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#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
using namespace std;
namespace LogicExpressions
{
const int ENGLISH_ALPHABET_SIZE = 26;
struct BooleanInterpretation
{
bool values[ENGLISH_ALPHABET_SIZE];
BooleanInterpretation()
{
for (int i = 0; i < ENGLISH_ALPHABET_SIZE; i++)
values[i] = false;
}
void setVarValue(char v, bool value)
{
values[v - 'a'] = value;
}
bool getVarValue(char v) const
{
return values[v - 'a'];
}
};
struct LogicExpr
{
virtual void print() const = 0;
LogicExpr() = default;
LogicExpr(const LogicExpr&) = delete;
LogicExpr& operator=(const LogicExpr& other) = delete;
virtual bool evaluate(const BooleanInterpretation& interpret) const = 0;
virtual ~LogicExpr(){};
};
struct Var : public LogicExpr
{
char v;
Var(char v) :v(v){}
void print() const
{
cout << v;
}
bool evaluate(const BooleanInterpretation& interpret) const
{
return interpret.getVarValue(v);
}
};
struct Operation : public LogicExpr
{
LogicExpr* left;
char op;
LogicExpr* right;
Operation(LogicExpr* lhs, char op, LogicExpr* rhs) : left(lhs), op(op), right(rhs){}
void print() const
{
cout << "(";
left->print();
cout << op;
right->print();
cout << ")";
}
~Operation()
{
delete left;
delete right;
}
bool evaluate(const BooleanInterpretation& interpret) const
{
bool res1 = left->evaluate(interpret);
bool res2 = right->evaluate(interpret);
switch (op)
{
case '^':return res1 && res2;
case '|':return res1 || res2;
case '>':return !res1 || res2;
case '+': return res1 ^ res2;
case '-': return (res1 && res2) || (!res1 && !res2);
}
}
};
struct Negation : public LogicExpr
{
LogicExpr* current;
Negation(LogicExpr* current) :current(current){}
void print() const
{
cout << "!(";
current->print();
cout << ")";
}
~Negation()
{
delete current;
}
bool evaluate(const BooleanInterpretation& interpret) const
{
bool result = current->evaluate(interpret);
return !result;
}
};
BooleanInterpretation convertNumberToInterpretation(size_t n, const std::vector<char>& vars)
{
BooleanInterpretation current;
for (int i = vars.size() - 1; i >= 0; i--, n/=2)
current.setVarValue(vars[i], n % 2);
return std::move(current);
}
bool CheckValues(LogicExpr* expr, const std::vector<char>& vars, bool value)
{
size_t checksCounts = 1 << vars.size();
for (int i = 0; i < checksCounts; i++)
{
BooleanInterpretation currentInterpret = convertNumberToInterpretation(i, vars);
if (expr->evaluate(currentInterpret) != value)
return false;
}
return true;
}
bool isTautology(LogicExpr* expr, const std::vector<char>& vars)
{
return CheckValues(expr, vars, true);
}
bool isContradiction(LogicExpr* expr, const std::vector<char>& vars)
{
return CheckValues(expr, vars, false);
}
}
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