5

我在这里的第一篇文章:)

我看到有很多关于调车场算法的问题，但我希望仍然有论坛成员有兴趣帮助我解决关于这个算法的另一个问题。

我确实搜索了其他帖子，看看我的答案是否已经得到回答，我在其他论坛和互联网上做了一些研究：

http://stackoverflow.com/questions/16877546/modifying-the-shunting-yard-algorithm-c
http://www.computerhope.com/forum/index.php?topic=146535.0
http://en.wikipedia.org/wiki/Shunting-yard_algorithm
http://www.autoitscript.com/forum/topic/164627-shunting-yard-with-functions/

我的代码是用 vb-script 编写的，因为我喜欢它的简单性，而且我不懂 java 或 c 之类的语言..

我的问题：

目前该算法允许错误使用“（”和“）”示例：函数（（10,20，）30）是允许的，但它显然不是调用函数的正确方法..

我也不确定我的代码是否正确编写，来自维基百科的伪代码是我的参考，但不是很清楚:(

我还计划用 if-else 语句和嵌套循环之类的东西来扩展它，因为主要目标是用类似 vb 的语言编写某种解释器作为学习项目:)

我的代码[编辑]：

SET PRECEDENCE = CREATEOBJECT("SCRIPTING.DICTIONARY")
WITH PRECEDENCE
    .ADD "^",3
    .ADD "*",2
    .ADD "/",2
    .ADD "%",2
    .ADD "+",1
    .ADD "-",1
    .ADD "FUNCTION",0
    .ADD "(",0
    .ADD ",",0
    .ADD ")",0
END WITH

'#############################################################################
tokenArray = split("FUNCTION ( ( A , B ) , C )")
msgbox SHUNTINGYARD(tokenArray)
'#############################################################################

FUNCTION SHUNTINGYARD(INPUT)

    TOKEN_QUEUE = ARRAY()
    TOKEN_STACK = ARRAY()

    FOR TOKEN_NUMBER = 0 TO UBOUND(INPUT)
        SELECT CASE INPUT(TOKEN_NUMBER)

            CASE "("
                CALL PUSH(INPUT(TOKEN_NUMBER), TOKEN_STACK)

            CASE ")"
                DO WHILE NOT( PRECEDENCE( PEEK(TOKEN_STACK) ) = 0 )
                    CALL PUSH(POP(TOKEN_STACK), TOKEN_QUEUE)
                    IF STACKISEMPTY(TOKEN_STACK) THEN CALL ERRORS("Can't find a matching ""("".", TRUE)
                LOOP

                IF PEEK(TOKEN_STACK) = "FUNCTION" THEN
                    DISCARD = POP(TOKEN_STACK)
                    CALL PUSH("@", TOKEN_QUEUE)
                ELSE
                    DISCARD = POP(TOKEN_STACK)
                END IF

            CASE ","
                DO WHILE NOT( PRECEDENCE( PEEK(TOKEN_STACK) ) = 0 )
                    CALL PUSH(POP(TOKEN_STACK), TOKEN_QUEUE)
                    IF STACKISEMPTY(TOKEN_STACK) THEN CALL ERRORS("Can't find a matching function ""("".", TRUE)
                LOOP

            CASE "+","-","*","/","^","%"
                TOKEN_A = INPUT(TOKEN_NUMBER)
                DO WHILE ISOPERATOR(PEEK(TOKEN_STACK))
                    TOKEN_B = PEEK(TOKEN_STACK)
                    IF (ASSOCIATIVITY(TOKEN_B) = "left" AND PRECEDENCE(TOKEN_A) = PRECEDENCE(TOKEN_B)) OR (PRECEDENCE(TOKEN_A) < PRECEDENCE(TOKEN_B)) THEN
                        CALL PUSH(POP(TOKEN_STACK), TOKEN_QUEUE)
                    ELSE
                        EXIT DO
                    END IF
                LOOP
                CALL PUSH(TOKEN_A, TOKEN_STACK)

            CASE ELSE
                CALL PUSH(INPUT(TOKEN_NUMBER), TOKEN_QUEUE)

        END SELECT
    NEXT

    FOR ITEMCOUNT = 0 TO UBOUND(TOKEN_STACK)
        IF PEEK(TOKEN_STACK) = "(" THEN CALL ERRORS("Can't find a matching "")"".", TRUE)'(
        CALL PUSH(POP(TOKEN_STACK), TOKEN_QUEUE)
    NEXT

    SHUNTINGYARD = JOIN(TOKEN_QUEUE,"|")

END FUNCTION

'#############################################################################

FUNCTION ASSOCIATIVITY(ASSOC)
    SELECT CASE LCASE(ASSOC)
        CASE "^","\"
            ASSOCIATIVITY = "right"
        CASE ELSE
            ASSOCIATIVITY = "left"
    END SELECT
END FUNCTION

FUNCTION ISOPERATOR(ITEM)
    ISOPERATOR = LEN(ITEM) = 1 AND INSTR("+-*/%^",ITEM)
END FUNCTION

SUB PUSH(ITEM,BYREF STACK)
    IF UBOUND(STACK) > -1 THEN
        REDIM PRESERVE STACK(UBOUND(STACK) + 1)
        STACK(UBOUND(STACK)) = ITEM
    ELSE
        STACK = ARRAY(ITEM)
    END IF
END SUB

FUNCTION POP(BYREF STACK)
    IF UBOUND(STACK) > -1 THEN
        POP = STACK(UBOUND(STACK))
        REDIM PRESERVE STACK(UBOUND(STACK) - 1)
    END IF
END FUNCTION

FUNCTION STACKISEMPTY(STACK)
    IF UBOUND(STACK) > -1 THEN
        STACKISEMPTY = FALSE
    ELSE
        STACKISEMPTY = TRUE
    END IF
END FUNCTION

FUNCTION PEEK(STACK)
    IF UBOUND(STACK) > -1 THEN
        PEEK = STACK(UBOUND(STACK))
    END IF
END FUNCTION
4

1 回答 1

5

您可以将“FUN”、“(”、“)”、“”与其他运算符类似地对待，并且可以被推送到 TOKEN_STACK。（为了简洁起见，我将 FUNCTION 简称为 FUN）。“FUN”，“（”，“）”，“，”的优先级低于“+​​”，所以优先级表看起来像

^                    4
*  /  %              3
+  -                 2
( ) ,   FUN          1

考虑解析 1+FUN(2*3) 时会发生什么

Remaining Input     Stack             Output
1+FUN(2*3)                          
+FUN(2*3)                           1
FUN(2*3)          +                 1
(2*3)             +  FUN            1
2*3)              +  FUN  (         1
*3)               +  FUN  (         1  2
3)                +  FUN  (  *      1  2
)                 +  FUN  (  *      1  2  3
                  +  FUN  (  *  )   1  2  3          Note 1
                  +  FUN  ( )       1  2  3  *       Note 2
                  +                 1  2  3  * FUN() 
                                    1  2  3  * FUN() +

输出标记“FUN()”代表函数评估。

注意 1：当我们尝试将“)”压入堆栈时，所有具有较高优先级的运算符都会从堆栈中取出并移至输出。

注2：当栈尾的项是匹配的“(”时，则从栈中删除。有两种情况需要处理，简单的括号匹配，如 1+(2*3) 或如果有是堆栈上“（”之前的函数标记。在这种情况下，从堆栈中弹出 FUN 并将函数评估标记添加到输出中。

"," 将以与 ")" 类似的方式处理，从而导致弹出具有更高优先级的运算符。但它不会导致函数评估被输出。你需要一些方法来记录一个函数有多少个参数。

在我的代码中，我使用基于递归的算法。解析算法可以递归调用并给出一个停止标记。当遇到停止标记时，它会退出递归。当遇到一个函数时，它调用递归等待“，”或“）”。

我设法让 iut 使用 cscript 命令行程序运行。我还用 Wscript.Echo 添加了一些调试代码。

查看 TOKEN_STACK 您从未将 FUNCTION 令牌添加到堆栈中，因此当您搜索它时它不存在。

添加 CASE "FUNCTION" CALL PUSH(INPUT(TOKEN_NUMBER), TOKEN_STACK)

似乎给了正确的东西。虽然我不确定当你匹配第一个右括号时会发生什么。像“E + FUNCTION（（A，B），C）+ F”这样的输入也会出现严重错误。

SET PRECEDENCE = CREATEOBJECT("SCRIPTING.DICTIONARY")
WITH PRECEDENCE
    .ADD "^",3
    .ADD "*",2
    .ADD "/",2
    .ADD "%",2
    .ADD "+",1
    .ADD "-",1
    .ADD "FUNCTION",0
    .ADD "(",0
    .ADD ",",0
    .ADD ")",0
END WITH

Wscript.Echo "Start"

'#############################################################################
tokenArray = split("FUNCTION ( ( A , B ) , C )")
'#tokenArray = split("A + B * C")


Wscript.Echo "Result " + SHUNTINGYARD(tokenArray)
'#############################################################################

FUNCTION SHUNTINGYARD(INPUT)

    TOKEN_QUEUE = ARRAY()
    TOKEN_STACK = ARRAY()

    FOR TOKEN_NUMBER = 0 TO UBOUND(INPUT)
    Wscript.Echo "Token " + INPUT(TOKEN_NUMBER)
    Wscript.Echo "Stack " + JOIN(TOKEN_STACK,"|")

        SELECT CASE INPUT(TOKEN_NUMBER)

            CASE "("
                CALL PUSH(INPUT(TOKEN_NUMBER), TOKEN_STACK)

            CASE ")"

                DO WHILE NOT( PRECEDENCE( PEEK(TOKEN_STACK) ) = 0 )

                    CALL PUSH(POP(TOKEN_STACK), TOKEN_QUEUE)
                    IF STACKISEMPTY(TOKEN_STACK) THEN CALL ERRORS("Can't find a matching ""("".", TRUE)
                LOOP

                IF PEEK(TOKEN_STACK) = "FUNCTION" THEN
                    DISCARD = POP(TOKEN_STACK)
                    CALL PUSH("@", TOKEN_QUEUE)
                ELSE
                    DISCARD = POP(TOKEN_STACK)
                END IF

            CASE ","
                DO WHILE NOT( PRECEDENCE( PEEK(TOKEN_STACK) ) = 0 )
                    CALL PUSH(POP(TOKEN_STACK), TOKEN_QUEUE)
                    IF STACKISEMPTY(TOKEN_STACK) THEN CALL ERRORS("Can't find a matching function ""("".", TRUE)
                LOOP

            CASE "+","-","*","/","^","%"
                TOKEN_A = INPUT(TOKEN_NUMBER)
                DO WHILE ISOPERATOR(PEEK(TOKEN_STACK))
                    TOKEN_B = PEEK(TOKEN_STACK)
                    IF (ASSOCIATIVITY(TOKEN_B) = "left" AND PRECEDENCE(TOKEN_A) = PRECEDENCE(TOKEN_B)) OR (PRECEDENCE(TOKEN_A) < PRECEDENCE(TOKEN_B)) THEN
                        CALL PUSH(POP(TOKEN_STACK), TOKEN_QUEUE)
                    ELSE
                        EXIT DO
                    END IF
                LOOP
                CALL PUSH(TOKEN_A, TOKEN_STACK)

            CASE "FUNCTION"
                CALL PUSH(INPUT(TOKEN_NUMBER), TOKEN_STACK)

            CASE ELSE
                CALL PUSH(INPUT(TOKEN_NUMBER), TOKEN_QUEUE)

        END SELECT
    NEXT

    FOR ITEMCOUNT = 0 TO UBOUND(TOKEN_STACK)
        IF PEEK(TOKEN_STACK) = "(" THEN CALL ERRORS("Can't find a matching "")"".", TRUE)'(
        CALL PUSH(POP(TOKEN_STACK), TOKEN_QUEUE)
    NEXT

    SHUNTINGYARD = JOIN(TOKEN_QUEUE,"|")

END FUNCTION

'#############################################################################

FUNCTION ASSOCIATIVITY(ASSOC)
    SELECT CASE LCASE(ASSOC)
        CASE "^","\"
            ASSOCIATIVITY = "right"
        CASE ELSE
            ASSOCIATIVITY = "left"
    END SELECT
END FUNCTION

FUNCTION ISOPERATOR(ITEM)
    ISOPERATOR = LEN(ITEM) = 1 AND INSTR("+-*/%^",ITEM)
END FUNCTION

SUB PUSH(ITEM,BYREF STACK)
    IF UBOUND(STACK) > -1 THEN
        REDIM PRESERVE STACK(UBOUND(STACK) + 1)
        STACK(UBOUND(STACK)) = ITEM
    ELSE
        STACK = ARRAY(ITEM)
    END IF
END SUB

FUNCTION POP(BYREF STACK)
    IF UBOUND(STACK) > -1 THEN
        POP = STACK(UBOUND(STACK))
        REDIM PRESERVE STACK(UBOUND(STACK) - 1)
    END IF
END FUNCTION

FUNCTION STACKISEMPTY(STACK)
    IF UBOUND(STACK) > -1 THEN
        STACKISEMPTY = FALSE
    ELSE
        STACKISEMPTY = TRUE
    END IF
END FUNCTION

FUNCTION PEEK(STACK)
    IF UBOUND(STACK) > -1 THEN
        PEEK = STACK(UBOUND(STACK))
    END IF
END FUNCTION
于 2014-10-02T08:14:43.090 回答