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iterative_basic_sat.cpp
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iterative_basic_sat.cpp
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/*
Basic SAT
basic_sat.cpp
Author: Rui-Jie Fang
Date: June 2018
*/
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <unordered_set>
#include <stack>
#include <utility>
//#define VERBOSE
//#define MEMINFO
using namespace std;
struct bexpr {
char val;
char op;
char neg;
char isfree;
bexpr *expr;
bexpr * n_expr;
};
inline static void err()
{
printf("syntax error\n");
exit(1);
}
inline static char* skip(char* s)
{
while (*s == ' ' || *s == '\n' || *s == '\t') ++s;
//printf("skip: @%c\n", *s);
return s;
}
// grammar:
// <S>: <bool> <op> <S> | <bool> | <t>
// <bool>: '~' <bval> | <bval> | '(' <S> ')'
// <bval>: '1' | '0' | 't' | 'f' | 'T' | 'F'
// <op>: '^' | '&' | '|'
inline static bool is_free_variable(char c)
{
return ((c >= 'a') && (c <= 'z')) || ((c >= 'A') && (c <= 'Z'));
}
void S(bexpr* expr, char** prog);
void B(bexpr* expr, char** prog)
{
#ifdef MEMINFO
printf("addr *prog = %p\n", *prog);
#endif
*prog = skip(*prog);
if (!(*prog) || !(**prog)) err(); // <bool> does not allow <t>
printf("B(): @%c\n", **prog);
expr->isfree= 0;
expr->neg = 0;
switch (**prog) {
case '(': {
++(*prog);
expr->n_expr = new bexpr;
S(expr->n_expr, prog);
++(*prog);
printf("B(): S() returned, **prog=%d\n",**prog=='\0');
return;
break;
}
case '~': {
expr->neg = 1;
++(*prog);
}
case '1':
case '0':
case 't':
case 'f':
case 'T':
case 'F':
expr->n_expr = NULL;
expr->val = **prog;
++(*prog);
break;
default:
if (is_free_variable(**prog)) {
expr->isfree = 1;
expr->n_expr = NULL;
expr->val = **prog;
++(*prog);
break;
}
err();
}
}
void OP(bexpr* expr, char** prog)
{
#ifdef MEMINFO
printf("addr *prog = %p\n", *prog);
#endif
char *s = *prog;
s = skip(s);
if (!s || !(*s)) err(); // <op> does not allow <term> either
printf("OP(): @%c\n", *s);
switch (*s) {
case '^':
case '&':
case '|':
expr->op = *s;
++s;
break;
default:
err();
}
*prog = s;
}
#define _T(expr,prog) \
if (!(*prog) || !(**prog) || (**prog==0) || (**prog=='\0') || (**prog==';')||(**prog==')')){\
expr->op=';';\
printf("T(): return\n");\
return 1;}
bool T(bexpr* expr, char** prog)
{
_T(expr,prog);
*prog = skip(*prog);
_T(expr,prog);
return 0;
}
void S(bexpr* expr, char** prog)
{
#ifdef MEMINFO
printf("addr *prog = %p\n", *prog);
#endif
printf("S(): check\n");
if (T(expr,prog)) return; // the <t> case
printf("S(): parsing B()\n");
B(expr, prog);
printf("S(): next: %d\n", **prog);
if (T(expr,prog)) return;
printf("S(): parsing OP(), %d\n",**prog);
OP(expr, prog);
if (T(expr,prog)) err(); // strict check for next <S>, no term allowed here
expr->expr = new bexpr;
printf("S(): parsing S()\n");
S(expr->expr, prog);
}
void RPN_print(bexpr * expr)
{
if (expr->op == ';') {
if (expr->n_expr==NULL)
printf("%c", expr->val);
else {
printf("(");
RPN_print(expr->n_expr);
printf(")");
}
return;
} else if (expr->n_expr != NULL) {
printf("(");
printf("%c ", expr->op);
RPN_print(expr->n_expr);
if (expr->expr)
RPN_print(expr->expr);
printf(")");
}
printf("(");
printf("%c ", expr->op);
if (expr->neg) printf("%c",'~');
printf("%c ", expr->val);
if(expr->expr)
RPN_print(expr->expr);
printf(")");
}
inline static bool _cast(char v)
{
switch (v) {
case 't':
case 'T':
case '1':
case 1:
return 1;
case 'f':
case 'F':
case '0':
case 0:
return 0;
default:
printf("err: _cast() failure, val = %c\n", v);
exit(1);
}
}
inline static bool _eval(char v1, char v2, char op)
{
#ifdef VERBOSE
printf("_eval: %d,%d\n",(bool) v1,(bool) v2);
#endif
bool b1 = _cast(v1), b2 = _cast(v2);
switch (op) {
case '^':
return b1 ^ b2;
case '|':
return b1 | b2;
case '&':
return b1 & b2;
default:
printf("err: _eval() failure, op = %c\n", op);
exit(1);
}
}
bool eval(bexpr* expr)
{
if (expr->op == ';') {
if (expr->n_expr==NULL) {
return expr->neg ? ~_cast(expr->val) : _cast(expr->val);
} else {
return expr->neg ? (~eval(expr->n_expr)) : eval(expr->n_expr);
}
} else if (expr->n_expr != NULL) {
bool p = eval(expr->n_expr);
return _eval(expr->neg ? ~p : p, eval(expr->expr), expr->op);
} else { // expr->n_expr == NULL, is val
if (expr->isfree) {
printf("err: eval(): cannot evaluate a boolean expression with a free variable\n");
exit(1);
}
return _eval(expr->neg ? ~_cast(expr->val) : _cast(expr->val), eval(expr->expr), expr->op);
}
}
char _table[1000];
inline static void init_solve()
{ for(unsigned i = 0; i < 1000; ++i) _table[i] = 2; }
inline static void _set(char var, char val)
{ _table[var] = val; }
inline static char _lookup(char var)
{ return _table[var]; }
inline static char to_printout(char x)
{
switch (x) {
case 0: return 'F';
case 1: return 'T';
default: return 'X';
}
}
void print_solution(bexpr* expr)
{
if (expr==NULL) return;
while (expr->op != ';') {
if (expr->n_expr)
print_solution(expr->n_expr);
if (expr->isfree) {
printf("Variable [%c] := %c\n", expr->val, to_printout(_lookup(expr->val)));
}
expr = expr->expr;
}
if (expr->n_expr)
print_solution(expr->n_expr);
if (expr->isfree) {
printf("Variable [%c] := %c\n", expr->val, to_printout(_lookup(expr->val)));
}
#ifdef VERBOSE
printf("print_solution(): all free variables printed, returning...\n");
#endif
return;
}
bool _feval(bexpr* expr)
{
if (expr->op == ';') {
#ifdef VERBOSE
printf("_feval(): reached end of expression\n");
#endif
if (expr->n_expr) {
return _feval(expr->n_expr);
} else {
if (expr->isfree) {
#ifdef VERBOSE
printf("_feval(): lookup variable %c = %d\n", expr->val, (bool) _lookup(expr->val));
#endif
return (bool) _lookup(expr->val);
} else
return _cast(expr->val);
}
} else {
if (expr->n_expr) {
bool p = _feval(expr->n_expr);
return _eval(p, _feval(expr->expr), expr->op);
} else {
#ifdef VERBOSE
printf("_feval(): @ variable %c\n", expr->val);
#endif
if (expr->isfree) {
#ifdef VERBOSE
printf("_feval(): lookup variable %c = %d\n", expr->val, (bool) _lookup (expr->val));
#endif
bool f = (bool) _lookup(expr->val);
return _eval(f, _feval(expr->expr), expr->op);
} else {
return _eval(_cast(expr->val), _feval(expr->expr), expr->op);
}
}
}
}
inline static void err_none()
{
printf("err: SAT: nothing to solve.\n");
exit(1);
}
void _register_free_variables(bexpr* expr, unordered_set<char>& vs)
{
if (expr->op == ';') {
if (expr->n_expr) {
_register_free_variables(expr->n_expr, vs);
#ifdef VERBOSE
printf("reg(): end reached, vs.size() == %lu\n", vs.size());
#endif
if (vs.size() == 0) err_none();
} else {
if (expr->isfree && (vs.find(expr->val) == vs.end())) {
vs.insert(expr->val);
}
#ifdef VERBOSE
printf("reg(): end reached, vs.size() == %lu\n", vs.size());
#endif
if (vs.size() == 0) err_none();
}
} else {
if (expr->n_expr) {
_register_free_variables(expr->n_expr, vs);
}
if (expr->isfree && (vs.find(expr->val) == vs.end())) {
#ifdef VERBOSE
printf("reg(): free variable found [%c]\n", expr->val);
#endif
vs.insert(expr->val);
}
_register_free_variables(expr->expr, vs);
}
}
void _backtrack(bexpr* expr, unordered_set<char>& vs, unordered_set<char>::iterator ptr)
{
if (ptr == vs.end()) {
#ifdef VERBOSE
printf("_backtrack(): size %lu reached, evaling...\n", vs.size());
#endif
if (_feval(expr)) {
#ifdef VERBOSE
printf("_backtrack(): found correct solution, printing out...\n");
#endif
printf("::::: Viable Solution :::::\n");
print_solution(expr);
printf("..... ............... .....\n");
}
return;
}
unordered_set<char>::iterator optr = ptr;
++ptr;
_set(*optr, 1);
_backtrack(expr, vs, ptr);
_set(*optr, 0);
_backtrack(expr, vs, ptr);
}
void _backtrack_iterative(bexpr* expr, unordered_set<char>& vs)
{
pair<unordered_set<char>::iterator, bool> arg;
unordered_set<char>::iterator optr;
stack< pair<unordered_set<char>::iterator, bool> > stk;
stk.push(make_pair<unordered_set<char>::iterator, bool>(vs.begin(), 0));
stk.push(make_pair<unordered_set<char>::iterator, bool>(vs.begin(), 1));
do {
arg = stk.top();
stk.pop();
//printf("iter(): Variable %c, State %d\n", *(arg.first), arg.second);
_set(*(arg.first), arg.second);
optr = arg.first;
++optr;
// do check here to avoid printing out identical solution twice
// nasty hack for STL behaviour
if (optr == vs.end()) {
#ifdef VERBOSE
printf("_backtrack(): size %lu reached, evaling...\n", vs.size());
#endif
if (_feval(expr)) {
#ifdef VERBOSE
printf("_backtrack(): found correct solution, printing out...\n");
#endif
printf("::::: Viable Solution :::::\n");
print_solution(expr);
printf("..... ............... .....\n");
}
continue;
} else {
stk.push(make_pair<unordered_set<char>::iterator, bool>(optr, 0));
stk.push(make_pair<unordered_set<char>::iterator, bool>(optr, 1));
}
} while (!stk.empty());
}
inline static void solve(bexpr* expr)
{
#ifdef VERBOSE
printf("solve(): init_solve\n");
#endif
init_solve();
unordered_set<char> free_vars;
#ifdef VERBOSE
printf("solve(): finding free variables\n");
for(char x : free_vars)
printf("[Free Variable Found]: %c\n", x);
#endif
_register_free_variables(expr, free_vars);
#ifdef VERBOSE
printf("solve(): free vars found, backtracking...\n");
#endif
// _backtrack(expr, free_vars, free_vars.begin());
_backtrack_iterative(expr, free_vars);
#ifdef VERBOSE
printf("solve(): backtracking done.\n");
#endif
}
void bexpr_free(bexpr* expr)
{
bexpr* next;
while ( expr->op != ';' )
{
if (expr->n_expr != NULL)
bexpr_free(expr->n_expr);
next = expr->expr;
delete expr;
expr = next;
}
delete expr;
}
int main()
{
char * s, * sp;
size_t len;
cin >> len;
sp = s = (char*) malloc(len);
memset(s, '\0', len);
scanf("%s", s);
// ++s;
printf("input: %s\n", s);
#ifdef MEMINFO
printf("addr s = %p, addr s_end = %p\n", s, s + strlen(s) + 1);
printf("s_end=%c %c\n", *(s+strlen(s)), *(s+strlen(s)+1));
#endif
bexpr *expr = new bexpr;
S(expr, &s);
RPN_print(expr);
puts("");
// printf("eval result is %d\n", eval(expr));
printf(" === solving === \n");
solve(expr);
bexpr_free(expr);
free(sp);
return 0;
}