摘要：下面我們用棧來(lái)實(shí)現(xiàn)簡(jiǎn)易的四則運(yùn)算計(jì)算器。列一下本文的思路實(shí)現(xiàn)鏈棧的數(shù)據(jù)結(jié)構(gòu)及其操作中綴表達(dá)式轉(zhuǎn)后綴表達(dá)式后綴表達(dá)式求值首先先實(shí)現(xiàn)一個(gè)鏈棧。是否是四則運(yùn)算符號(hào)計(jì)算后綴表達(dá)式的值為空則跳過(guò)最后，我們測(cè)試一下所實(shí)現(xiàn)的計(jì)算器。

列一下本文的思路:

實(shí)現(xiàn)鏈棧的數(shù)據(jù)結(jié)構(gòu)及其操作

中綴表達(dá)式轉(zhuǎn)后綴表達(dá)式

后綴表達(dá)式求值

1、首先, 先實(shí)現(xiàn)一個(gè)鏈棧。

//定義棧的數(shù)據(jù)結(jié)構(gòu)
class Node
{
    public $symbol;
    public $next;

    public function __construct( $symbol, $next )
    {
        $this->symbol = $symbol;
        $this->next   = $next;
    }
}

//初始化棧,生成頭結(jié)點(diǎn)
function initStack( &$node )
{
    $node = new Node( "", null );
}

//入棧
function push( Node &$node, $symbol )
{
    $p          = new Node( $symbol, null );
    $p->next    = $node->next;
    $node->next = $p;
}

//出棧
function pop( Node &$node, &$symbol )
{
    if ( null == $node->next ) {
        echo "?？?";

        return;
    }

    $q          = $node->next;
    $symbol     = $q->symbol;
    $node->next = $node->next->next;
    unset( $q );
}

2、其次, 利用第一步實(shí)現(xiàn)的鏈棧，將中綴表達(dá)式轉(zhuǎn)為后綴表達(dá)式。

//獲取運(yùn)算符的優(yōu)先級(jí)
function get_priority( $symbol )
{
    switch ( $symbol ) {
        case "(":
            $priority = 3;
            break;
        case "*":
        case "/":
            $priority = 2;
            break;
        case "+":
        case "-":
            $priority = 1;
            break;
        case ")":
            $priority = 0;
            break;
        default:
            $priority = 0;
            break;
    }

    return $priority;
}

//棧頂依次出棧,如果遇到"("則停止
function clear_stack( &$list )
{
    $res = "";
    while ( null != $list->next ) {
        if ( "(" != $list->next->symbol ) {
            pop( $list, $item );
            $res .= $item;

        } else {
            pop( $list, $item );

            return $res;
        }
    }

    return $res;
}

//中綴表達(dá)式轉(zhuǎn)后綴表達(dá)式
function middle_to_back( $middle_expression )
{
    initStack( $list );
    $back_expression = "";
    $length          = strlen( $middle_expression );
    for ( $i = 0; $i < $length; $i ++ ) {
        $symbol = $middle_expression[ $i ];
        if ( " " != $symbol ) {
            if ( is_numeric( $symbol ) ) { //數(shù)字直接輸出
                $back_expression .= $symbol;
            } else {//非數(shù)字則比較優(yōu)先級(jí)
                $stack_top_priority      = get_priority( null == $list->next ? "" : $list->next->symbol );
                $current_symbol_priority = get_priority( $symbol );
                if ( $current_symbol_priority > $stack_top_priority ) {//優(yōu)先級(jí)比棧頂高則進(jìn)棧
                    push( $list, $symbol );
                } else {
                    $output          = clear_stack( $list );
                    $back_expression .= $output;
                    if ( ")" != $symbol ) {
                        push( $list, $symbol );
                    }
                }
            }
        }
    }

    while ( null != $list->next ) {//將棧清空
        pop( $list, $item );
        $back_expression .= $item;
    }

    return $back_expression;
}

3、接下來(lái), 我們利用第一步實(shí)現(xiàn)的鏈棧，和第二步得到的后綴表達(dá)式，計(jì)算最后的值。

//是否是四則運(yùn)算符號(hào)
function is_arithmetic_symbol( $symbol )
{
    $arithmetic_symbols = array( "+", "-", "*", "/" );
    if ( in_array( $symbol, $arithmetic_symbols ) ) {
        return true;
    } else {
        return false;
    }
}

//計(jì)算后綴表達(dá)式的值
function calculate( $expression )
{
    $stack  = new Node( "", null );
    $length = strlen( $expression );
    for ( $i = 0; $i < $length; $i ++ ) {
        if ( " " != $expression[ $i ] ) {//為空則跳過(guò)
            if ( is_numeric( $expression[ $i ] ) ) {
                push( $stack, $expression[ $i ] );
            } else if ( is_arithmetic_symbol( $expression[ $i ] ) ) {
                pop( $stack, $n1 );
                pop( $stack, $n2 );
                $res = get_result( $n2, $n1, $expression[ $i ] );
                push( $stack, $res );
            } else {
                echo "wrong symbol, exit";
                exit();
            }
        }
    }

    $value = $stack->next->symbol;

    return $value;
}

最后，我們測(cè)試一下所實(shí)現(xiàn)的計(jì)算器。

function main()
{
    $back_expression = middle_to_back( "((1+2)*3-4) * 5" );
    $result          = calculate( $back_expression );
    echo "后綴表達(dá)式的值為: " . $back_expression, PHP_EOL;
    echo "result : " . $result, PHP_EOL;
}

main();

得到的結(jié)果如下:

簡(jiǎn)易的計(jì)算器就實(shí)現(xiàn)啦！~~~
（代碼中有一些細(xì)節(jié)未做判斷，希望讀者理解。歡迎大家提出批評(píng)修改意見(jiàn)，感謝~）