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I'm trying to calculate the e constant (AKA Euler's Number) by calculating the formula
In order to calculate the factorial and division in one shot, I wrote this:
my #e = 1, { state $a=1; 1 / ($_ * $a++) } ... *;
say reduce * + * , #e[^10];
But it didn't work out. How to do it correctly?
I analyze your code in the section Analyzing your code. Before that I present a couple fun sections of bonus material.
One liner One letter1
say e; # 2.718281828459045
"A treatise on multiple ways"2
Click the above link to see Damian Conway's extraordinary article on computing e in Raku.
The article is a lot of fun (after all, it's Damian). It's a very understandable discussion of computing e. And it's a homage to Raku's bicarbonate reincarnation of the TIMTOWTDI philosophy espoused by Larry Wall.3
As an appetizer, here's a quote from about halfway through the article:
Given that these efficient methods all work the same way—by summing (an initial subset of) an infinite series of terms—maybe it would be better if we had a function to do that for us. And it would certainly be better if the function could work out by itself exactly how much of that initial subset of the series it actually needs to include in order to produce an accurate answer...rather than requiring us to manually comb through the results of multiple trials to discover that.
And, as so often in Raku, it’s surprisingly easy to build just what we need:
sub Σ (Unary $block --> Numeric) {
(0..∞).map($block).produce(&[+]).&converge
}
Analyzing your code
Here's the first line, generating the series:
my #e = 1, { state $a=1; 1 / ($_ * $a++) } ... *;
The closure ({ code goes here }) computes a term. A closure has a signature, either implicit or explicit, that determines how many arguments it will accept. In this case there's no explicit signature. The use of $_ (the "topic" variable) results in an implicit signature that requires one argument that's bound to $_.
The sequence operator (...) repeatedly calls the closure on its left, passing the previous term as the closure's argument, to lazily build a series of terms until the endpoint on its right, which in this case is *, shorthand for Inf aka infinity.
The topic in the first call to the closure is 1. So the closure computes and returns 1 / (1 * 1) yielding the first two terms in the series as 1, 1/1.
The topic in the second call is the value of the previous one, 1/1, i.e. 1 again. So the closure computes and returns 1 / (1 * 2), extending the series to 1, 1/1, 1/2. It all looks good.
The next closure computes 1 / (1/2 * 3) which is 0.666667. That term should be 1 / (1 * 2 * 3). Oops.
Making your code match the formula
Your code is supposed to match the formula:
In this formula, each term is computed based on its position in the series. The kth term in the series (where k=0 for the first 1) is just factorial k's reciprocal.
(So it's got nothing to do with the value of the prior term. Thus $_, which receives the value of the prior term, shouldn't be used in the closure.)
Let's create a factorial postfix operator:
sub postfix:<!> (\k) { [×] 1 .. k }
(× is an infix multiplication operator, a nicer looking Unicode alias of the usual ASCII infix *.)
That's shorthand for:
sub postfix:<!> (\k) { 1 × 2 × 3 × .... × k }
(I've used pseudo metasyntactic notation inside the braces to denote the idea of adding or subtracting as many terms as required.
More generally, putting an infix operator op in square brackets at the start of an expression forms a composite prefix operator that is the equivalent of reduce with => &[op],. See Reduction metaoperator for more info.
Now we can rewrite the closure to use the new factorial postfix operator:
my #e = 1, { state $a=1; 1 / $a++! } ... *;
Bingo. This produces the right series.
... until it doesn't, for a different reason. The next problem is numeric accuracy. But let's deal with that in the next section.
A one liner derived from your code
Maybe compress the three lines down to one:
say [+] .[^10] given 1, { 1 / [×] 1 .. ++$ } ... Inf
.[^10] applies to the topic, which is set by the given. (^10 is shorthand for 0..9, so the above code computes the sum of the first ten terms in the series.)
I've eliminated the $a from the closure computing the next term. A lone $ is the same as (state $), an anonynous state scalar. I made it a pre-increment instead of post-increment to achieve the same effect as you did by initializing $a to 1.
We're now left with the final (big!) problem, pointed out by you in a comment below.
Provided neither of its operands is a Num (a float, and thus approximate), the / operator normally returns a 100% accurate Rat (a limited precision rational). But if the denominator of the result exceeds 64 bits then that result is converted to a Num -- which trades performance for accuracy, a tradeoff we don't want to make. We need to take that into account.
To specify unlimited precision as well as 100% accuracy, simply coerce the operation to use FatRats. To do this correctly, just make (at least) one of the operands be a FatRat (and none others be a Num):
say [+] .[^500] given 1, { 1.FatRat / [×] 1 .. ++$ } ... Inf
I've verified this to 500 decimal digits. I expect it to remain accurate until the program crashes due to exceeding some limit of the Raku language or Rakudo compiler. (See my answer to Cannot unbox 65536 bit wide bigint into native integer for some discussion of that.)
Footnotes
1 Raku has a few important mathematical constants built in, including e, i, and pi (and its alias π). Thus one can write Euler's Identity in Raku somewhat like it looks in math books. With credit to RosettaCode's Raku entry for Euler's Identity:
# There's an invisible character between <> and iπ character pairs!
sub infix:<> (\left, \right) is tighter(&infix:<**>) { left * right };
# Raku doesn't have built in symbolic math so use approximate equal
say e**iπ + 1 ≅ 0; # True
2 Damian's article is a must read. But it's just one of several admirable treatments that are among the 100+ matches for a google for 'raku "euler's number"'.
3 See TIMTOWTDI vs TSBO-APOO-OWTDI for one of the more balanced views of TIMTOWTDI written by a fan of python. But there are downsides to taking TIMTOWTDI too far. To reflect this latter "danger", the Perl community coined the humorously long, unreadable, and understated TIMTOWTDIBSCINABTE -- There Is More Than One Way To Do It But Sometimes Consistency Is Not A Bad Thing Either, pronounced "Tim Toady Bicarbonate". Strangely enough, Larry applied bicarbonate to Raku's design and Damian applies it to computing e in Raku.
There is fractions in $_. Thus you need 1 / (1/$_ * $a++) or rather $_ /$a++.
By Raku you could do this calculation step by step
1.FatRat,1,2,3 ... * #1 1 2 3 4 5 6 7 8 9 ...
andthen .produce: &[*] #1 1 2 6 24 120 720 5040 40320 362880
andthen .map: 1/* #1 1 1/2 1/6 1/24 1/120 1/720 1/5040 1/40320 1/362880 ...
andthen .produce: &[+] #1 2 2.5 2.666667 2.708333 2.716667 2.718056 2.718254 2.718279 2.718282 ...
andthen .[50].say #2.71828182845904523536028747135266249775724709369995957496696762772
In scala, pattern match has guard pattern:
val ch = 23
val sign = ch match {
case _: Int if 10 < ch => 65
case '+' => 1
case '-' => -1
case _ => 0
}
Is the Raku version like this?
my $ch = 23;
given $ch {
when Int and * > 10 { say 65}
when '+' { say 1 }
when '-' { say -1 }
default { say 0 }
}
Is this right?
Update: as jjmerelo suggested, i post my result as follows, the signature version is also interesting.
multi washing_machine(Int \x where * > 10 ) { 65 }
multi washing_machine(Str \x where '+' ) { 1 }
multi washing_machine(Str \x where '-' ) { -1 }
multi washing_machine(\x) { 0 }
say washing_machine(12); # 65
say washing_machine(-12); # 0
say washing_machine('+'); # 1
say washing_machine('-'); # -1
say washing_machine('12'); # 0
say washing_machine('洗衣机'); # 0
TL;DR I've written another answer that focuses on using when. This answer focuses on using an alternative to that which combines Signatures, Raku's powerful pattern matching construct, with a where clause.
"Does pattern match in Raku have guard clause?"
Based on what little I know about Scala, some/most Scala pattern matching actually corresponds to using Raku signatures. (And guard clauses in that context are typically where clauses.)
Quoting Martin Odersky, Scala's creator, from The Point of Pattern Matching in Scala:
instead of just matching numbers, which is what switch statements do, you match what are essentially the creation forms of objects
Raku signatures cover several use cases (yay, puns). These include the Raku equivalent of the functional programming paradigmatic use in which one matches values' or functions' type signatures (cf Haskell) and the object oriented programming paradigmatic use in which one matches against nested data/objects and pulls out desired bits (cf Scala).
Consider this Raku code:
class body { has ( $.head, #.arms, #.legs ) } # Declare a class (object structure).
class person { has ( $.mom, $.body, $.age ) } # And another that includes first.
multi person's-age-and-legs # Declare a function that matches ...
( person # ... a person ...
( :$age where * > 40, # ... whose age is over 40 ...
:$body ( :#legs, *% ), # ... noting their body's legs ...
*% ) ) # ... and ignoring other attributes.
{ say "$age {+#legs}" } # Display age and number of legs.
my $age = 42; # Let's demo handy :$var syntax below.
person's-age-and-legs # Call function declared above ...
person # ... passing a person.
.new: # Explicitly construct ...
:$age, # ... a middle aged ...
body => body.new:
:head,
:2arms,
legs => <left middle right> # ... three legged person.
# Displays "42 3"
Notice where there's a close equivalent to a Scala pattern matching guard clause in the above -- where * > 40. (This can be nicely bundled up into a subset type.)
We could define other multis that correspond to different cases, perhaps pulling out the "names" of the person's legs ('left', 'middle', etc.) if their mom's name matches a particular regex or whatever -- you hopefully get the picture.
A default case (multi) that doesn't bother to deconstruct the person could be:
multi person's-age-and-legs (|otherwise)
{ say "let's not deconstruct this person" }
(In the above we've prefixed a parameter in a signature with | to slurp up all remaining structure/arguments passed to a multi. Given that we do nothing with that slurped structure/data, we could have written just (|).)
Unfortunately, I don't think signature deconstruction is mentioned in the official docs. Someone could write a book about Raku signatures. (Literally. Which of course is a great way -- the only way, even -- to write stuff. My favorite article that unpacks a bit of the power of Raku signatures is Pattern Matching and Unpacking from 2013 by Moritz. Who has authored Raku books. Here's hoping.)
Scala's match/case and Raku's given/when seem simpler
Indeed.
As #jjmerelo points out in the comments, using signatures means there's a multi foo (...) { ...} for each and every case, which is much heavier syntactically than case ... => ....
In mitigation:
Simpler cases can just use given/when, just like you wrote in the body of your question;
Raku will presumably one day get non-experimental macros that can be used to implement a construct that looks much closer to Scala's match/case construct, eliding the repeated multi foo (...)s.
From what I see in this answer, that's not really an implementation of a guard pattern in the same sense Haskell has them. However, Perl 6 does have guards in the same sense Scala has: using default patterns combined with ifs.
The Haskell to Perl 6 guide does have a section on guards. It hints at the use of where as guards; so that might answer your question.
TL;DR You've encountered what I'd call a WTF?!?: when Type and ... fails to check the and clause. This answer talks about what's wrong with the when and how to fix it. I've written another answer that focuses on using where with a signature.
If you want to stick with when, I suggest this:
when (condition when Type) { ... } # General form
when (* > 10 when Int) { ... } # For your specific example
This is (imo) unsatisfactory, but it does first check the Type as a guard, and then the condition if the guard passes, and works as expected.
"Is this right?"
No.
given $ch {
when Int and * > 10 { say 65}
}
This code says 65 for any given integer, not just one over 10!
WTF?!? Imo we should mention this on Raku's trap page.
We should also consider filing an issue to make Rakudo warn or fail to compile if a when construct starts with a compile-time constant value that's a type object, and continues with and (or &&, andthen, etc), which . It could either fail at compile-time or display a warning.
Here's the best option I've been able to come up with:
when (* > 10 when Int) { say 65 }
This takes advantage of the statement modifier (aka postfix) form of when inside the parens. The Int is checked before the * > 10.
This was inspired by Brad++'s new answer which looks nice if you're writing multiple conditions against a single guard clause.
I think my variant is nicer than the other options I've come up with in previous versions of this answer, but still unsatisfactory inasmuch as I don't like the Int coming after the condition.
Ultimately, especially if/when RakuAST lands, I think we will experiment with new pattern matching forms. Hopefully we'll come up with something nice that provides a nice elimination of this wart.
Really? What's going on?
We can begin to see the underlying problem with this code:
.say for ('TrueA' and 'TrueB'),
('TrueB' and 'TrueA'),
(Int and 42),
(42 and Int)
displays:
TrueB
TrueA
(Int)
(Int)
The and construct boolean evaluates its left hand argument. If that evaluates to False, it returns it, otherwise it returns its right hand argument.
In the first line, 'TrueA' boolean evaluates to True so the first line returns the right hand argument 'TrueB'.
In the second line 'TrueB' evaluates to True so the and returns its right hand argument, in this case 'TrueA'.
But what happens in the third line? Well, Int is a type object. Type objects boolean evaluate to False! So the and duly returns its left hand argument which is Int (which the .say then displays as (Int)).
This is the root of the problem.
(To continue to the bitter end, the compiler evaluates the expression Int and * > 10; immediately returns the left hand side argument to and which is Int; then successfully matches that Int against whatever integer is given -- completely ignoring the code that looks like a guard clause (the and ... bit).)
If you were using such an expression as the condition of, say, an if statement, the Int would boolean evaluate to False and you'd get a false negative. Here you're using a when which uses .ACCEPTS which leads to a false positive (it is an integer but it's any integer, disregarding the supposed guard clause). This problem quite plausibly belongs on the traps page.
Years ago I wrote a comment mentioning that you had to be more explicit about matching against $_ like this:
my $ch = 23;
given $ch {
when $_ ~~ Int and $_ > 10 { say 65}
when '+' { say 1 }
when '-' { say -1 }
default { say 0 }
}
After coming back to this question, I realized there was another way.
when can safely be inside of another when construct.
my $ch = 23;
given $ch {
when Int:D {
when $_ > 10 { say 65}
proceed
}
when '+' { say 1 }
when '-' { say -1 }
default { say 0 }
}
Note that the inner when will succeed out of the outer one, which will succeed out of the given block.
If the inner when doesn't match we want to proceed on to the outer when checks and default, so we call proceed.
This means that we can also group multiple when statements inside of the Int case, saving having to do repeated type checks. It also means that those inner when checks don't happen at all if we aren't testing an Int value.
when Int:D {
when $_ < 10 { say 5 }
when 10 { say 10}
when $_ > 10 { say 65}
}
I wrote a code for concatenation as below:
module p2;
int n[1:2][1:3] = {2{{3{1}}}};
initial
begin
$display("val:%d",n[2][1]);
end
endmodule
It is showing errors.
Please explain?
Unpacked arrays require a '{} format. See IEEE Std 1800-2012 § 5.11 (or search for '{ in the LRM for many examples).
Therefore update your assignment to:
int n[1:2][1:3] = '{2{'{3{1}}}};
int n[1:2][1:3] = {2{{3{1}}}};
Just looking at {3{1}} this is a 96 bit number 3 integers concatenated together.
It is likely that {3{1'b1}} was intended.
The main issue looks to be the the left hand side is an unpacked array, and the left hand side is a packed array.
{ 2 { {3{1'b1}} } } => 6'b111_111
What is required is [[3'b111],[3'b111]],
From IEEE std 1800-2009 the array assignments section will be of interest here
10.9.1 Array assignment patterns
Concatenation braces are used to construct and deconstruct simple bit vectors.
A similar syntax is used to support the construction and deconstruction of arrays. The expressions shall match element for element, and the braces shall match the array dimensions. Each expression item shall be evaluated in the context of an
assignment to the type of the corresponding element in the array. In other words, the following examples are not required to cause size warnings:
bit unpackedbits [1:0] = '{1,1}; // no size warning required as
// bit can be set to 1
int unpackedints [1:0] = '{1'b1, 1'b1}; // no size warning required as
// int can be set to 1’b1
A syntax resembling replications (see 11.4.12.1) can be used in array assignment patterns as well. Each replication shall represent an entire single dimension.
unpackedbits = '{2 {y}} ; // same as '{y, y}
int n[1:2][1:3] = '{2{'{3{y}}}}; // same as '{'{y,y,y},'{y,y,y}}
I'm new here. After reading through how to ask and format, I hope this will be an OK question. I'm not very skilled in perl, but it is the programming language what I known most.
I trying apply Perl to real life but I didn't get an great understanding - especially not from my wife. I tell her that:
if she didn't bring to me 3 beers in the evening, that means I got zero (or nothing) beers.
As you probably guessed, without much success. :(
Now factually. From perlop:
Unary "!" performs logical negation, that is, "not".
Languages, what have boolean types (what can have only two "values") is OK:
if it is not the one value -> must be the another one.
so naturally:
!true -> false
!false -> true
But perl doesn't have boolean variables - have only a truth system, whrere everything is not 0, '0' undef, '' is TRUE. Problem comes, when applying logical negation to an not logical value e.g. numbers.
E.g. If some number IS NOT 3, thats mean it IS ZERO or empty, instead of the real life meaning, where if something is NOT 3, mean it can be anything but 3 (e.g. zero too).
So the next code:
use 5.014;
use Strictures;
my $not_3beers = !3;
say defined($not_3beers) ? "defined, value>$not_3beers<" : "undefined";
say $not_3beers ? "TRUE" : "FALSE";
my $not_4beers = !4;
printf qq{What is not 3 nor 4 mean: They're same value: %d!\n}, $not_3beers if( $not_3beers == $not_4beers );
say qq(What is not 3 nor 4 mean: #{[ $not_3beers ? "some bears" : "no bears" ]}!) if( $not_3beers eq $not_4beers );
say ' $not_3beers>', $not_3beers, "<";
say '-$not_3beers>', -$not_3beers, "<";
say '+$not_3beers>', -$not_3beers, "<";
prints:
defined, value><
FALSE
What is not 3 nor 4 mean: They're same value: 0!
What is not 3 nor 4 mean: no bears!
$not_3beers><
-$not_3beers>0<
+$not_3beers>0<
Moreover:
perl -E 'say !!4'
what is not not 4 IS 1, instead of 4!
The above statements with wife are "false" (mean 0) :), but really trying teach my son Perl and he, after a while, asked my wife: why, if something is not 3 mean it is 0 ? .
So the questions are:
how to explain this to my son
why perl has this design, so why !0 is everytime 1
Is here something "behind" what requires than !0 is not any random number, but 0.
as I already said, I don't know well other languages - in every language is !3 == 0?
I think you are focussing to much on negation and too little on what Perl booleans mean.
Historical/Implementation Perspective
What is truth? The detection of a higher voltage that x Volts.
On a higher abstraction level: If this bit here is set.
The abstraction of a sequence of bits can be considered an integer. Is this integer false? Yes, if no bit is set, i.e. the integer is zero.
A hardware-oriented language will likely use this definition of truth, e.g. C, and all C descendants incl Perl.
The negation of 0 could be bitwise negation—all bits are flipped to 1—, or we just set the last bit to 1. The results would usually be decoded as integers -1 and 1 respectively, but the latter is more energy efficient.
Pragmatic Perspective
It is convenient to think of all numbers but zero as true when we deal with counts:
my $wordcount = ...;
if ($wordcount) {
say "We found $wordcount words";
} else {
say "There were no words";
}
or
say "The array is empty" unless #array; # notice scalar context
A pragmatic language like Perl will likely consider zero to be false.
Mathematical Perspective
There is no reason for any number to be false, every number is a well-defined entity. Truth or falseness emerges solely through predicates, expressions which can be true or false. Only this truth value can be negated. E.g.
¬(x ≤ y) where x = 2, y = 3
is false. Many languages which have a strong foundation in maths won't consider anything false but a special false value. In Lisps, '() or nil is usually false, but 0 will usually be true. That is, a value is only true if it is not nil!
In such mathematical languages, !3 == 0 is likely a type error.
Re: Beers
Beers are good. Any number of beers are good, as long as you have one:
my $beers = ...;
if (not $beers) {
say "Another one!";
} else {
say "Aaah, this is good.";
}
Boolification of a beer-counting variable just tells us if you have any beers. Consider !! to be a boolification operator:
my $enough_beer = !! $beers;
The boolification doesn't concern itself with the exact amount. But maybe any number ≥ 3 is good. Then:
my $enough_beer = ($beers >= 3);
The negation is not enough beer:
my $not_enough_beer = not($beers >= 3);
or
my $not_enough_beer = not $beers;
fetch_beer() if $not_enough_beer;
Sets
A Perl scalar does not symbolize a whole universe of things. Especially, not 3 is not the set of all entities that are not three. Is the expression 3 a truthy value? Yes. Therefore, not 3 is a falsey value.
The suggested behaviour of 4 == not 3 to be true is likely undesirable: 4 and “all things that are not three” are not equal, the four is just one of many things that are not three. We should write it correctly:
4 != 3 # four is not equal to three
or
not( 4 == 3 ) # the same
It might help to think of ! and not as logical-negation-of, but not as except.
How to teach
It might be worth introducing mathematical predicates: expressions which can be true or false. If we only ever “create” truthness by explicit tests, e.g. length($str) > 0, then your issues don't arise. We can name the results: my $predicate = (1 < 2), but we can decide to never print them out, instead: print $predicate ? "True" : "False". This sidesteps the problem of considering special representations of true or false.
Considering values to be true/false directly would then only be a shortcut, e.g. foo if $x can considered to be a shortcut for
foo if defined $x and length($x) > 0 and $x != 0;
Perl is all about shortcuts.
Teaching these shortcuts, and the various contexts of perl and where they turn up (numeric/string/boolean operators) could be helpful.
List Context
Even-sized List Context
Scalar Context
Numeric Context
String Context
Boolean Context
Void Context
as I already said, I don't know well other languages - in every language is !3 == 0?
Yes. In C (and thus C++), it's the same.
void main() {
int i = 3;
int n = !i;
int nn = !n;
printf("!3=%i ; !!3=%i\n", n, nn);
}
Prints (see http://codepad.org/vOkOWcbU )
!3=0 ; !!3=1
how to explain this to my son
Very simple. !3 means "opposite of some non-false value, which is of course false". This is called "context" - in a Boolean context imposed by negation operator, "3" is NOT a number, it's a statement of true/false.
The result is also not a "zero" but merely something that's convenient Perl representation of false - which turns into a zero if used in a numeric context (but an empty string if used in a string context - see the difference between 0 + !3 and !3 . "a")
The Boolean context is just a special kind of scalar context where no conversion to a string or a number is ever performed. (perldoc perldata)
why perl has this design, so why !0 is everytime 1
See above. Among other likely reasons (though I don't know if that was Larry's main reason), C has the same logic and Perl took a lot of its syntax and ideas from C.
For a VERY good underlying technical detail, see the answers here: " What do Perl functions that return Boolean actually return " and here: " Why does Perl use the empty string to represent the boolean false value? "
Is here something "behind" what requires than !0 is not any random number, but 0.
Nothing aside from simplicity of implementation. It's easier to produce a "1" than a random number.
if you're asking a different question of "why is it 1 instead of the original # that was negated to get 0", the answer to that is simple - by the time Perl interpreter gets to negate that zero, it no longer knows/remembers that zero was a result of "!3" as opposed to some other expression that resulted in a value of zero/false.
If you want to test that a number is not 3, then use this:
my_variable != 3;
Using the syntax !3, since ! is a boolean operator, first converts 3 into a boolean (even though perl may not have an official boolean type, it still works this way), which, since it is non-zero, means it gets converted to the equivalent of true. Then, !true yields false, which, when converted back to an integer context, gives 0. Continuing with that logic shows how !!3 converts 3 to true, which then is inverted to false, inverted again back to true, and if this value is used in an integer context, gets converted to 1. This is true of most modern programming languages (although maybe not some of the more logic-centered ones), although the exact syntax may vary some depending on the language...
Logically negating a false value requires some value be chosen to represent the resulting true value. "1" is as good a choice as any. I would say it is not important which value is returned (or conversely, it is important that you not rely on any particular true value being returned).
I had programming interview which consisted of 3 interviewers, 45 min each.
While first two interviewers gave me 2-3 short coding questions (i.e reverse linked list, implement rand(7) using rand(5) etc ) third interviewer used whole timeslot for single question:
You are given string representing correctly formed and parenthesized
boolean expression consisting of characters T, F, &, |, !, (, ) an
spaces. T stands for True, F for False, & for logical AND, | for
logical OR, ! for negate. & has greater priority than |. Any of these
chars is followed by a space in input string. I was to evaluate value
of expression and print it (output should be T or F). Example: Input:
! ( T | F & F ) Output: F
I tried to implement variation of Shunting Yard algorithm to solve the problem (to turn input in postfix form, and then to evaluate postfix expression), but failed to code it properly in given timeframe, so I ended up explaining in pseudocode and words what I wanted.
My recruiter said that first two interviewers gave me "HIRE", while third interviewer gave me "NO HIRE", and since the final decision is "logical AND", he thanked me for my time.
My questions:
Do you think that this question is appropriate to code on whiteboard in approx. 40 mins? To me it seems to much code for such a short timeslot and dimensions of whiteboard.
Is there shorter approach than to use Shunting yard algorithm for this problem?
Well, once you have some experience with parsers postfix algorithm is quite simple.
1. From left to right evaluate for each char:
if its operand, push on the stack.
if its operator, pop A, then pop B then push B operand A onto the stack. Last item on the stack will be the result. If there's none or more than one means you're doing it wrong (assuming the postfix notation is valid).
Infix to postfix is quite simple as well. That being said I don't think it's an appropriate task for 40 minutes if You don't know the algorithms. Here is a boolean postfix evaluation method I wrote at some stage (uses Lambda as well):
public static boolean evaluateBool(String s)
{
Stack<Object> stack = new Stack<>();
StringBuilder expression =new StringBuilder(s);
expression.chars().forEach(ch->
{
if(ch=='0') stack.push(false);
else if(ch=='1') stack.push(true);
else if(ch=='A'||ch=='R'||ch=='X')
{
boolean op1 = (boolean) stack.pop();
boolean op2 = (boolean) stack.pop();
switch(ch)
{
case 'A' : stack.push(op2&&op1); break;
case 'R' : stack.push(op2||op1); break;
case 'X' : stack.push(op2^op1); break;
}//endSwitch
}else
if(ch=='N')
{
boolean op1 = (boolean) stack.pop();
stack.push(!op1);
}//endIF
});
return (boolean) stack.pop();
}
In your case to make it working (with that snippet) you would first have to parse the expression and replace special characters like "!","|","^" etc with something plain like letters or just use integer char value in your if cases.