使用正则表达式计算数学表达式

Question

I need to create a method that will receive a string containing a mathematical expression and has to:

• Validate it first.
• Return the problem/problems, if they exist (for example, something like this: 4+3+4/0 or 4+4+(((2-2*4)- ).
• If everything is ok, solve it and return the final value.

What I've done so far was:

• I know that eval does exactly what I need, however it has the problem of SQL injection and so on.
• I discovered Regex.

I really don't know the best way to design this method for it to be safe and work with parenthesis, operators and numbers. What I'm thinking is to use regex to check if the initial string is equal to the matched string. If it is, I was thinking on using eval to calculate the final value. In your opinion is this the correct way to do it?

Not being sure what I should do, I wrote:

def math_eval(expression)
   a = /\(* \s* \d+ \s* (( [-\+\*\/] \s* \d+ \)* \s* ) | ( [-\+\*\/] \s* \(* \s* \d+ \s* ))+/
   puts "Let's Go"
   puts a.match(expression)
end

math_eval("lets see if this works 1/ 2 * 3 hello world")

This is returning:

Let's Go
Empty string

I've seen Stack Overflow posts that this

/\(* \s* \d+ \s* (( [-\+\*\/] \s* \d+ \)* \s* ) | ( [-\+\*\/] \s* \(* \s* \d+ \s* ))+/

would be the correct regex filter to use.

What am I doing wrong? Should I change my approach?

Edit: I followed a different approach. Do you think the following approach is safe?

class FormulaCalculator

    def formula_validator(string_formula)
        extracted_formula = string_formula.tr('Ⓐⓐ⒜AaẠạÅåÄäẢảḀḁẤấẦầẨẩȂȃẪẫẬậẮắẰằẲẳẴẵẶặĀāĄąȀȁǺǻȦȧÁáǞǟǍǎÀàÃãǠǡÂâȺⱥÆæǢǣǼǽⱯꜲꜳꜸꜹꜺꜻⱭ℀⅍℁ªⒷⓑ⒝BbḂḃḄḅḆḇƁɃƀƂƃƄƅℬⒸⓒ⒞CcḈḉĆćĈĉĊċČčÇçƇƈȻȼℂ℃ƆꜾꜿℭ℅℆℄Ⓓⓓ⒟DdḊḋḌḍḎḏḐḑḒḓĎďƊƋƌƉĐđȡDZDzdzDŽDždžȸⅅⅆⒺⓔ⒠EeḔḕḖḗḘḙḚḛḜḝẸẹẺẻẾếẼẽỀềỂểỄễỆệĒēĔĕĖėĘęĚěÈèÉéÊêËëȄȅȨȩȆȇƎⱻɆɇƏǝℰⱸℯ℮ℇƐⒻⓕ⒡FfḞḟƑƒꜰℲⅎꟻℱ℻Ⓖⓖ⒢GgƓḠḡĜĝĞğĠġǤǥǦǧǴℊ⅁ǵĢģⒽⓗ⒣HhḢḣḤḥḦḧḨḩḪḫĤĥȞȟĦħⱧⱨꜦℍǶẖℏℎℋℌꜧⒾⓘ⒤IiḬḭḮḯIJijÍíÌìÎîÏïĨĩĪīĬĭĮįǏǐıƚỺⅈⅉℹℑℐⒿⓙ⒥JjĴĵɈɉȷⱼǰⓀⓚ⒦KkḰḱḲḳḴḵĶķƘƙꝀꝁꝂꝃꝄꝅǨǩⱩⱪĸⓁⓛ⒧LlḶḷḸḹḺḻḼḽĹĺĻļĽľĿŀŁłỈỉⱠⱡȽꝉꝈⱢLJLjljỊİịꞁ⅃⅂ȈȉȊȋℓℒⓂⓜ⒨MmḾḿṀṁṂṃꟿꟽⱮƜℳⓃⓝ⒩NnṄṅṆṇṈṉṊṋŃńŅņŇňǸǹÑñȠƞŊŋƝʼnNJNjnjȵℕ№Ⓞⓞ⒪OoÖöṎṏṌṍṐṑṒṓȪȫȬȭȮȯȰȱǪǫǬǭỌọỎỏỐốỒồỔổỖỗỘộỚớỜờỞởỠỡỢợƠơŌōŎŏŐőÒòÓóÔôÕõǑǒȌȍȎȏŒœØøǾǿꝊꝎꝏ⍥⍤ℴⓅⓟ⒫℗PpṔṕṖṗƤƥⱣℙǷꟼ℘Ⓠⓠ⒬QqɊɋℚ℺ȹⓇⓡ⒭RrŔŕŖŗŘřṘṙṚṛṜṝṞṟȐȑȒȓɌɍƦꝚꝛⱤ℞ℜℛ℟ℝⓈⓢ⒮SsṠṡṢṣṤṥṦṧṨṩŚśŜŝŞşŠšȘșȿꜱƧƨϨϩẞßẛẜẝ℠Ⓣⓣ⒯TtṪṫṬṭṮṯṰṱŢţŤťŦŧȚțȾⱦƬƮƫƭẗȶ℡™Ⓤⓤ⒰UuṲṳṴṵṶṷṸṹṺṻỦủỤụỨứỪừỬửỮữỰựŨũŪūŬŭŮůŰűǙǚǗǘǛǜŲųǓǔȔȕÛûȖȗÙùÚúÜüƯưɄƲƱⓋⓥ⒱VvṼṽṾṿɅ℣ỼⱱⱴⱽⓌⓦ⒲WwẀẁẂẃẄẅẆẇẈẉŴŵⱲⱳϢϣẘⓍⓧ⒳XxẊẋẌẍℵ×Ⓨⓨ⒴yYẎẏỾỿỲỳỴỵỶỷỸỹŶŷƳƴŸÿÝýɎɏȲȳƔẙ⅄ℽⓏⓩ⒵ZzẐẑẒẓẔẕŹźŻżŽžȤȥⱫⱬƵƶɀℨℤ', '')
     if string_formula = extracted_formula
            return true
        else
            return false
        end
     end

     def formula_evaluation(string_formula)
        if formula_validator(string_formula) == true
            return eval(string_formula)
        end
     rescue Exception => e
        puts e
     end
 end

Answer 1

You can't use a regular expression to identify correctly formed mathematical expressions.

A regular expression can in theory be matched with a finite state automaton, and the finite number of states of such an automaton can't keep track of the unbounded number of opening parentheses it might encounter. The language of correctly matched parentheses is not a regular language .

What you can do is tokenize the string using regular expressions and then parse the token stream.

See also Regular expression for math operations with parentheses .