Evaluating a string of simple mathematical expressions [closed]

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Python

Number of characters: 235

Fully obfuscated function:

def g(a):
 i=len(a)
 while i:
  try:m=g(a[i+1:]);n=g(a[:i]);a=str({'+':n+m,'-':n-m,'*':n*m,'/':n/(m or 1)}[a[i]])
  except:i-=1;j=a.rfind('(')+1
  if j:k=a.find(')',j);a=a[:j-1]+str(g(a[j:k]))+a[k+1:]
 return float(a.replace('--',''))

Semi-obfuscated:

def g(a):
    i=len(a);
    # do the math
    while i:
        try:
            # recursively evaluate left and right
            m=g(a[i+1:])
            n=g(a[:i])
            # try to do the math assuming that a[i] is an operator
            a=str({'+':n+m,'-':n-m,'*':n*m,'/':n/(m or 1)}[a[i]])
        except:
            # failure -> next try
            i-=1
            j=a.rfind('(')+1
        # replace brackets in parallel (this part is executed first)
        if j:
            k=a.find(')',j)
            a=a[:j-1]+str(g(a[j:k]))+a[k+1:]
    return float(a.replace('--',''))

FWIW, the n+1th Python solution. In a blatant abuse of try-except I use a trial-and-error approach. It should handle all cases properly including stuff like -(8), --8 and g('-(1 - 3)'). It is re-entrant. Without support for the -- case which many implementations don't support, it is at 217 chars (see previous revision).

Thanks for an interesting hour on a Sunday and another 30 mins on Monday. Thanks to krubo for his nice dict.

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醉话见心

2020-11-28 01:27

SQL (SQL Server 2008)

Number of characters: 4202

Fully obfuscated function:

WITH Input(id,str)AS(SELECT 1,'1 + 3 / -8'UNION ALL SELECT 2,'2*3*4*5+99'UNION ALL SELECT 3,'4 * (9 - 4)/ (2 * 6 - 2)+ 8'UNION ALL SELECT 4,'1 + ((123 * 3 - 69)/ 100)'UNION ALL SELECT 5,'2.45/8.5*9.27+(5*0.0023)'),Separators(i,ch,str_src,priority)AS(SELECT 1,'-',1,1UNION ALL SELECT 2,'+',1,1UNION ALL SELECT 3,'*',1,1UNION ALL SELECT 4,'/',1,1UNION ALL SELECT 5,'(',0,0UNION ALL SELECT 6,')',0,0),SeparatorsStrSrc(str,i)AS(SELECT CAST('['AS varchar(max)),0UNION ALL SELECT str+ch,SSS.i+1FROM SeparatorsStrSrc SSS INNER JOIN Separators S ON SSS.i=S.i-1WHERE str_src<>0),SeparatorsStr(str)AS(SELECT str+']'FROM SeparatorsStrSrc WHERE i=(SELECT COUNT(*)FROM Separators WHERE str_src<>0)),ExprElementsSrc(id,i,tmp,ele,pre_ch,input_str)AS(SELECT id,1,CAST(LEFT(str,1)AS varchar(max)),CAST(''AS varchar(max)),CAST(' 'AS char(1)),SUBSTRING(str,2,LEN(str))FROM Input UNION ALL SELECT id,CASE ele WHEN''THEN i ELSE i+1 END,CAST(CASE WHEN LEFT(input_str,1)=' 'THEN''WHEN tmp='-'THEN CASE WHEN pre_ch LIKE(SELECT str FROM SeparatorsStr)THEN tmp+LEFT(input_str,1)ELSE LEFT(input_str,1)END WHEN LEFT(input_str,1)IN(SELECT ch FROM Separators)OR tmp IN(SELECT ch FROM Separators)THEN LEFT(input_str,1)ELSE tmp+LEFT(input_str,1)END AS varchar(max)),CAST(CASE WHEN LEFT(input_str,1)=' 'THEN tmp WHEN LEFT(input_str,1)='-'THEN CASE WHEN tmp IN(SELECT ch FROM Separators)THEN tmp ELSE''END WHEN LEFT(input_str,1)IN(SELECT ch FROM Separators)OR tmp IN(SELECT ch FROM Separators)THEN CASE WHEN tmp='-'AND pre_ch LIKE(SELECT str FROM SeparatorsStr)THEN''ELSE tmp END ELSE''END AS varchar(max)),CAST(LEFT(ele,1)AS char(1)),SUBSTRING(input_str,2,LEN(input_str))FROM ExprElementsSrc WHERE input_str<>''OR tmp<>''),ExprElements(id,i,ele)AS(SELECT id,i,ele FROM ExprElementsSrc WHERE ele<>''),Scanner(id,i,val)AS(SELECT id,i,CAST(ele AS varchar(max))FROM ExprElements WHERE ele<>''UNION ALL SELECT id,MAX(i)+1,NULL FROM ExprElements GROUP BY id),Operator(op,priority)AS(SELECT ch,priority FROM Separators WHERE priority<>0),Calc(id,c,i,pop_count,s0,s1,s2,stack,status)AS(SELECT Scanner.id,1,1,0,CAST(scanner.val AS varchar(max)),CAST(NULL AS varchar(max)),CAST(NULL AS varchar(max)),CAST(''AS varchar(max)),CAST('init'AS varchar(max))FROM Scanner WHERE Scanner.i=1UNION ALL SELECT Calc.id,Calc.c+1,Calc.i,3,NULL,NULL,NULL,CASE Calc.s1 WHEN'+'THEN CAST(CAST(Calc.s2 AS real)+CAST(Calc.s0 AS real)AS varchar(max))WHEN'-'THEN CAST(CAST(Calc.s2 AS real)-CAST(Calc.s0 AS real)AS varchar(max))WHEN'*'THEN CAST(CAST(Calc.s2 AS real)*CAST(Calc.s0 AS real)AS varchar(max))WHEN'/'THEN CAST(CAST(Calc.s2 AS real)/CAST(Calc.s0 AS real)AS varchar(max))ELSE NULL END+' '+stack,CAST('calc '+Calc.s1 AS varchar(max))FROM Calc INNER JOIN Scanner NextVal ON Calc.id=NextVal.id AND Calc.i+1=NextVal.i WHERE Calc.pop_count=0AND ISNUMERIC(Calc.s2)=1AND Calc.s1 IN(SELECT op FROM Operator)AND ISNUMERIC(Calc.s0)=1AND(SELECT priority FROM Operator WHERE op=Calc.s1)>=COALESCE((SELECT priority FROM Operator WHERE op=NextVal.val),0)UNION ALL SELECT Calc.id,Calc.c+1,Calc.i,3,NULL,NULL,NULL,s1+' '+stack,CAST('paren'AS varchar(max))FROM Calc WHERE pop_count=0AND s2='('AND ISNUMERIC(s1)=1AND s0=')'UNION ALL SELECT Calc.id,Calc.c+1,Calc.i,Calc.pop_count-1,s1,s2,CASE WHEN LEN(stack)>0THEN SUBSTRING(stack,1,CHARINDEX(' ',stack)-1)ELSE NULL END,CASE WHEN LEN(stack)>0THEN SUBSTRING(stack,CHARINDEX(' ',stack)+1,LEN(stack))ELSE''END,CAST('pop'AS varchar(max))FROM Calc WHERE Calc.pop_count>0UNION ALL SELECT Calc.id,Calc.c+1,Calc.i+1,Calc.pop_count,CAST(NextVal.val AS varchar(max)),s0,s1,coalesce(s2,'')+' '+stack,cast('read'as varchar(max))FROM Calc INNER JOIN Scanner NextVal ON Calc.id=NextVal.id AND Calc.i+1=NextVal.i WHERE NextVal.val IS NOT NULL AND Calc.pop_count=0AND((Calc.s0 IS NULL OR calc.s1 IS NULL OR calc.s2 IS NULL)OR NOT(ISNUMERIC(Calc.s2)=1AND Calc.s1 IN(SELECT op FROM Operator)AND ISNUMERIC(calc.s0)=1AND (SELECT priority FROM Operator WHERE op=Calc.s1)>=COALESCE((SELECT priority FROM Operator WHERE op=NextVal.val),0))AND NOT(s2='('AND ISNUMERIC(s1)=1AND s0=')')))SELECT Calc.id,Input.str,Calc.s0 AS result FROM Calc INNER JOIN Input ON Calc.id=Input.id WHERE Calc.c=(SELECT MAX(c)FROM Calc calc2 WHERE Calc.id=Calc2.id)ORDER BY id

Clear/semi-obfuscated function:

WITH
  Input(id, str) AS (    
    SELECT 1, '1 + 3 / -8'
    UNION ALL SELECT 2, '2*3*4*5+99'
    UNION ALL SELECT 3, '4 * (9 - 4) / (2 * 6 - 2) + 8'
    UNION ALL SELECT 4, '1 + ((123 * 3 - 69) / 100)'
    UNION ALL SELECT 5, '2.45/8.5*9.27+(5*0.0023)'
  )
, Separators(i, ch, str_src, priority) AS (
    SELECT 1, '-', 1, 1
    UNION ALL SELECT 2, '+', 1, 1
    UNION ALL SELECT 3, '*', 1, 1
    UNION ALL SELECT 4, '/', 1, 1
    UNION ALL SELECT 5, '(', 0, 0
    UNION ALL SELECT 6, ')', 0, 0
  )
, SeparatorsStrSrc(str, i) AS (
    SELECT CAST('[' AS varchar(max)), 0
    UNION ALL
    SELECT
        str + ch
      , SSS.i + 1
    FROM
        SeparatorsStrSrc SSS
          INNER JOIN Separators S ON SSS.i = S.i - 1
    WHERE
        str_src <> 0
  )
, SeparatorsStr(str) AS (
    SELECT str + ']' FROM SeparatorsStrSrc
    WHERE i = (SELECT COUNT(*) FROM Separators WHERE str_src <> 0)
  )
, ExprElementsSrc(id, i, tmp, ele, pre_ch, input_str) AS (
    SELECT
        id
      , 1
      , CAST(LEFT(str, 1) AS varchar(max))
      , CAST('' AS varchar(max))
      , CAST(' ' AS char(1))
      , SUBSTRING(str, 2, LEN(str))
    FROM
        Input
    UNION ALL
    SELECT
        id
      , CASE ele
        WHEN '' THEN i
                ELSE i + 1
        END
      , CAST(
          CASE
          WHEN LEFT(input_str, 1) = ' '
            THEN ''
          WHEN tmp = '-'
            THEN CASE
                 WHEN pre_ch LIKE (SELECT str FROM SeparatorsStr)
                   THEN tmp + LEFT(input_str, 1)
                   ELSE LEFT(input_str, 1)
                 END
          WHEN LEFT(input_str, 1) IN (SELECT ch FROM Separators)
               OR
               tmp IN (SELECT ch FROM Separators)
            THEN LEFT(input_str, 1)
            ELSE tmp + LEFT(input_str, 1)
          END
        AS varchar(max))
      , CAST(
          CASE
          WHEN LEFT(input_str, 1) = ' '
            THEN tmp
          WHEN LEFT(input_str, 1) = '-'
            THEN CASE
                 WHEN tmp IN (SELECT ch FROM Separators)
                   THEN tmp
                   ELSE ''
                 END
          WHEN LEFT(input_str, 1) IN (SELECT ch FROM Separators)
               OR
               tmp IN (SELECT ch FROM Separators)
            THEN CASE
                 WHEN tmp = '-' AND pre_ch LIKE (SELECT str FROM SeparatorsStr)
                   THEN ''
                   ELSE tmp
                 END
            ELSE ''
          END
        AS varchar(max))
      , CAST(LEFT(ele, 1) AS char(1))
      , SUBSTRING(input_str, 2, LEN(input_str))
    FROM
        ExprElementsSrc
    WHERE
        input_str <> ''
        OR
        tmp <> ''
  )
, ExprElements(id, i, ele) AS (
    SELECT
        id
      , i
      , ele
    FROM
        ExprElementsSrc
    WHERE
        ele <> ''
  )
, Scanner(id, i, val) AS (
    SELECT
        id
      , i
      , CAST(ele AS varchar(max))
    FROM
        ExprElements
    WHERE
        ele <> ''
    UNION ALL
    SELECT
        id
      , MAX(i) + 1
      , NULL
    FROM
        ExprElements
    GROUP BY
        id
  )
, Operator(op, priority) AS (
    SELECT
        ch
      , priority 
    FROM
        Separators
    WHERE
        priority <> 0
  )
, Calc(id, c, i, pop_count, s0, s1, s2, stack, status) AS (
    SELECT
        Scanner.id
      , 1
      , 1
      , 0
      , CAST(scanner.val AS varchar(max))
      , CAST(NULL AS varchar(max))
      , CAST(NULL AS varchar(max))
      , CAST('' AS varchar(max))
      , CAST('init' AS varchar(max))
    FROM
        Scanner
    WHERE
        Scanner.i = 1
    UNION ALL
    SELECT
        Calc.id
      , Calc.c + 1
      , Calc.i
      , 3
      , NULL
      , NULL
      , NULL
      , CASE Calc.s1
        WHEN '+' THEN CAST(CAST(Calc.s2 AS real) + CAST(Calc.s0 AS real) AS varchar(max))
        WHEN '-' THEN CAST(CAST(Calc.s2 AS real) - CAST(Calc.s0 AS real) AS varchar(max))
        WHEN '*' THEN CAST(CAST(Calc.s2 AS real) * CAST(Calc.s0 AS real) AS varchar(max))
        WHEN '/' THEN CAST(CAST(Calc.s2 AS real) / CAST(Calc.s0 AS real) AS varchar(max))
                 ELSE NULL
        END
          + ' '
          + stack
      , CAST('calc ' + Calc.s1 AS varchar(max))
    FROM
        Calc
          INNER JOIN Scanner NextVal ON Calc.id = NextVal.id
                                          AND Calc.i + 1 = NextVal.i
    WHERE
        Calc.pop_count = 0
          AND ISNUMERIC(Calc.s2) = 1
          AND Calc.s1 IN (SELECT op FROM Operator)
          AND ISNUMERIC(Calc.s0) = 1
          AND (SELECT priority FROM Operator WHERE op = Calc.s1)
            >= COALESCE((SELECT priority FROM Operator WHERE op = NextVal.val), 0)
    UNION ALL
    SELECT
        Calc.id
      , Calc.c + 1
      , Calc.i
      , 3
      , NULL
      , NULL
      , NULL
      , s1 + ' ' + stack
      , CAST('paren' AS varchar(max))
    FROM
        Calc
    WHERE
        pop_count = 0
          AND s2 = '('
          AND ISNUMERIC(s1) = 1
          AND s0 = ')'
    UNION ALL
    SELECT
        Calc.id
      , Calc.c + 1
      , Calc.i
      , Calc.pop_count - 1
      , s1
      , s2
      , CASE
        WHEN LEN(stack) > 0
          THEN SUBSTRING(stack, 1, CHARINDEX(' ', stack) - 1)
          ELSE NULL
        END
      , CASE
        WHEN LEN(stack) > 0
          THEN SUBSTRING(stack, CHARINDEX(' ', stack) + 1, LEN(stack))
          ELSE ''
        END
      , CAST('pop' AS varchar(max))
    FROM
        Calc
    WHERE
        Calc.pop_count > 0
    UNION ALL
    SELECT
        Calc.id
      , Calc.c + 1
      , Calc.i + 1
      , Calc.pop_count
      , CAST(NextVal.val AS varchar(max))
      , s0
      , s1
      , coalesce(s2, '') + ' ' + stack
      , cast('read' as varchar(max))
    FROM
        Calc
          INNER JOIN Scanner NextVal ON Calc.id = NextVal.id
                                          AND Calc.i + 1 = NextVal.i
    WHERE
        NextVal.val IS NOT NULL
          AND Calc.pop_count = 0
          AND (
            (Calc.s0 IS NULL or calc.s1 is null or calc.s2 is null)
            OR
            NOT(
              ISNUMERIC(Calc.s2) = 1
                AND Calc.s1 IN (SELECT op FROM Operator)
                AND ISNUMERIC(calc.s0) = 1
                AND (SELECT priority FROM Operator WHERE op = Calc.s1)
                  >= COALESCE((SELECT priority FROM Operator WHERE op = NextVal.val), 0)
            )
              AND NOT(s2 = '(' AND ISNUMERIC(s1) = 1 AND s0 = ')')
          )
  )
SELECT
    Calc.id
  , Input.str
  , Calc.s0 AS result
FROM
    Calc
      INNER JOIN Input ON Calc.id = Input.id
WHERE
    Calc.c = (SELECT MAX(c) FROM Calc calc2
              WHERE Calc.id = Calc2.id)
ORDER BY
    id

It is not shortest. But I think that it is very flexible for SQL. It's easy to add new operators. It's easy to change priority of operators.

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南方客

2020-11-28 01:27

MATLAB (v7.8.0)

Number of characters: 239

Obfuscated function:

function [v,s]=m(s),r=1;while s,s=regexp(s,'( ?)(?(1)-?)[\.\d]+|\S','match');c=s{end};s=[s{1:end-1}];if any(c>47),v=str2num(c);elseif c>41,[l,s]=m(s);v=[l/v l*v l+v l-v];v=v(c=='/*+-');if r,break;end;r=1;elseif c<41,break;end;r=r&c~=41;end

Clear(er) function:

function [value,str] = math(str)
  returnNow = 1;
  while str,
    str = regexp(str,'( ?)(?(1)-?)[\.\d]+|\S','match');
    current = str{end};
    str = [str{1:end-1}];
    if any(current > 47),
      value = str2num(current);
    elseif current > 41,
      [leftValue,str] = math(str);
      value = [leftValue/value leftValue*value ...
               leftValue+value leftValue-value];
      value = value(current == '/*+-');
      if returnNow,
        break;
      end;
      returnNow = 1;
    elseif current < 41,
      break;
    end;
    returnNow = returnNow & (c ~= 41);
  end

Test:

>> [math('1 + 3 / -8'); ...
math('2*3*4*5+99'); ...
math('4 * (9 - 4) / (2 * 6 - 2) + 8'); ...
math('1 + ((123 * 3 - 69) / 100)'); ...
math('2.45/8.5*9.27+(5*0.0023)')]

ans =

   -0.5000
  219.0000
   10.0000
    4.0000
    2.6834

Synopsis: A mixture of regular expressions and recursion. Pretty much the best I have been able to do so far, without cheating and using EVAL.

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一整个雨季

2020-11-28 01:29

Perl (no eval)

Number of characters: ~~167~~ 106 (see below for the 106 character version)

Fully obfuscated function: (167 characters if you join these three lines into one)

sub e{my$_="($_[0])";s/\s//g;$n=q"(-?\d++(\.\d+)?+)";
@a=(sub{$1},1,sub{$3*$6},sub{$3+$6},4,sub{$3-$6},6,sub{$3/$6});
while(s:\($n\)|(?<=\()$n(.)$n:$a[7&ord$5]():e){}$_}

Clear/deobfuscated version:

sub e {
  my $_ = "($_[0])";
  s/\s//g;
  $n=q"(-?\d++(\.\d+)?+)"; # a regex for "number", including capturing groups
                           # q"foo" in perl means the same as 'foo'
                           # Note the use of ++ and ?+ to tell perl
                           # "no backtracking"

  @a=(sub{$1},             # 0 - no operator found
      1,                   # placeholder
      sub{$3*$6},          # 2 - ord('*') = 052
      sub{$3+$6},          # 3 - ord('+') = 053
      4,                   # placeholder
      sub{$3-$6},          # 5 - ord('-') = 055
      6,                   # placeholder
      sub{$3/$6});         # 7 - ord('/') = 057

  # The (?<=... bit means "find a NUM WHATEVER NUM sequence that happens
  # immediately after a left paren", without including the left
  # paren.  The while loop repeatedly replaces "(" NUM WHATEVER NUM with
  # "(" RESULT and "(" NUM ")" with NUM.  The while loop keeps going
  # so long as those replacements can be made.

  while(s:\($n\)|(?<=\()$n(.)$n:$a[7&ord$5]():e){}

  # A perl function returns the value of the last statement
  $_
}

I had misread the rules initially, so I'd submitted a version with "eval". Here's a version without it.

The latest bit of insight came when I realized that the last octal digit in the character codes for +, -, /, and * is different, and that ord(undef) is 0. This lets me set up the dispatch table @a as an array, and just invoke the code at the location 7 & ord($3).

There's an obvious spot to shave off one more character - change q"" into '' - but that would make it harder to cut-and-paste into the shell.

Even shorter

Number of characters: ~~124~~ 106

Taking edits by ephemient into account, it's now down to 124 characters: (join the two lines into one)

sub e{$_=$_[0];s/\s//g;$n=q"(-?\d++(\.\d+)?+)";
1while s:\($n\)|$n(.)$n:($1,1,$3*$6,$3+$6,4,$3-$6,6,$6&&$3/$6)[7&ord$5]:e;$_}

Shorter still

Number of characters: ~~110~~ 106

The ruby solution down below is pushing me further, though I can't reach its 104 characters:

sub e{($_)=@_;$n='( *-?[.\d]++ *)';
s:\($n\)|$n(.)$n:(($1,$2-$4,$4&&$2/$4,$2*$4,$2+$4)x9)[.8*ord$3]:e?e($_):$_}

I had to give in and use ''. That ruby send trick is really useful for this problem.

Squeezing water from a stone

Number of characters: 106

A small contortion to avoid the divide-by-zero check.

sub e{($_)=@_;$n='( *-?[.\d]++ *)';
s:\($n\)|$n(.)$n:($1,0,$2*$4,$2+$4,0,$2-$4)[7&ord$3]//$2/$4:e?e($_):$_}

Here's the test harness for this function:

perl -le 'sub e{($_)=@_;$n='\''( *-?[.\d]++ *)'\'';s:\($n\)|$n(.)$n:($1,0,$2*$4,$2+$4,0,$2-$4)[7&ord$3]//$2/$4:e?e($_):$_}' -e 'print e($_) for @ARGV' '1 + 3' '1 + ((123 * 3 - 69) / 100)' '4 * (9 - 4) / (2 * 6 - 2) + 8' '2*3*4*5+99' '2.45/8.5*9.27+(5*0.0023) ' '1 + 3 / -8'

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北恋

2020-11-28 01:30

C99

Number of characters: 239 (But see below for 209)

compressed function:

#define S while(*e==32)++e
#define F float
F strtof();char*e;F v();F g(){S;return*e++-40?strtof(e-1,&e):v();}F v(){F b,a=g();for(;;){S;F o=*e++;if(!o|o==41)return a;b=g();a=o==43?a+b:o==45?a-b:o==42?a*b:a/b;}}F f(char*x){e=x;return v();}

decompressed function:

float strtof();

char* e;
float v();

float g() {
    while (*e == ' ') ++e;
    return *e++ != '(' ? strtof(e-1, &e) : v();
}

float v() {
    float b, a = g();
    for (;;) {
        while (*e == ' ') ++e;
        float op = *e++;
        if (op == 0 || op == ')') return a;
        b = g();
        a = op == '+' ? a + b : op == '-' ? a - b : op == '*' ? a * b : a / b;
    }
}

float eval(char* x) {
    e = x;
    return v();
}

Function is not re-entrant.

EDIT from Chris Lutz: I hate to trample on another man's code, but here is a 209-character version:

#define S for(;*e==32;e++)
#define X (*e++-40?strtof(e-1,&e):v())
float strtof();char*e;float v(){float o,a=X;for(;;){S;o=*e++;if(!o|o==41)return a;S;a=o-43?o-45?o-42?a/X:a*X:a-X:a+X;}}
#define f(x) (e=x,v())

Readable (well, not really very readable, but decompressed):

float strtof();
char *e;
float v() {
    float o, a = *e++ != '(' ? strtof(e - 1, &e) : v();
    for(;;) {
        for(; *e == ' '; e++);
        o = *e++;
        if(o == 0 || o==')') return a;
        for(; *e == ' '; e++);
        // I have no idea how to properly indent nested conditionals
        // and this is far too long to fit on one line.
        a = o != '+' ?
          o != '-' ?
            o != '*' ?
              a / (*e++ != '(' ? strtof(e - 1, &e) : v()) :
              a * (*e++ != '(' ? strtof(e - 1, &e) : v()) :
            a - (*e++ != '(' ? strtof(e - 1, &e) : v()) :
          a + (*e++ != '(' ? strtof(e - 1, &e) : v());
      }
}
#define f(x) (e = x, v())

Yeah, f() is a macro, not a function, but it works. The readable version has some of the logic rewritten but not reordered (like o != '+' instead of o - '+'), but is otherwise just an indented (and preprocessed) version of the other one. I keep trying to simplify the if(!o|o==41)return a; part into the for() loop, but it never makes it shorter. I still believe it can be done, but I'm done golfing. If I work on this question anymore, it will be in the language that must not be named.

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