I'm trying to write a function which will recursively find the largest element in a list of integers. I know how to do this in Java, but can't understand how to do this at Scala.
Here is what I have so far, but without recursion:
def max(xs: List[Int]): Int = {
if (xs.isEmpty) throw new java.util.NoSuchElementException();
else xs.max;
}
How can we find it recursively with Scala semantic.
This is the most minimal recursive implementation of max I've ever been able to think up:
def max(xs: List[Int]): Option[Int] = xs match {
case Nil => None
case List(x: Int) => Some(x)
case x :: y :: rest => max( (if (x > y) x else y) :: rest )
}
It works by comparing the first two elements on the list, discarding the smaller (or the first, if both are equal) and then calling itself on the remaining list. Eventually, this will reduce the list to one element which must be the largest.
I return an Option to deal with the case of being given an empty list without throwing an exception - which forces the calling code to recognise the possibility and deal with it (up to the caller if they want to throw an exception).
If you want it to be more generic, it should be written like this:
def max[A <% Ordered[A]](xs: List[A]): Option[A] = xs match {
case Nil => None
case x :: Nil => Some(x)
case x :: y :: rest => max( (if (x > y) x else y) :: rest )
}
Which will work with any type which either extends the Ordered trait or for which there is an implicit conversion from A to Ordered[A] in scope. So by default it works for Int, BigInt, Char, String and so on, because scala.Predef defines conversions for them.
We can become yet more generic like this:
def max[A <% Ordered[A]](xs: Seq[A]): Option[A] = xs match {
case s if s.isEmpty || !s.hasDefiniteSize => None
case s if s.size == 1 => Some(s(0))
case s if s(0) <= s(1) => max(s drop 1)
case s => max((s drop 1).updated(0, s(0)))
}
Which will work not just with lists but vectors and any other collection which extends the Seq trait. Note that I had to add a check to see if the sequence actually has a definite size - it might be an infinite stream, so we back away if that might be the case. If you are sure your stream will have a definite size, you can always force it before calling this function - it's going to work through the whole stream anyway. See notes at the end for why I really would not want to return None for an indefinite stream, though. I'm doing it here purely for simplicity.
But this doesn't work for sets and maps. What to do? The next common supertype is Iterable, but that doesn't support updated or anything equivalent. Anything we construct might be very poorly performing for the actual type. So my clean no-helper-function recursion breaks down. We could change to using a helper function but there are plenty of examples in the other answers and I'm going to stick with a one-simple-function approach. So at this point, we can to switch to reduceLeft (and while we are at it, let's go for `Traversable' and cater for all collections):
def max[A <% Ordered[A]](xs: Traversable[A]): Option[A] = {
if (xs.hasDefiniteSize)
xs reduceLeftOption({(b, a) => if (a >= b) a else b})
else None
}
but if you don't consider reduceLeft recursive, we can do this:
def max[A <% Ordered[A]](xs: Traversable[A]): Option[A] = xs match {
case i if i.isEmpty => None
case i if i.size == 1 => Some(i.head)
case i if (i collect { case x if x > i.head => x }).isEmpty => Some(i.head)
case _ => max(xs collect { case x if x > xs.head => x })
}
It uses the collect combinator to avoid some clumsy method of bodging a new Iterator out of xs.head and xs drop 2.
Either of these will work safely with almost any collection of anything which has an order. Examples:
scala> max(Map(1 -> "two", 3 -> "Nine", 8 -> "carrot"))
res1: Option[(Int, String)] = Some((8,carrot))
scala> max("Supercalifragilisticexpialidocious")
res2: Option[Char] = Some(x)
I don't usually give these others as examples, because it requires more expert knowledge of Scala.
Also, do remember that the basic Traversable trait provides a max method, so this is all just for practice ;)
Note: I hope that all my examples show how careful choice of the sequence of your case expressions can make each individual case expression as simple as possible.
More Important Note: Oh, also, while I am intensely comfortable returning None for an input of Nil, in practice I'd be strongly inclined to throw an exception for hasDefiniteSize == false. Firstly, a finite stream could have a definite or non-definite size dependent purely on the sequence of evaluation and this function would effectively randomly return Option in those cases - which could take a long time to track down. Secondly, I would want people to be able to differentiate between having passed Nil and having passed truly risk input (that is, an infinite stream). I only returned Option in these demonstrations to keep the code as simple as possible.
The easiest approach would be to use max function of TraversableOnce trait, as follows,
val list = (1 to 10).toList
list.max
to guard against the emptiness you can do something like this,
if(list.empty) None else Some(list.max)
Above will give you an Option[Int]
My second approach would be using foldLeft
(list foldLeft None)((o, i) => o.fold(Some(i))(j => Some(Math.max(i, j))))
or if you know a default value to be returned in case of empty list, this will become more simpler.
val default = 0
(list foldLeft default)(Math.max)
Anyway since your requirement is to do it in recursive manner, I propose following,
def recur(list:List[Int], i:Option[Int] = None):Option[Int] = list match {
case Nil => i
case x :: xs => recur(xs, i.fold(Some(x))(j => Some(Math.max(j, x))))
}
or as default case,
val default = 0
def recur(list:List[Int], i:Int = default):Int = list match {
case Nil => i
case x :: xs => recur(xs, i.fold(x)(j => Math.max(j, x)))
}
Note that, this is tail recursive. Therefore stack is also saved.
If you want functional approach to this problem then use reduceLeft:
def max(xs: List[Int]) = {
if (xs.isEmpty) throw new NoSuchElementException
xs.reduceLeft((x, y) => if (x > y) x else y)
}
This function specific for list of ints, if you need more general approach then use Ordering typeclass:
def max[A](xs: List[A])(implicit cmp: Ordering[A]): A = {
if (xs.isEmpty) throw new NoSuchElementException
xs.reduceLeft((x, y) => if (cmp.gteq(x, y)) x else y)
}
reduceLeft is a higher-order function, which takes a function of type (A, A) => A, it this case it takes two ints, compares them and returns the bigger one.
You could use pattern matching like that
def max(xs: List[Int]): Int = xs match {
case Nil => throw new NoSuchElementException("The list is empty")
case x :: Nil => x
case x :: tail => x.max(max(tail)) //x.max is Integer's class method
}
Scala is a functional language whereby one is encourage to think recursively. My solution as below. I recur it base on your given method.
def max(xs: List[Int]): Int = {
if(xs.isEmpty == true) 0
else{
val maxVal= max(xs.tail)
if(maxVal >= xs.head) maxVal
else xs.head
}
}
Updated my solution to tail recursive thanks to suggestions.
def max(xs: List[Int]): Int = {
def _max(xs: List[Int], maxNum: Int): Int = {
if (xs.isEmpty) maxNum
else {
val max = {
if (maxNum >= xs.head) maxNum
else xs.head
}
_max(xs.tail, max)
}
}
_max(xs.tail, xs.head)
}
I used just head() and tail()
def max(xs: List[Int]): Int = {
if (xs.isEmpty) throw new NoSuchElementException
else maxRecursive(xs.tail, xs.head)
}
def maxRecursive(xs: List[Int], largest: Int): Int = {
if (!xs.isEmpty) {
if (xs.head > largest) maxRecursive(xs.tail, xs.head)
else maxRecursive(xs.tail, largest)
} else {
largest
}
}
Here is tests for this logic:
test("max of a few numbers") {
assert(max(List(3, 7, 2, 1, 10)) === 10)
assert(max(List(3, -7, 2, -1, -10)) === 3)
assert(max(List(-3, -7, -2, -5, -10)) === -2)
}
Folding can help:
if(xs.isEmpty)
throw new NoSuchElementException
else
(Int.MinValue /: xs)((max, value) => math.max(max, value))
List and pattern matching (updated, thanks to #x3ro)
def max(xs:List[Int], defaultValue: =>Int):Int = {
#tailrec
def max0(xs:List[Int], maxSoFar:Int):Int = xs match {
case Nil => maxSoFar
case head::tail => max0(tail, math.max(maxSoFar, head))
}
if(xs.isEmpty)
defaultValue
else
max0(xs, Int.MinValue)
}
(This solution does not create Option instance every time. Also it is tail-recursive and will be as fast as an imperative solution.)
Looks like you're just starting out with scala so I try to give you the simplest answer to your answer, how do it recursively:
def max(xs: List[Int]): Int = {
def maxrec(currentMax : Int, l: List[Int]): Int = l match {
case Nil => currentMax
case head::tail => maxrec(head.max(currentMax), tail) //get max of head and curretn max
}
maxrec(xs.head, xs)
}
This method defines an own inner method (maxrec) to take care of the recursiveness. It will fail ( exception) it you give it an empty list ( there's no maximum on an empty List)
Here is my code (I am a newbie in functional programming) and I'm assuming whoever lands up under this question will be folks like me. The top answer, while great, is bit too much for newbies to take! So, here is my simple answer. Note that I was asked (as part of a Course) to do this using only head and tail.
/**
* This method returns the largest element in a list of integers. If the
* list `xs` is empty it throws a `java.util.NoSuchElementException`.
*
* #param xs A list of natural numbers
* #return The largest element in `xs`
* #throws java.util.NoSuchElementException if `xs` is an empty list
*/
#throws(classOf[java.util.NoSuchElementException])
def max(xs: List[Int]): Int = find_max(xs.head, xs.tail)
def find_max(max: Int, xs: List[Int]): Int = if (xs.isEmpty) max else if (max >= xs.head) find_max(max, xs.tail) else find_max(xs.head, xs.tail)
Some tests:
test("max of a few numbers") {
assert(max(List(3, 7, 2)) === 7)
intercept[NoSuchElementException] {
max(List())
}
assert(max(List(31,2,3,-31,1,2,-1,0,24,1,21,22)) === 31)
assert(max(List(2,31,3,-31,1,2,-1,0,24,1,21,22)) === 31)
assert(max(List(2,3,-31,1,2,-1,0,24,1,21,22,31)) === 31)
assert(max(List(Int.MaxValue,2,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,222,3,-31,1,2,-1,0,24,1,21,22)) === Int.MaxValue)
}
list.sortWith(_ > ).head & list.sortWith( > _).reverse.head for greatest and smallest number
If you are required to write a recursive max function on a list using isEmpty, head and tail and throw exception for empty list:
def max(xs: List[Int]): Int =
if (xs.isEmpty) throw new NoSuchElementException("max of empty list")
else if (xs.tail.isEmpty) xs.head
else if (xs.head > xs.tail.head) max(xs.head :: xs.tail.tail)
else max(xs.tail)
if you were to use max function on list it is simply (you don't need to write your own recursive function):
val maxInt = List(1, 2, 3, 4).max
def max(xs: List[Int]): Int = {
def _max(xs: List[Int], maxAcc:Int): Int = {
if ( xs.isEmpty )
maxAcc
else
_max( xs.tail, Math.max( maxAcc, xs.head ) ) // tail call recursive
}
if ( xs.isEmpty )
throw new NoSuchElementException()
else
_max( xs, Int.MinValue );
}
With tail-recursion
#tailrec
def findMax(x: List[Int]):Int = x match {
case a :: Nil => a
case a :: b :: c => findMax( (if (a > b) a else b) ::c)
}
With pattern matching to find max and return zero in case empty
def findMax(list: List[Int]) = {
def max(list: List[Int], n: Int) : Int = list match {
case h :: t => max(t, if(h > n) h else n)
case _ => n
}
max(list,0)
}
I presume this is for the progfun-example
This is the simplest recursive solution I could come up with
def max(xs: List[Int]): Int = {
if (xs.isEmpty) throw new NoSuchElementException("The list is empty")
val tail = xs.tail
if (!tail.isEmpty) maxOfTwo(xs.head, max(xs.tail))
else xs.head
}
def maxOfTwo(x: Int, y: Int): Int = {
if (x >= y) x
else y
}
def max(xs: List[Int]): Int = xs match {
case Nil => throw new NoSuchElementException("empty list!")
case x :: Nil => x
case x :: tail => if (x > max(tail)) x else max(tail)
}
Maybe this might be easy to fix but can you help me out or guide me to a solution. I have a remove function that goes through a List of tuples "List[(String,Any)]" and im trying to replace the 1 index of the value with Nil when the list is being looped over.
But when I try to replace the current v with Nil, it say the v is assigned to "val". Now I understand that scala lists are immutable. So maybe this is what is going wrong?
I tried a Tail recursion implementation as will but when I get out of the def there is a type mismatch. ie: is unit but required: Option[Any]
// remove(k) removes one value v associated with key k
// from the dictionary, if any, and returns it as Some(v).
// It returns None if k is associated to no value.
def remove(key:String):Option[Any] = {
for((k,v) <- d){
if(k == key){
var temp:Option[Any] = Some(v)
v = Nil
return temp
}
}; None
}
Here was the other way of trying to figure out
def remove(key:String):Option[Any] = {
def removeHelper(l:List[(String,Any)]):List[(String,Any)] =
l match {
case Nil => Nil
case (k,v)::t => if (key == k) t else (k,v)::removeHelper(t)
}
d = removeHelper(d)
}
Any Suggestions? This is a homework/Project for school thought I might add that for the people that don't like to help with homework.
Well, there are many ways of answering that question. I'll be outlining the ones I can think of here with my own implementations, but the list is by no means exhaustive (nor, probably, the implementations optimal).
First, you can try with existing combinators - the usual suspects are map, flatMap, foldLeft and foldRight:
def remove_flatMap(key: String, list: List[(String, Any)]): List[(String, Any)] =
// The Java developer in me rebels against creating that many "useless" instances.
list.flatMap {a => if(a._1 == key) Nil else List(a)}
def remove_foldLeft(key: String, list: List[(String, Any)]): List[(String, Any)] =
list.foldLeft(List[(String, Any)]()) {(acc, a) =>
if(a._1 == key) acc
else a :: acc
// Note the call to reverse here.
}.reverse
// This is more obviously correct than the foldLeft version, but is not tail-recursive.
def remove_foldRight(key: String, list: List[(String, Any)]): List[(String, Any)] =
list.foldRight(List[(String, Any)]()) {(a, acc) =>
if(a._1 == key) acc
else a :: acc
}
The problem with these is that, as far as I'm aware, you cannot stop them once a certain condition has been reached: I don't think they solve your problem directly, since they remove all instances of key rather than the first.
You also want to note that:
foldLeft must reverse the list once it's done, since it appends elements in the "wrong" order.
foldRight doesn't have that flaw, but is not tail recursive: it will cause memory issues on large lists.
map cannot be used for your problem, since it only lets us modify a list's values but not its structure.
You can also use your own implementation. I've included two versions, one that is tail-recursive and one that is not. The tail-recursive one is obviously the better one, but is also more verbose (I blame the ugliness of using a List[(String, Any)] rather than Map[String, Any]:
def remove_nonTailRec(key: String, list: List[(String, Any)]): List[(String, Any)] = list match {
case h :: t if h._1 == key => t
// This line is the reason our function is not tail-recursive.
case h :: t => h :: remove_nonTailRec(key, t)
case Nil => Nil
}
def remove_tailRec(key: String, list: List[(String, Any)]): List[(String, Any)] = {
#scala.annotation.tailrec
def run(list: List[(String, Any)], acc: List[(String, Any)]): List[(String, Any)] = list match {
// We've been aggregating in the "wrong" order again...
case h :: t if h._1 == key => acc.reverse ::: t
case h :: t => run(t, h :: acc)
case Nil => acc.reverse
}
run(list, Nil)
}
The better solution is of course to use the right tool for the job: a Map[String, Any].
Note that I do not think I answer your question fully: my examples remove key, while you want to set it to Nil. Since this is your homework, I'll let you figure out how to change my code to match your requirements.
List is the wrong collection to use if any key should only exist once. You should be using Map[String,Any]. With a list,
You have to do extra work to prevent duplicate entries.
Retrieval of a key will be slower, the further down the list it appears. Attempting to retrieve a non-existent key will be slow in proportion to the size of the list.
I guess point 2 is maybe why you are trying to replace it with Nil rather than just removing the key from the list. Nil is not the right thing to use here, really. You are going to get different things back if you try and retrieve a non-existent key compared to one that has been removed. Is that really what you want? How much sense does it make to return Some(Nil), ever?
Here's a couple of approaches which work with mutable or immutable lists, but which don't assume that you successfully stopped duplicates creeping in...
val l1: List[(String, Any)] = List(("apple", 1), ("pear", "violin"), ("banana", Unit))
val l2: List[(Int, Any)] = List((3, 1), (4, "violin"), (7, Unit))
def remove[A,B](key: A, xs: List[(A,B)]) = (
xs collect { case x if x._1 == key => x._2 },
xs map { case x if x._1 != key => x; case _ => (key, Nil) }
)
scala> remove("apple", l1)
res0: (List[(String, Any)], List[(String, Any)]) = (List((1)),List((apple, List()),(pear,violin), (banana,object scala.Unit)))
scala> remove(4, l2)
res1: (List[(Int, Any)], List[(Int, Any)]) = (List((violin)),List((3,1), (4, List()), (7,object scala.Unit)))
scala> remove("snark", l1)
res2: (List[Any], List[(String, Any)]) = (List(),List((apple,1), (pear,violin), (banana,object scala.Unit)))
That returns a list of matching values (so an empty list rather than None if no match) and the remaining list, in a tuple. If you want a version that just completely removes the unwanted key, do this...
def remove[A,B](key: A, xs: List[(A,B)]) = (
xs collect { case x if x._1 == key => x._2 },
xs filter { _._1 != key }
)
But also look at this:
scala> l1 groupBy {
case (k, _) if k == "apple" => "removed",
case _ => "kept"
}
res3: scala.collection.immutable.Map[String,List[(String, Any)]] = Map(removed -> List((apple,1)), kept -> List((pear,violin), (banana,object scala.Unit)))
That is something you could develop a bit. All you need to do is add ("apple", Nil) to the "kept" list and extract the value(s) from the "removed" list.
Note that I am using the List combinator functions rather than writing my own recursive code; this usually makes for clearer code and is often as fast or faster than a hand-rolled recursive function.
Note also that I don't change the original list. This means my function works with both mutable and immutable lists. If you have a mutable list, feel free to assign my returned list as the new value for your mutable var. Win, win.
But please use a map for this. Look how simple things become:
val m1: Map[String, Any] = Map(("apple", 1), ("pear", "violin"), ("banana", Unit))
val m2: Map[Int, Any] = Map((3, 1), (4, "violin"), (7, Unit))
def remove[A,B](key: A, m: Map[A,B]) = (m.get(key), m - key)
scala> remove("apple", m1)
res0: (Option[Any], scala.collection.immutable.Map[String,Any]) = (Some(1),Map(pear -> violin, banana -> object scala.Unit))
scala> remove(4, m2)
res1: (Option[Any], scala.collection.immutable.Map[Int,Any]) = (Some(violin),Map(3 -> 1, 7 -> object scala.Unit))
scala> remove("snark", m1)
res2: res26: (Option[Any], scala.collection.immutable.Map[String,Any]) = (None,Map(apple -> 1, pear -> violin, banana -> object scala.Unit))
The combinator functions make things easier, but when you use the right collection, it becomes so easy that it is hardly worth writing a special function. Unless, of course, you are trying to hide the data structure - in which case you should really be hiding it inside an object.