如何使用 Shunting-Yard 算法构建 PHP 计算器？

如何用 PHP 制作计算器

问题：

创建一个 PHP 计算器，可以计算输入的简单代数表达式由用户使用标准代数符号，包括表达式

常见方法：

一个低效但临时的解决方案涉及替换表达式的字符串表示形式中的表达式，例如：

for ($a=1; $a < 1000; $a++) {
    for ($b=1; $b < 1000; $b++) {
        string_replace($a . '*' . $b, $a*$b, $string);
    }
}

调车场算法：

A更有效的方法是使用 Shunting Yard 算法。

实现：

终端表达式（值和运算符）：

abstract class TerminalExpression {
    protected $value = '';

    public static function factory($value) {
        // Create terminal expressions based on the provided value (number, operator, or parenthesis)
    }

    abstract public function operate(Stack $stack);
}

class Number extends TerminalExpression {
    public function operate(Stack $stack) {
        return $this->value;
    }
}

class Operator extends TerminalExpression {
    protected $precidence = 0;
    protected $leftAssoc = true;

    public function getPrecidence() {
        return $this->precidence;
    }

    public function isLeftAssoc() {
        return $this->leftAssoc;
    }
}

class Addition extends Operator {
    protected $precidence = 4;
}

class Subtraction extends Operator {
    protected $precidence = 4;
}

class Multiplication extends Operator {
    protected $precidence = 5;
}

class Division extends Operator {
    protected $precidence = 5;
}

class Parenthesis extends TerminalExpression {
    protected $precidence = 7;

    public function isParenthesis() {
        return true;
    }
}

堆栈实现：

class Stack {
    protected $data = [];
    public function push($element) {
        array_push($this->data, $element);
    }
    public function pop() {
        return array_pop($this->data);
    }
}

数学类（执行器）：

class Math {
    protected $variables = [];

    public function evaluate($string) {
        $stack = $this->parse($string);
        return $this->run($stack);
    }

    public function parse($string) {
        // Tokenize expression
        $tokens = array_map('trim', preg_split('((\d+|\+|-|\(|\)|\*|/)|\s+)', $string, null, PREG_SPLIT_NO_EMPTY | PREG_SPLIT_DELIM_CAPTURE));

        // Parse operators and parentheses using the Shunting Yard algorithm
        $output = new Stack();
        $operators = new Stack();

        foreach ($tokens as $token) {
            $expression = TerminalExpression::factory($token);

            if ($expression->isOperator()) {
                $this->parseOperator($expression, $output, $operators);
            } elseif ($expression->isParenthesis()) {
                $this->parseParenthesis($expression, $output, $operators);
            } else {
                $output->push($expression);
            }
        }

        // Pop remaining operators on stack and push to output
        while (($op = $operators->pop()) && $op->isOperator()) {
            if ($op->isParenthesis()) {
                throw new RuntimeException('Mismatched Parenthesis');
            }
            $output->push($op);
        }

        return $output;
    }

    public function run(Stack $stack) {
        // Evaluate stack and return result
        while (($operator = $stack->pop()) && $operator->isOperator()) {
            $value = $operator->operate($stack);
            $stack->push(TerminalExpression::factory($value));
        }

        return $operator ? $operator->render() : $this->render($stack);
    }

    protected function extractVariables($token) {
        if ($token[0] == '$') {
            $key = substr($token, 1);
            return isset($this->variables[$key]) ? $this->variables[$key] : 0;
        }
        return $token;
    }

    // ...
}

使用此实现，您可以按如下方式计算表达式：

$math = new Math();
$answer = $math->evaluate('(2 + 3) * 4'); // 20
$answer = $math->evaluate('1 + 2 * ((3 + 4) * 5 + 6)'); // 83
$answer = $math->evaluate('(1 + 2) * (3 + 4) * (5 + 6)'); // 231
$math->registerVariable('a', 4);
$answer = $math->evaluate('($a + 3) * 4'); // 28

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