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I want to generate a list of Tuple2 objects. Each tuple (a,b) in the list should meeting the conditions:a and b both are perfect squares,(b/30)<a<b
and a>N and b>N ( N can even be a BigInt)
I am trying to write a scala function to generate the List of Tuples meeting the above requirements?
This is my attempt..it works fine for Ints and Longs..But for BigInt there is sqrt problem I am facing..Here is my approach in coding as below:
scala> def genTups(N:Long) ={
| val x = for(s<- 1L to Math.sqrt(N).toLong) yield s*s;
| val y = x.combinations(2).map{ case Vector(a,b) => (a,b)}.toList
| y.filter(t=> (t._1*30/t._2)>=1)
| }
genTups: (N: Long)List[(Long, Long)]
scala> genTups(30)
res32: List[(Long, Long)] = List((1,4), (1,9), (1,16), (1,25), (4,9), (4,16), (4,25), (9,16), (9,25), (16,25))
Improved this using BigInt square-root algorithm as below:
def genTups(N1:BigInt,N2:BigInt) ={
def sqt(n:BigInt):BigInt = {
var a = BigInt(1)
var b = (n>>5)+BigInt(8)
while((b-a) >= 0) {
var mid:BigInt = (a+b)>>1
if(mid*mid-n> 0) b = mid-1
else a = mid+1
}; a-1 }
val x = for(s<- sqt(N1) to sqt(N2)) yield s*s;
val y = x.combinations(2).map{ case Vector(a,b) => (a,b)}.toList
y.filter(t=> (t._1*30/t._2)>=1)
}
I appreciate any help to improve in my algorithm .
You can avoid sqrt in you algorithm by changing the way you calculate x to this:
val x = (BigInt(1) to N).map(x => x*x).takeWhile(_ <= N)
The final function is then:
def genTups(N: BigInt) = {
val x = (BigInt(1) to N).map(x => x*x).takeWhile(_ <= N)
val y = x.combinations(2).map { case Vector(a, b) if (a < b) => (a, b) }.toList
y.filter(t => (t._1 * 30 / t._2) >= 1)
}
You can also re-write this as a single chain of operations like this:
def genTups(N: BigInt) =
(BigInt(1) to N)
.map(x => x * x)
.takeWhile(_ <= N)
.combinations(2)
.map { case Vector(a, b) if a < b => (a, b) }
.filter(t => (t._1 * 30 / t._2) >= 1)
.toList
In a quest for performance, I came up with this recursive version that appears to be significantly faster
def genTups(N1: BigInt, N2: BigInt) = {
def sqt(n: BigInt): BigInt = {
var a = BigInt(1)
var b = (n >> 5) + BigInt(8)
while ((b - a) >= 0) {
var mid: BigInt = (a + b) >> 1
if (mid * mid - n > 0) {
b = mid - 1
} else {
a = mid + 1
}
}
a - 1
}
#tailrec
def loop(a: BigInt, rem: List[BigInt], res: List[(BigInt, BigInt)]): List[(BigInt, BigInt)] =
rem match {
case Nil => res
case head :: tail =>
val a30 = a * 30
val thisRes = rem.takeWhile(_ <= a30).map(b => (a, b))
loop(head, tail, thisRes.reverse ::: res)
}
val squares = (sqt(N1) to sqt(N2)).map(s => s * s).toList
loop(squares.head, squares.tail, Nil).reverse
}
Each recursion of the loop adds all the matching pairs for a given value of a. The result is built in reverse because adding to the front of a long list is much faster than adding to the tail.
Firstly create a function to check if number if perfect square or not.
def squareRootOfPerfectSquare(a: Int): Option[Int] = {
val sqrt = math.sqrt(a)
if (sqrt % 1 == 0)
Some(sqrt.toInt)
else
None
}
Then, create another func that will calculate this list of tuples according to the conditions mentioned above.
def generateTuples(n1:Int,n2:Int)={
for{
b <- 1 to n2;
a <- 1 to n1 if(b>a && squareRootOfPerfectSquare(b).isDefined && squareRootOfPerfectSquare(a).isDefined)
} yield ( (a,b) )
}
Then on calling the function with parameters generateTuples(5,10)
you will get an output as
res0: scala.collection.immutable.IndexedSeq[(Int, Int)] = Vector((1,4), (1,9), (4,9))
Hope that helps !!!
What is a nice and efficient functional way of solving the following problem? In imperative style, this can be done in linear time.
Given two sorted sequences p and q, f returns a sequence r (or any collection) of triples where for every triple (a,b,c) in r, the following hold:
(a < b < c)
One of the following two holds:
a,c are two consecutive elements p, and b is in q
a,c are two consecutive elements q, and b is in p
Example: Consider the following two sequences.
val p = Seq(1,4,5,7,8,9)
val q = Seq(2,3,6,7,8,10)
Then f(p,s) computes the following sequence:
Seq((1,2,4), (1,3,4), (5,6,7), (3,4,6), (3,5,6), (8,9,10))
Current solution: I do not find this one very elegant. I am looking for a better one.
def consecutiveTriplesOneWay(s1: Seq[Int], s2:Seq[Int]) = {
for {
i <- 0 until s1.size - 1 if s1(i) < s1(i+1)
j <- 0 until s2.size if s1(i) < s2(j) && s2(j) < s1(i+1)
} yield (s1(i), s2(j), s1(i+1))
}
def consecutiveTriples(s1: Seq[Int], s2:Seq[Int]) =
consecutiveTriplesOneWay(s1, s2) ++ consecutiveTriplesOneWay(s2, s1)
def main(args: Array[String]) {
val p = Seq(1,4,5,7,8,9)
val q = Seq(2,3,6,7,8,10)
consecutiveTriples(p, q).foreach(println(_))
}
Edit: My imperative solution
def consecutiveTriplesOneWayImperative(s1: Seq[Int], s2:Seq[Int]) = {
var i = 0
var j = 0
val triples = mutable.MutableList.empty[(Int,Int,Int)]
while (i < s1.size - 1 && j < s2.size) {
if (s1(i) < s2(j) && s2(j) < s1(i + 1)) {
triples += ((s1(i), s2(j), s1(i + 1)))
j += 1
} else if (s1(i) >= s2(j))
j += 1
else
i += 1
}
triples.toSeq
}
def consecutiveTriples(s1: Seq[Int], s2:Seq[Int]) =
consecutiveTriplesOneWayImperative(s1,s2) ++
consecutiveTriplesOneWayImperative(s2,s1)
Imperative solution translated to tailrec. Bit verbose but works
def consecutiveTriplesRec(s1: Seq[Int], s2: Seq[Int]) = {
#tailrec
def consTriplesOneWay(left: Seq[Int], right: Seq[Int],
triples: Seq[(Int, Int, Int)]): Seq[(Int, Int, Int)] = {
(left, right) match {
case (l1 :: l2 :: ls, r :: rs) =>
if (l1 < r && r < l2) consTriplesOneWay(left, rs, (l1, r, l2) +: triples)
else if (l1 >= r) consTriplesOneWay(left, rs, triples)
else consTriplesOneWay(l2 :: ls, right, triples)
case _ => triples
}
}
consTriplesOneWay(s1, s2, Nil) ++ consTriplesOneWay(s2, s1, Nil)
}
I have to write a method "all()" which returns a list of tuples; each tuple will contain the row, column and set relevant to a particular given row and column, when the function meets a 0 in the list. I already have written the "hyp" function which returns the set part I need, eg: Set(1,2). I am using a list of lists:
| 0 | 0 | 9 |
| 0 | x | 0 |
| 7 | 0 | 8 |
If Set (1,2) are referring to the cell marked as x, all() should return: (1,1, Set(1,2)) where 1,1 are the index of the row and column.
I wrote this method by using zipWithIndex. Is there any simpler way how to access an index as in this case without zipWithIndex? Thanks in advance
Code:
def all(): List[(Int, Int, Set[Int])] =
{
puzzle.list.zipWithIndex flatMap
{
rowAndIndex =>
rowAndIndex._1.zipWithIndex.withFilter(_._1 == 0) map
{
colAndIndex =>
(rowAndIndex._2, colAndIndex._2, hyp(rowAndIndex._2, colAndIndex._2))
}
}
}
The (_._1 == 0 ) is because the function has to return the (Int,Int, Set()) only when it finds a 0 in the grid
It's fairly common to use zipWithIndex. Can minimise wrestling with Tuples/Pairs through pattern matching vars within the tuple:
def all(grid: List[List[Int]]): List[(Int, Int, Set[Int])] =
grid.zipWithIndex flatMap {case (row, r) =>
row.zipWithIndex.withFilter(_._1 == 0) map {case (col, c) => (r, c, hyp(r, c))}
}
Can be converted to a 100% equivalent for-comprehension:
def all(grid: List[List[Int]]): List[(Int, Int, Set[Int])] =
for {(row, r) <- grid.zipWithIndex;
(col, c) <- row.zipWithIndex if (col == 0)} yield (r, c, hyp(r, c))
Both of above produce the same compiled code.
Note that your requirement means that all solutions are minimum O(n) = O(r*c) - you must visit each and every cell. However the overall behaviour of user60561's answer is O(n^2) = O((r*c)^2): for each cell, there's an O(n) lookup in list(x)(y):
for{ x <- list.indices
y <- list(0).indices
if list(x)(y) == 0 } yield (x, y, hyp(x, y))
Here's similar (imperative!) logic, but O(n):
var r, c = -1
for{ row <- list; col <- row if col == 0} yield {
r += 1
c += 1
(r, c, hyp(r, c))
}
Recursive version (uses results-accumulator to enable tail-recursion):
type Grid = List[List[Int]]
type GridHyp = List[(Int, Int, Set[Int])]
def all(grid: Grid): GridHyp = {
def rowHypIter(row: List[Int], r: Int, c: Int, accum: GridHyp) = row match {
case Nil => accum
case col :: othCols => rowHypIter(othCols, r, c + 1, hyp(r, c) :: accum)}
def gridHypIter(grid: Grid, r: Int, accum: GridHyp) = grid match {
case Nil => accum
case row :: othRows => gridHypIter(othRows, r + 1, rowHyp(row, r, 0, accum))}
gridHypIter(grid, 0, Nil)
}
'Monadic' logic (flatmap/map/withFilter OR equivalent for-comprehensions) is often/usually neater than recursion + pattern-matching - evident here.
The simplest way I can think of is just a classic for loop:
for{ x <- list.indices
y <- list(0).indices
if list(x)(y) == 0 } yield (x, y, hyp(x, y))
It assumes that your second dimension is of an uniform size. With this code, I would also recommend you use an Array or Vector if your grid sizes are larger then 100 or so because list(x)(y) is a O(n) operation.
In Scala language, I want to write a function that yields odd numbers within a given range. The function prints some log when iterating even numbers. The first version of the function is:
def getOdds(N: Int): Traversable[Int] = {
val list = new mutable.MutableList[Int]
for (n <- 0 until N) {
if (n % 2 == 1) {
list += n
} else {
println("skip even number " + n)
}
}
return list
}
If I omit printing logs, the implementation become very simple:
def getOddsWithoutPrint(N: Int) =
for (n <- 0 until N if (n % 2 == 1)) yield n
However, I don't want to miss the logging part. How do I rewrite the first version more compactly? It would be great if it can be rewritten similar to this:
def IWantToDoSomethingSimilar(N: Int) =
for (n <- 0 until N) if (n % 2 == 1) yield n else println("skip even number " + n)
def IWantToDoSomethingSimilar(N: Int) =
for {
n <- 0 until N
if n % 2 != 0 || { println("skip even number " + n); false }
} yield n
Using filter instead of a for expression would be slightly simpler though.
I you want to keep the sequentiality of your traitement (processing odds and evens in order, not separately), you can use something like that (edited) :
def IWantToDoSomethingSimilar(N: Int) =
(for (n <- (0 until N)) yield {
if (n % 2 == 1) {
Option(n)
} else {
println("skip even number " + n)
None
}
// Flatten transforms the Seq[Option[Int]] into Seq[Int]
}).flatten
EDIT, following the same concept, a shorter solution :
def IWantToDoSomethingSimilar(N: Int) =
(0 until N) map {
case n if n % 2 == 0 => println("skip even number "+ n)
case n => n
} collect {case i:Int => i}
If you will to dig into a functional approach, something like the following is a good point to start.
First some common definitions:
// use scalaz 7
import scalaz._, Scalaz._
// transforms a function returning either E or B into a
// function returning an optional B and optionally writing a log of type E
def logged[A, E, B, F[_]](f: A => E \/ B)(
implicit FM: Monoid[F[E]], FP: Pointed[F]): (A => Writer[F[E], Option[B]]) =
(a: A) => f(a).fold(
e => Writer(FP.point(e), None),
b => Writer(FM.zero, Some(b)))
// helper for fixing the log storage format to List
def listLogged[A, E, B](f: A => E \/ B) = logged[A, E, B, List](f)
// shorthand for a String logger with List storage
type W[+A] = Writer[List[String], A]
Now all you have to do is write your filtering function:
def keepOdd(n: Int): String \/ Int =
if (n % 2 == 1) \/.right(n) else \/.left(n + " was even")
You can try it instantly:
scala> List(5, 6) map(keepOdd)
res0: List[scalaz.\/[String,Int]] = List(\/-(5), -\/(6 was even))
Then you can use the traverse function to apply your function to a list of inputs, and collect both the logs written and the results:
scala> val x = List(5, 6).traverse[W, Option[Int]](listLogged(keepOdd))
x: W[List[Option[Int]]] = scalaz.WriterTFunctions$$anon$26#503d0400
// unwrap the results
scala> x.run
res11: (List[String], List[Option[Int]]) = (List(6 was even),List(Some(5), None))
// we may even drop the None-s from the output
scala> val (logs, results) = x.map(_.flatten).run
logs: List[String] = List(6 was even)
results: List[Int] = List(5)
I don't think this can be done easily with a for comprehension. But you could use partition.
def getOffs(N:Int) = {
val (evens, odds) = 0 until N partition { x => x % 2 == 0 }
evens foreach { x => println("skipping " + x) }
odds
}
EDIT: To avoid printing the log messages after the partitioning is done, you can change the first line of the method like this:
val (evens, odds) = (0 until N).view.partition { x => x % 2 == 0 }
I want to implement a lazy iterator that yields the next element in each call, in a 3-level nested loop.
Is there something similar in scala to this snippet of c#:
foreach (int i in ...)
{
foreach (int j in ...)
{
foreach (int k in ...)
{
yield return do(i,j,k);
}
}
}
Thanks, Dudu
Scala sequence types all have a .view method which produces a lazy equivalent of the collection. You can play around with the following in the REPL (after issuing :silent to stop it from forcing the collection to print command results):
def log[A](a: A) = { println(a); a }
for (i <- 1 to 10) yield log(i)
for (i <- (1 to 10) view) yield log(i)
The first will print out the numbers 1 to 10, the second will not until you actually try to access those elements of the result.
There is nothing in Scala directly equivalent to C#'s yield statement, which pauses the execution of a loop. You can achieve similar effects with the delimited continuations which were added for scala 2.8.
If you join iterators together with ++, you get a single iterator that runs over both. And the reduceLeft method helpfully joins together an entire collection. Thus,
def doIt(i: Int, j: Int, k: Int) = i+j+k
(1 to 2).map(i => {
(1 to 2).map(j => {
(1 to 2).iterator.map(k => doIt(i,j,k))
}).reduceLeft(_ ++ _)
}).reduceLeft(_ ++ _)
will produce the iterator you want. If you want it to be even more lazy than that, you can add .iterator after the first two (1 to 2) also. (Replace each (1 to 2) with your own more interesting collection or range, of course.)
You can use a Sequence Comprehension over Iterators to get what you want:
for {
i <- (1 to 10).iterator
j <- (1 to 10).iterator
k <- (1 to 10).iterator
} yield doFunc(i, j, k)
If you want to create a lazy Iterable (instead of a lazy Iterator) use Views instead:
for {
i <- (1 to 10).view
j <- (1 to 10).view
k <- (1 to 10).view
} yield doFunc(i, j, k)
Depending on how lazy you want to be, you may not need all of the calls to iterator / view.
If your 3 iterators are generally small (i.e., you can fully iterate them without concern for memory or CPU) and the expensive part is computing the result given i, j, and k, you can use Scala's Stream class.
val tuples = for (i <- 1 to 3; j <- 1 to 3; k <- 1 to 3) yield (i, j, k)
val stream = Stream(tuples: _*) map { case (i, j, k) => i + j + k }
stream take 10 foreach println
If your iterators are too large for this approach, you could extend this idea and create a Stream of tuples that calculates the next value lazily by keeping state for each iterator. For example (although hopefully someone has a nicer way of defining the product method):
def product[A, B, C](a: Iterable[A], b: Iterable[B], c: Iterable[C]): Iterator[(A, B, C)] = {
if (a.isEmpty || b.isEmpty || c.isEmpty) Iterator.empty
else new Iterator[(A, B, C)] {
private val aItr = a.iterator
private var bItr = b.iterator
private var cItr = c.iterator
private var aValue: Option[A] = if (aItr.hasNext) Some(aItr.next) else None
private var bValue: Option[B] = if (bItr.hasNext) Some(bItr.next) else None
override def hasNext = cItr.hasNext || bItr.hasNext || aItr.hasNext
override def next = {
if (cItr.hasNext)
(aValue get, bValue get, cItr.next)
else {
cItr = c.iterator
if (bItr.hasNext) {
bValue = Some(bItr.next)
(aValue get, bValue get, cItr.next)
} else {
aValue = Some(aItr.next)
bItr = b.iterator
(aValue get, bValue get, cItr.next)
}
}
}
}
}
val stream = product(1 to 3, 1 to 3, 1 to 3).toStream map { case (i, j, k) => i + j + k }
stream take 10 foreach println
This approach fully supports infinitely sized inputs.
I think the below code is what you're actually looking for... I think the compiler ends up translating it into the equivalent of the map code Rex gave, but is closer to the syntax of your original example:
scala> def doIt(i:Int, j:Int) = { println(i + ","+j); (i,j); }
doIt: (i: Int, j: Int)(Int, Int)
scala> def x = for( i <- (1 to 5).iterator;
j <- (1 to 5).iterator ) yield doIt(i,j)
x: Iterator[(Int, Int)]
scala> x.foreach(print)
1,1
(1,1)1,2
(1,2)1,3
(1,3)1,4
(1,4)1,5
(1,5)2,1
(2,1)2,2
(2,2)2,3
(2,3)2,4
(2,4)2,5
(2,5)3,1
(3,1)3,2
(3,2)3,3
(3,3)3,4
(3,4)3,5
(3,5)4,1
(4,1)4,2
(4,2)4,3
(4,3)4,4
(4,4)4,5
(4,5)5,1
(5,1)5,2
(5,2)5,3
(5,3)5,4
(5,4)5,5
(5,5)
scala>
You can see from the output that the print in "doIt" isn't called until the next value of x is iterated over, and this style of for generator is a bit simpler to read/write than a bunch of nested maps.
Turn the problem upside down. Pass "do" in as a closure. That's the entire point of using a functional language
Iterator.zip will do it:
iterator1.zip(iterator2).zip(iterator3).map(tuple => doSomething(tuple))
Just read the 20 or so first related links that are show on the side (and, indeed, where shown to you when you first wrote the title of your question).