I have seen that there are two similar functions to create lists in maxima: create_list() and makelist(). In both cases, the arguments can be
(<an expression>, <a variable>, <the initial value>, <the final value>, < the step>) or
(<an expression>, <a variable>, <a list of values for the variable>).
What is the difference between these two functions? I have tried a couple of examples and they seem to work in the same way:
makelist(i^i,i,1,3); -> [1,4,27]
create_list(i^i,i,1,3); -> [1,4,27]
makelist(i^i,i,[1,2,3]); -> [1,4,27]
create_list(i^i,i,[1,2,3]); -> [1,4,27]
If you wish, you can create your own function, with its own syntax, in maxima.
For example, there is no operator ".." but this makes it happen.
infix("..",80,80,expr,expr,expr);
You can then define the semantics ...
here I just call a function named range.
(a..b):= range(a,b)
This doesn't provide for all the embroidery that you might like.
I think a superior technique for syntax and semantics is to enhance the "for" loop as in this example:
for i:1 thru 5 do collect i;
which returns [1,2,3,4,5]
All the varied mechanisms for "for", including step size, limit, iterating through sets, etc. can then be included in computing a list explicitly comprising a range. The code for this is about 7 lines of lisp, inserted into the source code for "parse-$do".
I also allow
for i in [a,b] summing f(i) ; which returns f(b)+f(a).
This enhancement is redundant for the (few) people who are comfortable with map, cons, lambda, apply, append ... in Maxima.
The code, which can be read in to any maxima, is here.
https://people.eecs.berkeley.edu/~fateman/lisp/doparsesum.lisp
I need a help with following:
flatten ([]) -> [];
flatten([H|T]) -> H ++ flatten(T).
Input List contain other lists with a different length
For example:
flatten([[1,2,3],[4,7],[9,9,9,9,9,9]]).
What is the time complexity of this function?
And why?
I got it to O(n) where n is a number of elements in the Input list.
For example:
flatten([[1,2,3],[4,7],[9,9,9,9,9,9]]) n=3
flatten([[1,2,3],[4,7],[9,9,9,9,9,9],[3,2,4],[1,4,6]]) n=5
Thanks for help.
First of all I'm not sure your code will work, at least not in the way standard library works. You could compare your function with lists:flatten/1 and maybe improve on your implementation. Try lists such as [a, [b, c]] and [[a], [b, [c]], [d]] as input and verify if you return what you expected.
Regarding complexity it is little tricky due to ++ operator and functional (immutable) nature of the language. All lists in Erlang are linked lists (not arrays like in C++), and you can not just add something to end of one without modifying it; before it was pointing to end of list, now you would like it to link to something else. And again, since it is not mutable language you have to make copy of whole list left of ++ operator, which increases complexity of this operator.
You could say that complexity of A ++ B is length(A), and it makes complexity of your function little bit greater. It would go something like length(FirstElement) + (lenght(FirstElement) + length(SecondElement)) + .... up to (without) last, which after some math magic could be simplified to (n -1) * 1/2 * k * k where n is number of elements, and k is average length of element. Or O(n^3).
If you are new to this it might seem little bit odd, but with some practice you can get hang of it. I would recommend going through few resources:
Good explanation of lists and how they are created
Documentation on list handling with DO and DO NOT parts
Short description of ++ operator myths and best practices
Chapter about recursion and tail-recursion with examples using ++ operator
How may I use tail recursion in Erlang to say I have lists [[1], [2], [3], [3,2]] and I'd like to output the list [[1], [1], [1], [2]] where each list in the output list represents the number of element(s) for each list in the input list?
I am a beginner in functional programming.
Thanks
I guess this is some homework or self learning exercise, usually it is a good idea to use the library functions or the native erlang constructions such as list comprehension:
List = [[1], [2], [3], [3,2]],
Result = lists:map(fun(X) -> [length(X)] end, List),
Result = [[length(X)] || X <- List],
The usual and straight recursive solution of this problem is
lengths_not_tail_recursive([]) -> []; % stop condition
lengths_not_tail_recursive([H|T]) -> [[length(H)]|lengths_not_tail_recursive(T)].
This solution is not so bad as long as List is not too big. It is not tail recursive because at each step of the recursion, except the last one, the result of the "local" work need to be combined with the result of the further steps.
To solve this issue, the general solution is to add a new parameter, called accumulator, it will record at each step what was evaluated so far, and the last step will return the final and complete result.
lengths_tail_recursive([],Acc) -> lists:reverse(Acc); % stop condition
% the result needs to be reverse due to the way the accumulator is built at each step
lengths_tail_recursive([H|T],Acc) -> lengths_tail_recursive(T,[[length(H)]|Acc]).
The difference is that at each recursion step you simply return, without modification, the result of the next step. Generally, this solution uses a second function which role is to hide the need of a second parameter, and initialize this one correctly for the first call
lengths(L) -> lengths_tail_recursive(L,[]).
Note: the tail recursive solution uses 2 library functions: length/1 and lists:reverse/1. I invite you to write them in a tail recursive manner
I have an algorithm which uses a bunch of different functions or steps during it's work. I would like to run the algorithm with different possible functions bound to those steps. In essence I want to prepare some sets of values (which specific function should be bound to this specific step) and run my algorithm with every one of those sets. And to capture results of every run alongside with input set.
Something like that:
(binding [step1 f1
step2 f2]
(do-my-job))
(binding [step1 f11
step2 f22]
(do-my-job))
but with dynamic binding expressions.
What are my options?
So you are trying to do something like a parameter sweep?
I can't see why you need to do a dynamic binding. Your algorithm is defined in terms of first class function calls. Just pass the functions in as parameters to your algorithms.
To try all the values, just generate a permutation of the values, and run map over this list. You will get all the results from this.
because binding is a macro you will need to write a macro that generates the dynamic binding forms.
Well, it seems I have it working the following way:
(def conditions [[`step1 f1 `step2 f2] [`step1 f11 `step2 f22]])
(map #(eval `(binding ~% body)) conditions)
So, I have tested this and as far as I can see, it all just works.
In the example below, I create a var, then rebind this var to a function.
As you can see the call to the function happens outside of the lexical scope of
binding form, so we have dynamic binding here.
(def
^{:dynamic true}
*bnd-fn*
nil
)
(defn fn1 []
(println "fn1"))
(defn fn2 []
(println "fn2"))
(defn callfn []
(*bnd-fn*))
;; crash with NPE
(callfn)
;; prints fn1
(binding [*bnd-fn* fn1]
(callfn))
;; prints fn2
(binding [*bnd-fn* fn2]
(callfn))
I've been using a similar approach for a library of my own (Clojure-owl if you are interested!), although in my case the thing I with to dynamically rebind is a Java object.
In that case, while I have allowed dynamic rebinding, in most cases I don't; I just use a different java object for different name spaces. This works nicely for me.
In reply to your comment, if you want to have a single binding form, then, this is easy to achieve. Add the following code.
(defn dobinding [fn]
(binding [*bnd-fn* fn]
(callfn)))
(dorun
(map dobinding
[fn1 fn2]))
The function dobinding runs all of the others. Then I eval this with a single map (and dorun or you get a lazy sequence). This runs two functions for each step. Obviously, you will need to pass a list of lists in. You should be able to parallelize the whole lot if you choose.
This is a lot easier than trying to splice in the whole vector. The value in a binding form is evaluated so it can be anything you like.
Is there a generic way, given a complex object in Erlang, to come up with a valid function declaration for it besides eyeballing it? I'm maintaining some code previously written by someone who was a big fan of giant structures, and it's proving to be error prone doing it manually.
I don't need to iterate the whole thing, just grab the top level, per se.
For example, I'm working on this right now -
[[["SIP",47,"2",46,"0"],32,"407",32,"Proxy Authentication Required","\r\n"],
[{'Via',
[{'via-parm',
{'sent-protocol',"SIP","2.0","UDP"},
{'sent-by',"172.20.10.5","5060"},
[{'via-branch',"z9hG4bKb561e4f03a40c4439ba375b2ac3c9f91.0"}]}]},
{'Via',
[{'via-parm',
{'sent-protocol',"SIP","2.0","UDP"},
{'sent-by',"172.20.10.15","5060"},
[{'via-branch',"12dee0b2f48309f40b7857b9c73be9ac"}]}]},
{'From',
{'from-spec',
{'name-addr',
[[]],
{'SIP-URI',
[{userinfo,{user,"003018CFE4EF"},[]}],
{hostport,"172.20.10.11",[]},
{'uri-parameters',[]},
[]}},
[{tag,"b7226ffa86c46af7bf6e32969ad16940"}]}},
{'To',
{'name-addr',
[[]],
{'SIP-URI',
[{userinfo,{user,"3966"},[]}],
{hostport,"172.20.10.11",[]},
{'uri-parameters',[]},
[]}},
[{tag,"a830c764"}]},
{'Call-ID',"90df0e4968c9a4545a009b1adf268605#172.20.10.15"},
{'CSeq',1358286,"SUBSCRIBE"},
["date",'HCOLON',
["Mon",44,32,["13",32,"Jun",32,"2011"],32,["17",58,"03",58,"55"],32,"GMT"]],
{'Contact',
[[{'name-addr',
[[]],
{'SIP-URI',
[{userinfo,{user,"3ComCallProcessor"},[]}],
{hostport,"172.20.10.11",[]},
{'uri-parameters',[]},
[]}},
[]],
[]]},
["expires",'HCOLON',3600],
["user-agent",'HCOLON',
["3Com",[]],
[['LWS',["VCX",[]]],
['LWS',["7210",[]]],
['LWS',["IP",[]]],
['LWS',["CallProcessor",[['SLASH',"v10.0.8"]]]]]],
["proxy-authenticate",'HCOLON',
["Digest",'LWS',
["realm",'EQUAL',['SWS',34,"3Com",34]],
[['COMMA',["domain",'EQUAL',['SWS',34,"3Com",34]]],
['COMMA',
["nonce",'EQUAL',
['SWS',34,"btbvbsbzbBbAbwbybvbxbCbtbzbubqbubsbqbtbsbqbtbxbCbxbsbybs",
34]]],
['COMMA',["stale",'EQUAL',"FALSE"]],
['COMMA',["algorithm",'EQUAL',"MD5"]]]]],
{'Content-Length',0}],
"\r\n",
["\n"]]
Maybe https://github.com/etrepum/kvc
I noticed your clarifying comment. I'd prefer to add a comment myself, but don't have enough karma. Anyway, the trick I use for that is to experiment in the shell. I'll iterate a pattern against a sample data structure until I've found the simplest form. You can use the _ match-all variable. I use an erlang shell inside an emacs shell window.
First, bind a sample to a variable:
A = [{a,b},[{c,d}, {e,f}]].
Now set the original structure against the variable:
[{a,b},[{c,d},{e,f}]] = A.
If you hit enter, you'll see they match. Hit alt-p (forget what emacs calls alt, but it's alt on my keyboard) to bring back the previous line. Replace some tuple or list item with an underscore:
[_,[{c,d},{e,f}]].
Hit enter to make sure you did it right and they still match. This example is trivial, but for deeply nested, multiline structures it's trickier, so it's handy to be able to just quickly match to test. Sometimes you'll want to try to guess at whole huge swaths, like using an underscore to match a tuple list inside a tuple that's the third element of a list. If you place it right, you can match the whole thing at once, but it's easy to misread it.
Anyway, repeat to explore the essential shape of the structure and place real variables where you want to pull out values:
[_, [_, _]] = A.
[_, _] = A.
[_, MyTupleList] = A. %% let's grab this tuple list
[{MyAtom,b}, [{c,d}, MyTuple]] = A. %% or maybe we want this atom and tuple
That's how I efficiently dissect and pattern match complex data structures.
However, I don't know what you're doing. I'd be inclined to have a wrapper function that uses KVC to pull out exactly what you need and then distributes to helper functions from there for each type of structure.
If I understand you correctly you want to pattern match some large datastructures of unknown formatting.
Example:
Input: {a, b} {a,b,c,d} {a,[],{},{b,c}}
function({A, B}) -> do_something;
function({A, B, C, D}) when is_atom(B) -> do_something_else;
function({A, B, C, D}) when is_list(B) -> more_doing.
The generic answer is of course that it is undecidable from just data to know how to categorize that data.
First you should probably be aware of iolists. They are created by functions such as io_lib:format/2 and in many other places in the code.
One example is that
[["SIP",47,"2",46,"0"],32,"407",32,"Proxy Authentication Required","\r\n"]
will print as
SIP/2.0 407 Proxy Authentication Required
So, I'd start with flattening all those lists, using a function such as
flatten_io(List) when is_list(List) ->
Flat = lists:map(fun flatten_io/1, List),
maybe_flatten(Flat);
flatten_io(Tuple) when is_tuple(Tuple) ->
list_to_tuple([flatten_io(Element) || Element <- tuple_to_list(Tuple)];
flatten_io(Other) -> Other.
maybe_flatten(L) when is_list(L) ->
case lists:all(fun(Ch) when Ch > 0 andalso Ch < 256 -> true;
(List) when is_list(List) ->
lists:all(fun(X) -> X > 0 andalso X < 256 end, List);
(_) -> false
end, L) of
true -> lists:flatten(L);
false -> L
end.
(Caveat: completely untested and quite inefficient. Will also crash for inproper lists, but you shouldn't have those in your data structures anyway.)
On second thought, I can't help you. Any data structure that uses the atom 'COMMA' for a comma in a string should be taken out and shot.
You should be able to flatten those things as well and start to get a view of what you are looking at.
I know that this is not a complete answer. Hope it helps.
Its hard to recommend something for handling this.
Transforming all the structures in a more sane and also more minimal format looks like its worth it. This depends mainly on the similarities in these structures.
Rather than having a special function for each of the 100 there must be some automatic reformatting that can be done, maybe even put the parts in records.
Once you have records its much easier to write functions for it since you don't need to know the actual number of elements in the record. More important: your code won't break when the number of elements changes.
To summarize: make a barrier between your code and the insanity of these structures by somehow sanitizing them by the most generic code possible. It will be probably a mix of generic reformatting with structure speicific stuff.
As an example already visible in this struct: the 'name-addr' tuples look like they have a uniform structure. So you can recurse over your structures (over all elements of tuples and lists) and match for "things" that have a common structure like 'name-addr' and replace these with nice records.
In order to help you eyeballing you can write yourself helper functions along this example:
eyeball(List) when is_list(List) ->
io:format("List with length ~b\n", [length(List)]);
eyeball(Tuple) when is_tuple(Tuple) ->
io:format("Tuple with ~b elements\n", [tuple_size(Tuple)]).
So you would get output like this:
2> eyeball({a,b,c}).
Tuple with 3 elements
ok
3> eyeball([a,b,c]).
List with length 3
ok
expansion of this in a useful tool for your use is left as an exercise. You could handle multiple levels by recursing over the elements and indenting the output.
Use pattern matching and functions that work on lists to extract only what you need.
Look at http://www.erlang.org/doc/man/lists.html:
keyfind, keyreplace, L = [H|T], ...