问题
I searched all over the internet for a good implementation in converting not numbers expressions but variable expressions from infix notation into prefix and postfix. All the searches I did weren't successful. Basically I want to see if there is any implementation yet in PHP so I could modify it to support more operators not only the (-,*,+,=).
For example convert:
a+b/c*(p/c)
While keeping the variable names, and not having to enter numbers to evaluate them.
回答1:
I have found a good implementation in the evalmath class provided by Miles Kaufmann here : http://www.phpclasses.org/package/2695-PHP-Safely-evaluate-mathematical-expressions.html
Infix to Postfix code :
// Convert infix to postfix notation
function nfx($expr) {
$index = 0;
$stack = new EvalMathStack;
$output = array(); // postfix form of expression, to be passed to pfx()
$expr = trim(strtolower($expr));
$ops = array('+', '-', '*', '/', '^', '_');
$ops_r = array('+'=>0,'-'=>0,'*'=>0,'/'=>0,'^'=>1); // right-associative operator?
$ops_p = array('+'=>0,'-'=>0,'*'=>1,'/'=>1,'_'=>1,'^'=>2); // operator precedence
$expecting_op = false; // we use this in syntax-checking the expression
// and determining when a - is a negation
if (preg_match("/[^\w\s+*^\/()\.,-]/", $expr, $matches)) { // make sure the characters are all good
return $this->trigger("illegal character '{$matches[0]}'");
}
while(1) { // 1 Infinite Loop ;)
$op = substr($expr, $index, 1); // get the first character at the current index
// find out if we're currently at the beginning of a number/variable/function/parenthesis/operand
$ex = preg_match('/^([a-z]\w*\(?|\d+(?:\.\d*)?|\.\d+|\()/', substr($expr, $index), $match);
//===============
if ($op == '-' and !$expecting_op) { // is it a negation instead of a minus?
$stack->push('_'); // put a negation on the stack
$index++;
} elseif ($op == '_') { // we have to explicitly deny this, because it's legal on the stack
return $this->trigger("illegal character '_'"); // but not in the input expression
//===============
} elseif ((in_array($op, $ops) or $ex) and $expecting_op) { // are we putting an operator on the stack?
if ($ex) { // are we expecting an operator but have a number/variable/function/opening parethesis?
$op = '*'; $index--; // it's an implicit multiplication
}
// heart of the algorithm:
while($stack->count > 0 and ($o2 = $stack->last()) and in_array($o2, $ops) and ($ops_r[$op] ? $ops_p[$op] < $ops_p[$o2] : $ops_p[$op] <= $ops_p[$o2])) {
$output[] = $stack->pop(); // pop stuff off the stack into the output
}
// many thanks: http://en.wikipedia.org/wiki/Reverse_Polish_notation#The_algorithm_in_detail
$stack->push($op); // finally put OUR operator onto the stack
$index++;
$expecting_op = false;
//===============
} elseif ($op == ')' and $expecting_op) { // ready to close a parenthesis?
while (($o2 = $stack->pop()) != '(') { // pop off the stack back to the last (
if (is_null($o2)) return $this->trigger("unexpected ')'");
else $output[] = $o2;
}
if (preg_match("/^([a-z]\w*)\($/", $stack->last(2), $matches)) { // did we just close a function?
$fnn = $matches[1]; // get the function name
$arg_count = $stack->pop(); // see how many arguments there were (cleverly stored on the stack, thank you)
$output[] = $stack->pop(); // pop the function and push onto the output
if (in_array($fnn, $this->fb)) { // check the argument count
if($arg_count > 1)
return $this->trigger("too many arguments ($arg_count given, 1 expected)");
} elseif (array_key_exists($fnn, $this->f)) {
if ($arg_count != count($this->f[$fnn]['args']))
return $this->trigger("wrong number of arguments ($arg_count given, " . count($this->f[$fnn]['args']) . " expected)");
} else { // did we somehow push a non-function on the stack? this should never happen
return $this->trigger("internal error");
}
}
$index++;
//===============
} elseif ($op == ',' and $expecting_op) { // did we just finish a function argument?
while (($o2 = $stack->pop()) != '(') {
if (is_null($o2)) return $this->trigger("unexpected ','"); // oops, never had a (
else $output[] = $o2; // pop the argument expression stuff and push onto the output
}
// make sure there was a function
if (!preg_match("/^([a-z]\w*)\($/", $stack->last(2), $matches))
return $this->trigger("unexpected ','");
$stack->push($stack->pop()+1); // increment the argument count
$stack->push('('); // put the ( back on, we'll need to pop back to it again
$index++;
$expecting_op = false;
//===============
} elseif ($op == '(' and !$expecting_op) {
$stack->push('('); // that was easy
$index++;
$allow_neg = true;
//===============
} elseif ($ex and !$expecting_op) { // do we now have a function/variable/number?
$expecting_op = true;
$val = $match[1];
if (preg_match("/^([a-z]\w*)\($/", $val, $matches)) { // may be func, or variable w/ implicit multiplication against parentheses...
if (in_array($matches[1], $this->fb) or array_key_exists($matches[1], $this->f)) { // it's a func
$stack->push($val);
$stack->push(1);
$stack->push('(');
$expecting_op = false;
} else { // it's a var w/ implicit multiplication
$val = $matches[1];
$output[] = $val;
}
} else { // it's a plain old var or num
$output[] = $val;
}
$index += strlen($val);
//===============
} elseif ($op == ')') { // miscellaneous error checking
return $this->trigger("unexpected ')'");
} elseif (in_array($op, $ops) and !$expecting_op) {
return $this->trigger("unexpected operator '$op'");
} else { // I don't even want to know what you did to get here
return $this->trigger("an unexpected error occured");
}
if ($index == strlen($expr)) {
if (in_array($op, $ops)) { // did we end with an operator? bad.
return $this->trigger("operator '$op' lacks operand");
} else {
break;
}
}
while (substr($expr, $index, 1) == ' ') { // step the index past whitespace (pretty much turns whitespace
$index++; // into implicit multiplication if no operator is there)
}
}
while (!is_null($op = $stack->pop())) { // pop everything off the stack and push onto output
if ($op == '(') return $this->trigger("expecting ')'"); // if there are (s on the stack, ()s were unbalanced
$output[] = $op;
}
return $output;
}
来源：https://stackoverflow.com/questions/17774360/variables-infix-to-prefix-to-postfix