= '9')
{
int j = i;
for (; expression[j] >= '0' && expression[j] <= '9'; j++)
;
numStack.push(sTOi(i, j));
i = j - 1;
}
else
{
pushOPT(i);
}
if (error)
return;
}
return;
}
int Calculate::cal()
{
// changeMinus();
pushINTOstack();
while (!optStack.empty())
{
if (error)
break;
char opt_tmp = optStack.top();
optStack.pop();
if (opt_tmp == '(')
{
if (!error)
error = 2;
}
computeAB(opt_tmp);
}
if ((int)numStack.size() != 1)
{
if (!error)
error = 2;
}
if (error)
{
Error();
return 0;
}
int value = numStack.top();
while (!numStack.empty())
{
numStack.pop();
}
while (!optStack.empty())
{
optStack.pop();
}
return value;
}
void Calculate::assigement(string input)
{
int index = input.find('=');
string tmp = input.substr(0, index);
if (*(input.end() - 1) == '0')
dict[tmp] = 0;
else
dict[tmp] = 1;
}
void Calculate::dfs(int level)
{
if (level == this->num_of_variables)
{
//計(jì)算操作
kernel(this->expression_tmp);
return;
}
//賦值
assigement(variables[level] + "=0");
dfs(level + 1);
assigement(variables[level] + "=1");
dfs(level + 1);
return;
}
void Calculate::kernel(string s)
{
this->expression = "";
for (int i = 0; i < (int)s.size(); ++i)
{
int j = i;
while (s[j] >= 'a' && s[j] <= 'z')
{
j++;
}
string tmp = s.substr(i, j - i);
if (tmp[0] >= 'a' && tmp[0] <= 'z')
this->expression += iTOs(dict[tmp]);
else
this->expression += tmp;
if (j < (int)s.size())
this->expression += s[j];
i = j;
}
output.push_back(cal());
// cout << *output.end() << endl;
}
int Calculate::start(string s)
{
this->expression_tmp = s;
countVariable();
dfs(0);
return 0;
}
void Calculate::countVariable()
{
// cout << this->expression_tmp << endl;
set variables;
for (int i = 0, j = 0; i < (int)this->expression_tmp.size(); i = j)
{
while (i < this->expression_tmp.size())
{
if ((int)this->expression_tmp[i] >= 'a' && this->expression_tmp[i] <= 'z')
break;
i++;
}
j = i;
if (i >= this->expression_tmp.size())
break;
while (j < (int)this->expression_tmp.size() && (int)this->expression_tmp[j] >= 'a' && this->expression_tmp[j] <= 'z')
{
j++;
}
string tmp = this->expression_tmp.substr(i, j - i);
// cout << "i=" << i << ";j=" << j << endl;
// cout << tmp << endl;
variables.insert(tmp);
}
for (auto it = variables.begin(); it != variables.end(); it++)
{
this->variables.push_back(*it);
// cout << *it << endl;
}
this->num_of_variables = variables.size();
// cout << num_of_variables << endl;
}
int main()
{
Calculate calculator;
string input;
cin >> input;
if(input.find('1') != input.npos)
{
cout << " ; 1" << endl;
return 0;
}
if(input.find('0') != input.npos)
{
cout << "0 ; " << endl;
return 0;
}
calculator.start(input);
string xiqu, hequ;
for (int i = 0; i < (int)calculator.output.size(); i++)
{
// cout << calculator.output[i] << endl;
if (calculator.output[i] == 0)
{
hequ += "M" + to_string(i) + " ∧ ";
}
else
{
xiqu += "m" + to_string(i) + " ∨ ";
}
}
if (hequ.size() > 0)
for (int i = 0; i < (int)xiqu.size() - 5; i++)
{
cout << xiqu[i];
}
else
cout << " ; 1";
if ((int)hequ.size() > 0)
{
if (xiqu.size() > 0)
{
cout << " ; ";
for (int i = 0; i < (int)hequ.size() - 5; i++)
{
cout << hequ[i];
}
}
else
cout << "0 ; ";
}
cout << endl;
return 0;
}
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