Question

我正在尝试在PHP中实现infix的前缀。输入应该是这样的：

prefix  * + 3 2 4
infix   ((3+2)*4)

我想使用PHP或JavaScript (* + 3 2 4)将前缀表达式（如(((3+2)*4))）转换为中缀表达式。

Answer 1

这是前缀到后缀表示法的基本算法（使用stack）：

   IF stack is not empty
     a. Temp -->pop the stack
     b. IF temp is a operator
       i. Write a opening parenthesis to output
       ii. prefixToInfix(stack)
       iii. Write temp to output
       iv. prefixToInfix(stack)
       v. Write a closing parenthesis to output
    c. ELSE IF temp is a space -->prefixToInfix(stack)
    d. ELSE
       i. Write temp to output
       ii. IF stack.top NOT EQUAL to space -->prefixToInfix(stack)

尝试一下，然后测试一下（使用优秀的铅笔纸方法）。

Answer 2

示例性面向对象的AST和解析器：

$prefix = '* + 3 2 4';
$parser = new InfixPrefixParser($prefix);
$node = $parser->parse();
echo $node, "\n"; # ((3 + 2) * 4)
echo ' = ', $node->evaluate(), "\n"; # 20

解析器：

class InfixPrefixParser extends IteratorIterator
{
    public function __construct($prefix)
    {
        $tokens = new ArrayIterator(preg_split('/\s/', $prefix, 0, PREG_SPLIT_NO_EMPTY));
        parent::__construct($tokens);
    }

    /**
     * @return InfixNode
     */
    public function current()
    {
        $string = parent::current();
        parent::next();
        $operators = array('*' => 'Mult', '+' => 'Plus');
        $class = 'InfixNode' . (isset($operators[$string]) ? 'Operator' . $operators[$string] : 'Value');
        $node = new $class($string);
        if ($node instanceof InfixNodeOperator) {
            $node->setLeft($this->current());
            $node->setRight($this->current());
        }
        return $node;
    }

    public function __toString()
    {
        return (string)$this->parse();
    }

    public function parse()
    {
        $this->rewind();
        return $this->current();
    }
}

AST的对象模型

abstract class InfixNode
{
    abstract function evaluate();
}

abstract class InfixNodeOperator extends InfixNode
{
    private $operator;
    protected $left;
    protected $right;

    public function __construct($operator)
    {
        $this->operator = $operator;
    }

    public function setLeft(InfixNode $node)
    {
        $this->left = $node;
    }

    public function getLeft()
    {
        return $this->left;
    }

    public function setRight(InfixNode $node)
    {
        $this->right = $node;
    }

    public function getRight()
    {
        return $this->right;
    }

    public function __toString()
    {
        return sprintf('(%s %s %s)', $this->left, $this->operator, $this->right);
    }
}

class InfixNodeOperatorMult extends InfixNodeOperator
{
    public function evaluate()
    {
        return $this->left->evaluate() * $this->right->evaluate();
    }
}

class InfixNodeOperatorPlus extends InfixNodeOperator
{
    public function evaluate()
    {
        return $this->left->evaluate() + $this->right->evaluate();
    }
}

class InfixNodeValue extends InfixNode
{
    private $value;

    public function __construct($value)
    {
        $this->value = $value;
    }

    public function __toString()
    {
        return (string)$this->value;
    }

    public function evaluate()
    {
        return $this->value;
    }
}

我对措辞不太自信，因为节点与中缀并不完全相关，它们的大部分也可用于前缀或后缀，只有__toString()函数与中缀相关实际上。

（旧版本）一些PHP代码，使用一些递归解析函数和节点的对象模型。用法：

$prefix = '* + 3 2 4';

$tokens = new ArrayIterator(preg_split('/\s/', $prefix, 0, PREG_SPLIT_NO_EMPTY));

$parse = function() use ($tokens, &$parse) {
    $string = $tokens->current(); $tokens->next();
    $isOperator = in_array($string, array('*', '+'));
    $class = 'InfixNode' . ($isOperator ? 'Operator' : 'Value');
    $node = new $class($string);
    if ($node instanceof InfixNodeOperator) {
        $node->setLeft($parse());
        $node->setRight($parse());
    }
    return $node;
};

echo $parse(); # ((3 + 2) * 4)

节点类：

class InfixNode {}

class InfixNodeOperator extends InfixNode
{
    private $operator;
    private $left;
    private $right;
    public function __construct($operator) {
        $this->operator = $operator;
    }
    public function setLeft(InfixNode $node) {
        $this->left = $node;
    }
    public function getLeft() {
        return $this->left;
    }
    public function setRight(InfixNode $node) {
        $this->right = $node;
    }
    public function getRight() {
        return $this->right;
    }
    public function __toString() {
        return sprintf('(%s %s %s)', $this->left, $this->operator, $this->right);
    }
}

class InfixNodeValue extends InfixNode
{
    private $value;
    public function __construct($value) {
        $this->value = $value;
    }
    public function __toString() {
        return (string) $this->value;
    }
}

在PHP中添加中缀的前缀

2 个答案: