Hi I am new to scala functional programming methodology. I want to input a number to my function and check if it is a good number or not.
A number is a good number if its every digit is larger than the sum of digits which are on the right side of that digit.
For example:
9620 is good as (2 > 0, 6 > 2+0, 9 > 6+2+0)
steps I am using to solve this is
1. converting a number to string and reversing it
2. storing all digits of the reversed number as elements of a list
3. applying for loop from i equals 1 to length of number - 1
4. calculating sum of first i digits as num2
5. extracting ith digit from the list as digit1 which is one digit ahead of the first i numbers for which we calculated sum because list starts from zero.
6. comparing output of 4th and 5th step. if num1 is greater than num2 then we will break the for loop and come out of the loop to print it is not a good number.
please find my code below
val num1 = 9521.toString.reverse
val list1 = num1.map(_.todigit).toList
for (i <- 1 to num1.length - 1) {
val num2 = num1.take(i).map(_.toDigits) sum
val digit1 = list1(i)
if (num2 > digit1) {
print("number is not a good number")
break
}
}
I know this is not the most optimized way to solve this problem. Also I am looking for a way to code this using tail recursion where I pass two numbers and get all the good numbers falling in between those two numbers.
Can this be done in more optimized way?
Thanks in advance!
No String conversions required.
val n = 9620
val isGood = Stream.iterate(n)(_/10)
.takeWhile(_>0)
.map(_%10)
.foldLeft((true,-1)){ case ((bool,sum),digit) =>
(bool && digit > sum, sum+digit)
}._1
Here is a purely numeric version using a recursive function.
def isGood(n: Int): Boolean = {
#tailrec
def loop(n: Int, sum: Int): Boolean =
(n == 0) || (n%10 > sum && loop(n/10, sum + n%10))
loop(n/10, n%10)
}
This should compile into an efficient loop.
Using this function:(This will be the efficient way as the function forall will not traverse the entire list of digits. it stops when it finds the false condition immediately ( ie., when v(i)>v.drop(i+1).sum becomes false) while traversing from left to right of the vector v. )
def isGood(n: Int)= {
val v1 = n.toString.map(_.asDigit)
val v = if(v1.last!=0) v1 else v1.dropRight(1)
(0 to v.size-1).forall(i=>v(i)>v.drop(i+1).sum)
}
If we want to find good numbers in an interval of integers ranging from n1 to n2 we can use this function:
def goodNums(n1:Int,n2:Int) = (n1 to n2).filter(isGood(_))
In Scala REPL:
scala> isGood(9620)
res51: Boolean = true
scala> isGood(9600)
res52: Boolean = false
scala> isGood(9641)
res53: Boolean = false
scala> isGood(9521)
res54: Boolean = true
scala> goodNums(412,534)
res66: scala.collection.immutable.IndexedSeq[Int] = Vector(420, 421, 430, 510, 520, 521, 530, 531)
scala> goodNums(3412,5334)
res67: scala.collection.immutable.IndexedSeq[Int] = Vector(4210, 5210, 5310)
This is a more functional way. pairs is a list of tuples between a digit and the sum of the following digits. It is easy to create these tuples with drop, take and slice (a combination of drop and take) methods.
Finally I can represent my condition in an expressive way with forall method.
val n = 9620
val str = n.toString
val pairs = for { x <- 1 until str.length } yield (str.slice(x - 1, x).toInt, str.drop(x).map(_.asDigit).sum)
pairs.forall { case (a, b) => a > b }
If you want to be functional and expressive avoid to use break. If you need to check a condition for each element is a good idea to move your problem to collections, so you can use forAll.
This is not the case, but if you want performance (if you don't want to create an entire pairs collection because the condition for the first element is false) you can change your for collection from a Range to Stream.
(1 until str.length).toStream
Functional style tends to prefer monadic type things, such as maps and reduces. To make this look functional and clear, I'd do something like:
def isGood(value: Int) =
value.toString.reverse.map(digit=>Some(digit.asDigit)).
reduceLeft[Option[Int]]
{
case(sum, Some(digit)) => sum.collectFirst{case sum if sum < digit => sum+digit}
}.isDefined
Instead of using tail recursion to calculate this for ranges, just generate the range and then filter over it:
def goodInRange(low: Int, high: Int) = (low to high).filter(isGood(_))
Related
I'm learning functional programming partially by reading the book Functional Programming in Scala a.k.a. The Red Book and I've run into my first real blocker. In Chapter 6, The book uses the example of a random number generator to illustrate how to change state by using side effects. Then the book goes on to demonstrate the patterns you would typically encounter as well as some of the tangents you might take in making a functional stateful api. My problem comes when trying to understand the following code:
type Rand[+A] = RNG => (A, RNG)
def map[A, B](s: Rand[A])(f: A => B): Rand[B] =
rng => {
val (nxt, nxtrng) = s(rng)
(f(nxt), nxtrng)
}
def nonNegativeLessThan(n: Int): Rand[Int] =
map(nonNegativeIntv2) { i =>
val mod = i % n
if (i + (n - 1) - mod >= 0) mod else nonNegativeLessThan(n)(???)
}
I hope this is enough context to get an idea what the code does. This is coming directly from the book on page 86. How does the if statement for method nonNegativeLessThan filters out values of i that are greater than the largest multiple of n in a 32 bit integer? Doesn't the recursive call in the else clause return a value of type Rand[Int]? In general I'm confused about what's going on in the code that is bolded. This is a pretty good book so I'm happy with how things are going so far and I feel I've learned a lot about functional programming. My apologies if this question is ill formed and if there is an issue with the formatting. This is my first post on stack overflow! Thank you to those who take a look at this and I hope it helps someone who has the same problem.
How does the if statement for method nonNegativeLessThan filters out values of i that are greater than the largest multiple of n in a 32 bit integer?
If i is greater than the largest multiple of n, then i + (n - 1) - mod will overflow and yield a negative number. The subsequent >= 0 is then false.
Doesn't the recursive call in the else clause return a value of type Rand[Int]?
Well, nonNegativeLessThan(n) is indeed of type Rand[Int]. However it says nonNegativeLessThan(n)(???), that is, it applies nonNegativeLessThan to n, and then it applies the resulting value (of type Rand[Int], which is a function type) to ???, and that yields an Int. Or rather it would do that if ??? ever yielded real value, which it doesn't.
The problem here is that you would have to pass the state of the RNG instead of ???, but the map function doesn't let you access that state. You'll need flatMap to solve this – presumably that's what the book is going to discuss next.
Imagine that you have a new domain of a set of integers, for example 0 to 11. The Rand type represents an aleatory number in that domain, but this type can not be skewed. That means that there can not be numbers that have a greater probability of being generated that others.
If you want to generate a number that is positive and less than four, you can use the map function of the Rand type, that allows to transform the result of a state action. First, it generates a nonnegative number and transform the result, via the map, applying the anonymous function: _ % n to obtain a number less than n.
def nonNegativeLessThan(n: Int): Rand[Int] =
map(nonNegativeInt) { _ % n }
It uses the modulo operation:
scala> 1 % 4
res0: Int = 1
scala> 2 % 4
res1: Int = 2
scala> 3 % 4
res2: Int = 3
scala> 4 % 4
res3: Int = 0
scala> 5 % 4
res4: Int = 1
scala> 6 % 4
res5: Int = 2
scala> 7 % 4
res6: Int = 3
scala> 8 % 4
res7: Int = 0
scala> 9 % 4
res8: Int = 1
scala> 10 % 4
res9: Int = 2
As you can see, the largest multiple of 4 in this domain is 8, so if the non-negative number that is generated is 9 or 10, we have a problem. The probability of having a 1 or 2 is greater than having a 3 or a 0. And for that reason, the other implementation detects that the number which is first generated as a result of the nonnegativeInt is not major than the largest multiple of n in a specific domain, the Int32 numbers domain in the book, to have a non- biased generator.
And yes, that book is amazing.
I am reading Functional Programming in Scala and am having trouble understanding a piece of code. I have checked the errata for the book and the passage in question does not have a misprint. (Actually, it does have a misprint, but the misprint does not affect the code that I have a question about.)
The code in question calculates a pseudo-random, non-negative integer that is less than some upper bound. The function that does this is called nonNegativeLessThan.
trait RNG {
def nextInt: (Int, RNG) // Should generate a random `Int`.
}
case class Simple(seed: Long) extends RNG {
def nextInt: (Int, RNG) = {
val newSeed = (seed * 0x5DEECE66DL + 0xBL) & 0xFFFFFFFFFFFFL // `&` is bitwise AND. We use the current seed to generate a new seed.
val nextRNG = Simple(newSeed) // The next state, which is an `RNG` instance created from the new seed.
val n = (newSeed >>> 16).toInt // `>>>` is right binary shift with zero fill. The value `n` is our new pseudo-random integer.
(n, nextRNG) // The return value is a tuple containing both a pseudo-random integer and the next `RNG` state.
}
}
type Rand[+A] = RNG => (A, RNG)
def nonNegativeInt(rng: RNG): (Int, RNG) = {
val (i, r) = rng.nextInt
(if (i < 0) -(i + 1) else i, r)
}
def nonNegativeLessThan(n: Int): Rand[Int] = { rng =>
val (i, rng2) = nonNegativeInt(rng)
val mod = i % n
if (i + (n-1) - mod >= 0) (mod, rng2)
else nonNegativeLessThan(n)(rng2)
}
I have trouble understanding the following code in nonNegativeLessThan that looks like this: if (i + (n-1) - mod >= 0) (mod, rng2), etc.
The book explains that this entire if-else expression is necessary because a naive implementation that simply takes the mod of the result of nonNegativeInt would be slightly skewed toward lower values since Int.MaxValue is not guaranteed to be a multiple of n. Therefore, this code is meant to check if the generated output of nonNegativeInt would be larger than the largest multiple of n that fits inside a 32 bit value. If the generated number is larger than the largest multiple of n that fits inside a 32 bit value, the function recalculates the pseudo-random number.
To elaborate, the naive implementation would look like this:
def naiveNonNegativeLessThan(n: Int): Rand[Int] = map(nonNegativeInt){_ % n}
where map is defined as follows
def map[A,B](s: Rand[A])(f: A => B): Rand[B] = {
rng =>
val (a, rng2) = s(rng)
(f(a), rng2)
}
To repeat, this naive implementation is not desirable because of a slight skew towards lower values when Int.MaxValue is not a perfect multiple of n.
So, to reiterate the question: what does the following code do, and how does it help us determine whether a number is smaller that the largest multiple of n that fits inside a 32 bit integer? I am talking about this code inside nonNegativeLessThan:
if (i + (n-1) - mod >= 0) (mod, rng2)
else nonNegativeLessThan(n)(rng2)
I have exactly the same confusion about this passage from the Functional Programming in Scala. And I absolutely agree with jwvh's analysis - the statement if (i + (n-1) - mod >= 0) will be always true.
In fact, if one tries the same example in Rust, the compiler warns about this (just an interesting comparison of how much static checking is being done). Of course the pencil and paper approach of jwvh is absolutely the right approach.
We first define some type aliases to make the code match closer to the Scala code (forgive my Rust if its not quite idiomatic).
pub type RNGType = Box<dyn RNG>;
pub type Rand<A> = Box<dyn Fn(RNGType) -> (A, RNGType)>;
pub fn non_negative_less_than_(n: u32) -> Rand<u32> {
let t = move |rng: RNGType| {
let (i, rng2) = non_negative_int(rng);
let rem = i % n;
if i + (n - 1) - rem >= 0 {
(rem, rng2)
} else {
non_negative_less_than(n)(rng2)
}
};
Box::new(t)
}
The compiler warning regarding if nn + (n - 1) - rem >= 0 is:
warning: comparison is useless due to type limits
For example, my input is:
scala> val myList = List("7842", "abf45", "abd", "56")
myList: List[String] = List(7842, abf45, abd, 56)
7842 and 56 can be converted to Int; therefore, my expected output is 2. We can assume that negative integers don't happen, so -67 is not possible.
This is what I have so far:
scala> myList.map(x => Try(x.toInt).getOrElse(-1)).count(_ > -1)
res15: Int = 2
This should work correctly, but I feel like I am missing a more elegant and readable solution, because all I have to do is count number of successes.
I would caution against using exception handling (like Try) in control flow -- it's very slow.
Here's a solution that uses idiomatic Scala collection operations, performs well, and will not count negative numbers:
scala> val myList = List("7842", "abf45", "abd", "56")
myList: List[String] = List(7842, abf45, abd, 56)
scala> myList.count(_.forall(_.isDigit))
res8: Int = 2
EDIT: #immibis pointed out that this won't detect strings of numbers that exceed Integer.MaxValue. If this is a concern, I would recommend one of the following approaches:
import scala.util.Try
myList.count(x => Try(x.toInt).filter(_ >= 0).isSuccess)
or, if you want to keep the performance of my first answer while still handling this edge case:
import scala.util.Try
myList.count(x => x.forall(_.isDigit) && Try(x.toInt).filter(_ >= 0).isSuccess)
This is a bit shorter:
myList.count(x => Try(x.toInt).isSuccess)
Note that this solution will handle any string that can be converted to integer via .toInt, including negative numbers.
You may consider string.matches method with regex as well, to match only positive integers:
val myList = List("7842", "abf45", "abd", "-56")
// myList: List[String] = List(7842, abf45, abd, -56)
myList.count(_.matches("\\d+"))
// res18: Int = 1
If negative integers need to be counted (and take into account possible +/- signs):
myList.count(_.matches("[+-]?\\d+"))
// res17: Int = 2
Starting Scala 2.13 and the introduction of String::toIntOption, we can count items ("34"/"2s3") for which applying toIntOption (Some(34)/None) is defined (true/false):
List("34", "abf45", "2s3", "56").count(_.toIntOption.isDefined) // 2
Total newbie question here...Today while trying to calculate sum of a list of integers(actually BitSet), I ran into overflow scenarios and noticed that the return type of(sum/product) is Int. Are there any methods in Range/List to sum up or say multiply all values to Long?
val x = 1 to Integer.MaxValue
println(x.sum) //prints -1453759936
thanks
Convert the elements to Long (or BigInt should that go that far) while summing:
x.view.map(_.toLong).sum
You can also go back to fold
x.foldLeft(0L)(_ + _)
(Note: should you sum over a range, maybe it would be better do a little math, but I understand that is not what you did in fact)
Compare:
>> val x = 1 to Int.MaxValue
x: scala.collection.immutable.Range.Inclusive with scala.collection.immutable.Range.ByOne = Range(...)
With:
>> val x = 1L to Int.MaxValue
x: scala.collection.immutable.NumericRange.Inclusive[Long] = NumericRange(...)
Note that the first uses Int.to, and the latter used Long.to (where Int.MaxValue is up-converted automatically). Of course, the sum of a consecutive integer sequence has a very nice discrete formula :)
Happy coding.
This isn't very efficient, but the easiest way:
val x = 1L to Int.MaxValue
println(x.sum) //prints 2305843008139952128
If you need x to contain Ints rather than Longs, you can do
val x = 1 to Int.MaxValue
println(x.foldLeft(0L)(_+_))
Range.Long(1, Int.MaxValue, 1).sum
I had asked this question on Javaranch, but couldn't get a response there. So posting it here as well:
I have this particular requirement where the increment in the loop variable is to be done by multiplying it with 5 after each iteration. In Java we could implement it this way:
for(int i=1;i<100;i=i*5){}
In scala I was trying the following code-
var j=1
for(i<-1.to(100).by(scala.math.pow(5,j).toInt))
{
println(i+" "+j)
j=j+1
}
But its printing the following output:
1 1
6 2
11 3
16 4
21 5
26 6
31 7
36 8
....
....
Its incrementing by 5 always. So how do I got about actually multiplying the increment by 5 instead of adding it.
Let's first explain the problem. This code:
var j=1
for(i<-1.to(100).by(scala.math.pow(5,j).toInt))
{
println(i+" "+j)
j=j+1
}
is equivalent to this:
var j = 1
val range: Range = Predef.intWrapper(1).to(100)
val increment: Int = scala.math.pow(5, j).toInt
val byRange: Range = range.by(increment)
byRange.foreach {
println(i+" "+j)
j=j+1
}
So, by the time you get to mutate j, increment and byRange have already been computed. And Range is an immutable object -- you can't change it. Even if you produced new ranges while you did the foreach, the object doing the foreach would still be the same.
Now, to the solution. Simply put, Range is not adequate for your needs. You want a geometric progression, not an arithmetic one. To me (and pretty much everyone else answering, it seems), the natural solution would be to use a Stream or Iterator created with iterate, which computes the next value based on the previous one.
for(i <- Iterator.iterate(1)(_ * 5) takeWhile (_ < 100)) {
println(i)
}
EDIT: About Stream vs Iterator
Stream and Iterator are very different data structures, that share the property of being non-strict. This property is what enables iterate to even exist, since this method is creating an infinite collection1, from which takeWhile will create a new2 collection which is finite. Let's see here:
val s1 = Stream.iterate(1)(_ * 5) // s1 is infinite
val s2 = s1.takeWhile(_ < 100) // s2 is finite
val i1 = Iterator.iterate(1)(_ * 5) // i1 is infinite
val i2 = i1.takeWhile(_ < 100) // i2 is finite
These infinite collections are possible because the collection is not pre-computed. On a List, all elements inside the list are actually stored somewhere by the time the list has been created. On the above examples, however, only the first element of each collection is known in advance. All others will only be computed if and when required.
As I mentioned, though, these are very different collections in other respects. Stream is an immutable data structure. For instance, you can print the contents of s2 as many times as you wish, and it will show the same output every time. On the other hand, Iterator is a mutable data structure. Once you used a value, that value will be forever gone. Print the contents of i2 twice, and it will be empty the second time around:
scala> s2 foreach println
1
5
25
scala> s2 foreach println
1
5
25
scala> i2 foreach println
1
5
25
scala> i2 foreach println
scala>
Stream, on the other hand, is a lazy collection. Once a value has been computed, it will stay computed, instead of being discarded or recomputed every time. See below one example of that behavior in action:
scala> val s2 = s1.takeWhile(_ < 100) // s2 is finite
s2: scala.collection.immutable.Stream[Int] = Stream(1, ?)
scala> println(s2)
Stream(1, ?)
scala> s2 foreach println
1
5
25
scala> println(s2)
Stream(1, 5, 25)
So Stream can actually fill up the memory if one is not careful, whereas Iterator occupies constant space. On the other hand, one can be surprised by Iterator, because of its side effects.
(1) As a matter of fact, Iterator is not a collection at all, even though it shares a lot of the methods provided by collections. On the other hand, from the problem description you gave, you are not really interested in having a collection of numbers, just in iterating through them.
(2) Actually, though takeWhile will create a new Iterator on Scala 2.8.0, this new iterator will still be linked to the old one, and changes in one have side effects on the other. This is subject to discussion, and they might end up being truly independent in the future.
In a more functional style:
scala> Stream.iterate(1)(i => i * 5).takeWhile(i => i < 100).toList
res0: List[Int] = List(1, 5, 25)
And with more syntactic sugar:
scala> Stream.iterate(1)(_ * 5).takeWhile(_ < 100).toList
res1: List[Int] = List(1, 5, 25)
Maybe a simple while-loop would do?
var i=1;
while (i < 100)
{
println(i);
i*=5;
}
or if you want to also print the number of iterations
var i=1;
var j=1;
while (i < 100)
{
println(j + " : " + i);
i*=5;
j+=1;
}
it seems you guys likes functional so how about a recursive solution?
#tailrec def quints(n:Int): Unit = {
println(n);
if (n*5<100) quints(n*5);
}
Update: Thanks for spotting the error... it should of course be power, not multiply:
Annoyingly, there doesn't seem to be an integer pow function in the standard library!
Try this:
def pow5(i:Int) = math.pow(5,i).toInt
Iterator from 1 map pow5 takeWhile (100>=) toList
Or if you want to use it in-place:
Iterator from 1 map pow5 takeWhile (100>=) foreach {
j => println("number:" + j)
}
and with the indices:
val iter = Iterator from 1 map pow5 takeWhile (100>=)
iter.zipWithIndex foreach { case (j, i) => println(i + " = " + j) }
(0 to 2).map (math.pow (5, _).toInt).zipWithIndex
res25: scala.collection.immutable.IndexedSeq[(Int, Int)] = Vector((1,0), (5,1), (25,2))
produces a Vector, with i,j in reversed order.