I am very new to SML and functional programming.
I have searched the site but was unable to find an answer to my question.
I am trying to write a basic range function with a start, stop, and step parameter.
For example, range(2, 12, 3) should return the list [2,5,8,11].
I don't get any errors, but when I try running range(2,12,3); the cursor advances to the next line and nothing happens, I can't even type anything into the smlnj app.
Here is my code:
fun range(start, stop, step) =
if start = stop then nil
else start::range(start+step, stop, step);
Which outputs this:
val range = fn : int * int * int -> int list
What changes do I need to make to my code so that when I run range(2,12,3) I get [2,5,8,11] ?
Thank you
Your condition (start = stop) to break the recursion is wrong. In your example you'll perform recursive calls with start=2, start=5, start=8, start=11, start=14, ... leading to an infinite loop. It's not that nothing happens, it's just that smnlj keeps computing...
You have an infinite recursion whenever stop - start is not a multiple of the step size (or zero).
Look at range(11,12,3), which should generate your last number:
if 11 = 12 then nil
else 11::range(11+3, 12, 3)
This will calculate range(14,12,3):
if 14 = 12 then nil
else 14::range(14+3, 12, 3)
and then range(17,12,3), and so on, ad infinitum.
You need to replace = with either > or >=, depending on whether stop should be included or not.
Related
I am learning recursion in my current class and the idea is a little tricky for me. From my understanding, when we build a function it will run as many times until our "base case" is satisfied. What I am wondering is how this looks and is returned on the stack. For an example I wrote the following function for a simple program to count how many times a digit shows up in an integer.
What does this look and work in a stack frame view? I don't completely understand how the returning works. I appreciate the help!
int count_digits(int n, int digit) {
// Base case: When n is a single digit.
if (n / 10 == 0) {
// Check if n is the same as the digit.
// When recursion hits the base case it will end the recursion.
if (n == digit) {
return 1;
} else {
return 0;
}
} else {
if (n % 10 == digit) {
return (1 + count_digits(n / 10, digit));
} else {
return (count_digits(n / 10, digit));
}
}
}
What does this look and work in a stack frame view? I don't completely understand how the returning works. I appreciate the help!
Let's try to build the solution bottom-up.
If you called the function - int count_digits(int n, int digit) as count_digits(4, 4) what would happen ?
This is the base case of your solution so it is very easy to see what is the return value. Your function would return 1.
Now, let's add one more digit and call the function like- count_digits(42, 4). What would happen ?
Your function will check the last digit which is 2 and compare with 4 since they are not equal so it will call the function count_digits(4, 4) and whatever is the returned value, will be returned as the result of count_digits(42, 4).
Now, let's add one more digit and call the function like - count_digits(424, 4). What would happen ?
Your function will check the last digit which is 4 and compare with 4 since they are equal so it will call the function count_digits(42, 4) and whatever is the returned value, will be returned by adding 1 to it. Since, number of 4s in 424 is 1 + number of 4s in 42. The result of count_digits(42,4) will be calculated exactly like it was done previously.
The recursive function builds up the solution in a top-down manner. If there are n digits initially, then your answer is (0 or 1 depending on the last digit) + answer with n-1 digits. And this process repeats recursively. So, your recursive code, reduces the problems by one digit at a time and it depends on the result of the immediate sub-problem.
You can use the C++ tutor at pythontutor.com website for step by step visualization of the stack frame. http://pythontutor.com/cpp.html#mode=edit
You can also try with smaller inputs and add some debug output to help you track and see how recursion works.
Check this stackoverflow answer for understanding what a stack frame is - Explain the concept of a stack frame in a nutshell
Check this stackoverflow answer for understanding recursion -
Understanding recursion
If you would like more help, please let me know in comments.
What I am trying to do is a little addon which would let me know how much time I have spent casting during combat in %,
function()
local spell, _, _, _, _, endTime = UnitCastingInfo("player")
-- getting information from the game itself whether im "Casting"
local inCombat = UnitAffectingCombat("player")
-- getting information form the game if combat is true (1) or not (nil)
local casting = {}
local sum = 0
if inCombat == 1 then
if spell then
table.insert(casting, 1)
else
table.insert(casting, 0)
end
else
for k in pairs (casting) do
casting [k] = nil
end
end
for i=1, #casting, 1 do
sum = sum + casting[i]
end
return( sum / #casting ) end
-- creating a list which adds 1 every frame I am casting and I am in combat,
-- or adds 0 every frame I'm not casting and I'm not in combat.
-- Then I sum all the numbers and divide it by the number of inputs to figure
-- out how much % I have spent "casting".
-- In case the combat condition is false, delete the list
For some reason these numbers don't add up at all, I only see "1" when both conditions are satisfied, or 0 if the combat condition is satisfied.
There might be some better approach I'm sure, but I am kind of new to lua and programming in general.
You say you're new to Lua, so I will attempt to explain in detail what is wrong and how it can be improved, so brace yourself for a long read.
I assume that your function will be called every frame/step/tick/whateveryouwanttocallit of your game. Since you set sum = 0 and casting = {} at the beginning of the function, this will be done every time the function is called. That's why you always get 0 or 1 in the end.
Upvalues to the rescue!
Lua has this nice thing called lexical scoping. I won't go into much detail, but the basic idea is: If a variable is accessible (in scope) when a function is defined, that function remembers that variable, no matter where it is called. For example:
local foo
do
local var = 10
foo = function() return var end
end
print(bar) -- nil
print(foo()) -- 10
You can also assign a new value to the variable and the next time you call the function, it will still have that new value. For example, here's a simple counter function:
local counter
do
count = 0
counter = function() count = count + 1; return count; end
end
print(counter()) -- 1
print(counter()) -- 2
-- etc.
Applying that to your situation, what are the values that need to persist from one call to the next?
Number of ticks spent in combat
Number of ticks spent casting
Define those two values outside of your function, and increment / read / reset them as needed; it will persist between repeated calls to your function.
Things to keep in mind:
You need to reset those counters when the player is no longer casting and/or in combat, or they will just continue where they left off.
casting doesn't need to be a table. Tables are slow compared to integers, even if you reuse them. If you need to count stuff, a number is more than enough. Just make casting = 0 when not in combat and increase it by 1 when in combat.
Thank you for feedback everyone, in the end after your suggestions and some research my code looks like this and works great:
function()
local spell, _, _, _, startTime, endTime, _, _, _ = UnitCastingInfo("player")
local inCombat = UnitAffectingCombat("player")
local inLockdown = InCombatLockdown()
local _, duration, _, _ = GetSpellCooldown("Fireball")
casting = casting or {}
local sum = 0
if inCombat == 1 or inLockdown == 1 then
if spell or duration ~= 0 then
casting[#casting+1] = 1
elseif spell == nil or duration == 0 then
casting[#casting+1] = 0
end
else
local next = next
local k = next(casting)
while k ~= nil do
casting[k] = nil
k = next(casting, k)
end
end
for i=1, #casting, 1 do
sum = sum + casting[i]
end
return(("%.1f"):format( (sum / #casting)*100 ).. "%%") end
what i noticed is there was a problem with reseting the table in the original code:
for k in pairs (casting) do
casting [k] = nil
it seemed like either some zeros stayed there, or the table size didnt "shrink" i dont know.
Maybe intereger would be faster then a table, but honestly i dont see any performance issues even when the table gets ridicolously big (5 min, 60 fps, thats 18k inputs) also for the sake of learning a new language its better to do it harder way in my opinion
Regards
I noticed that the following two for-loop cases behave differently sometimes while most of the time they are the same. I couldn't figure out the pattern, does anyone have any idea? Thanks!
case 1:
for (i <- myList.length - 1 to 0 by -1) { ... }
case 2:
for (i <- myList.length - 1 to 0) { ...}
Well, they definitely don't do the same things. n to 0 by -1 means "start at n and go to 0, counting backwards by 1. So:
5 to 0 by -1
// res0: scala.collection.immutable.Range = Range(5, 4, 3, 2, 1, 0)
Whereas n to 0 means "start at n and got to 0 counting forward by 1". But you'll notice that if n > 0, then there will be nothing in that list, since there is no way to count forward to 0 from anything greater than zero.
5 to 0
// res1: scala.collection.immutable.Range.Inclusive = Range()
The only way that they would produce the same result is if n=0 since counting from 0 to 0 is the same forwards and backwards:
0 to 0 by -1 // Range(0)
0 to 0 // Range(0)
In your case, since you're starting at myList.length - 1, they will produce the same result when the length of myList is 1.
In summary, the first version makes sense, because you want to count down to 0 by counting backward (by -1). And the second version doesn't make sense because you're not going to want to count forward to 0 from a length (which is necessarily non-negative).
First, we need to learn more about how value members to and by works.
to - Click Here for API documentation
to is a value member that appears in classes like int, double etc.
scala> 1 to 3
res35: scala.collection.immutable.Range.Inclusive = Range(1, 2, 3)
Honestly, you don't have to use start to end by step and start.to(end, step) will also work if you are more comfortable working with in this world. Basically, to will return you a Range.Inclusive object if we are talking about integer inputs.
by - Click Here for API documentation
Create a new range with the start and end values of this range and a new step
scala> Range(1,8) by 3
res54: scala.collection.immutable.Range = Range(1, 4, 7)
scala> Range(1,8).by(3)
res55: scala.collection.immutable.Range = Range(1, 4, 7)
In the end, lets spend some time looking at what happens when the step is on a different direction from start to end. Like 1 to 3 by -1
Here is the source code of the Range class and it is actually pretty straightforward to read:
def by(step: Int): Range = copy(start, end, step)
So by is actually calling a function copy, so what is copy?
protected def copy(start: Int, end: Int, step: Int): Range = new Range(start, end, step)
So copy is literally recreate a new range with different step, then lets look at the constructor or Range itself.
Reading this paragraph of code
override final val isEmpty = (
(start > end && step > 0)
|| (start < end && step < 0)
|| (start == end && !isInclusive)
)
These cases will trigger the exception and your result will be a empty Range in cases like 1 to 3 by -1..etc.
Sorry the length of my post is getting out of control since I am also learning Scala now.
Why don't you just read the source code of Range, it is written by Martin Odersky and it is only 500 lines including comments :)
I'm trying to implement this algorithm but I keep getting a syntax error on the 12th line but I cannot pinpoint what is causing it. I'm new to ocaml and any help would be greatly appreciated.
"To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method:
Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n).
Initially, let p equal 2, the first prime number.
Starting from p, enumerate its multiples by counting to n in increments of p, and mark them in the list (these will be 2p, 3p, 4p, ... ; the p itself should not be marked).
Find the first number greater than p in the list that is not marked. If there was no such number, stop. Otherwise, let p now equal this new number (which is the next prime), and repeat from step 3."
let prime(n) =
let arr = Array.create n false in
let set_marks (arr , n , prime ) = Array.set arr (n*prime) true in
for i = 2 to n do
set_marks(arr,i,2) done
let findNextPrimeNumberThatIsNotMarked (arr, prime , index ) =
let nextPrime = Array.get arr index in
let findNextPrimeNumberThatIsNotMarkedHelper (arr, prime, index) =
if nextPrime > prime then nextPrime
else prime in
;;
Adding to Jeffrey's answer,
As I have already answered to you at " What exactly is the syntax error here? ",
What you absolutely need to do right now is to install and use a proper OCaml indentation tool, and auto-indent lines. Unexpected auto-indent results often indicate syntactic mistakes like forgetting ;. Without such tools, it is very hard even for talented OCaml programmers to write OCaml code without syntax errors.
There are bunch of auto indenters for OCaml available:
ocp-indent for Emacs and Vim https://github.com/OCamlPro/ocp-indent
Caml mode and Tuareg mode for Emacs
Vim should have some other indenters but I do not know...
OCaml has an expression let a = b in c. Your code ends with in, but where is c? It looks like maybe you should just remove the in at the end.
Looking more closely I see there are more problems than this, sorry.
A function in OCaml is going to look like this roughly:
let f x =
let a = b in
let c = d in
val
Your definition for prime looks exactly like this, except that it ends at the for loop, i.e., with the keyword done.
The rest of the code forms a second, independent, function definition. It has a form like this:
let f x =
let a = b in
let g x = expr in
The syntactic problem is that you're missing an expression after in.
However, your use of indentation suggests you aren't trying to define two different functions. If this is true, you need to rework your code somewhat.
One thing that may be useful (for imperative style programming) is that you can write expr1; expr2 to evaluate two expressions one after the other.
I'm very new to OCaml / functional programming, and I'm confused about the implementation of some things that are relatively simple other languages I know. I could use any and all help.
Chiefly: in a program I'm working on, I either increment or decrement a variable based on a certain parameter. Here's something representative of what I have:
let tot = ref 0 in
for i = 0 to s do
if test_num > 0 then
tot := !tot + other_num
else
tot := !tot - other_num
done;;
This is obviously not the way to go about it, because even if the else statement is never taken, the code acts as if it is, each and every time, presumably because it's closer to the bottom of the program? I know OCaml has pretty sophisticated pattern matching, but within this level of coed I need access to a handful of lists I've already created, and, as far as I understand, I can't access those lists from a top-level function without passing them all as parameters.
I know I'm going about this the wrong way, but I have no idea how to do this idiomatically.
Suggestions? Thanks.
edit
Here's a more concise example:
let ex_list = [1; -2; 3; -4] in
let max_mem = ref 0 in
let mem = ref 0 in
let () =
for i = 0 to 3 do
let transition = List.nth ex_list i in
if transition > 0 then (
mem := (!mem + 10);
) else
mem := (!mem - 1);
if (!mem > !max_mem) then (max_mem := !mem);
done;
print_int !max_mem; print_string "\n";
in !mem;
At the end, when I print max_mem, I get 19, though this value should be (0 + 10 - 1 + 10 - 1 = 18). Am I doing the math wrong, or does the problem come from somewhere else?
Your code looks fine to me. It doesn't make a lot of sense as actual code, but I think you're just trying to show a general layout. It's also written in imperative style, which I usually try to avoid if possible.
The if in OCaml acts just like it does in other languages, there's no special thing about being near the bottom of the program. (More precisely, it acts like the ? : ternary operator from C and related languages; i.e., it's an expression.)
Your code doesn't return a useful value; it always returns () (the quintessentially uninteresting value known as "unit").
If we replace your free variables (ones not defined in this bit of code) by constants, and change the code to return a value, we can run it:
# let s = 8 in
let other_num = 7 in
let test_num = 3 in
let tot = ref 0 in
let () =
for i = 0 to s do
if test_num > 0 then
tot := !tot + other_num
else
tot := !tot - other_num
done
in
!tot;;
- : int = 63
#
If you're trying to learn to write in a functional style (i.e., without mutable variables), you would write this loop as a recursive function and make tot a parameter:
# let s = 8 in
let other_num = 7 in
let test_num = 3 in
let rec loop n tot =
if n > s then
tot
else
let tot' =
if test_num > 0 then tot + other_num else tot - other_num
in
loop (n + 1) tot'
in
loop 0 0;;
- : int = 63
It would probably be easier to help if you gave a (edited to add: small :-) self-contained problem that you're trying to solve.
The other parts of your question aren't clear enough to give any advice on. One thing that I might point out is that it's completely idiomatic to use pattern matching when processing lists.
Also, there's nothing wrong with passing things as parameters. That's why the language is called "functional" -- your code consists of functions, which have parameters.
Update
I like to write let () = expr1 in expr2 instead of expr1; expr2. It's just a habit I got into, sorry if it's confusing. The essence is that you're evaluating the first expression just for its side effects (it has type unit), and then returning the value of the second expression.
If you don't have something after the for, the code will evaluate to (), as I said. Since the purpose of the code seems to be to compute the value of !tot, this is what I returned. At the very least, this lets you see the calculated value in the OCaml top level.
tot' is just another variable. If you calculate a new value straightforwardly from a variable named var, it's conventional to name the new value var'. It reads as "var prime".
Update 2
Your example code works OK, but it has the problem that it uses List.nth to traverse a list, which is a slow (quadratic) operation. In fact your code is naturally considered a fold. Here's how you might write it in a functional style:
# let ex_list = [1; -2; 3; -4] in
let process (tot, maxtot) transition =
let tot' = if transition > 0 then tot + 10 else tot - 1 in
(tot', max maxtot tot')
in
List.fold_left process (0, 0) ex_list;;
- : int * int = (18, 19)
#
In addition to Jeffrey's answer, let me second that this is not how you would usually write such code in Ocaml, since it is a very low-level imperative approach. A more functional version would look like this:
let high ex_list =
let deltas = List.map (fun x -> if x > 0 then 10 else -1) ex_list in
snd (List.fold_left (fun (n, hi) d -> (n+d, max (n+d) hi)) (0, 0) deltas)
let test = high [1; -2; 3; -4]