# Scala algorithm: Make a queue using stacks (Lists in Scala)

Published

## Algorithm goal

Make a pure-functional queue using stacks (Lists). It would have the following methods: isEmpty: Boolean, enqueue(T), dequeue: Option[(T, Queue[T])].

Try to make it efficient, where possible.

## Test cases in Scala

assert(Queue.empty.isEmpty)
assert(Queue.empty.enqueue("A").dequeue.contains("A" -> Queue.empty))
assert(
Queue.empty.enqueue("A").enqueue("B").dequeue.map(_._1).contains("A")
)
assert(
Queue.empty
.enqueue("A")
.enqueue("B")
.dequeue
.map(_._2)
.flatMap(_.dequeue)
.map(_._1)
.contains("B")
)
assert(
Queue.empty
.enqueue("A")
.enqueue("B")
.dequeue
.map(_._2)
.flatMap(_.dequeue)
.map(_._2)
.flatMap(_.dequeue)
.isEmpty
)
assert(
Queue.empty
.enqueue("A")
.enqueue("B")
.dequeue
.map(_._2.enqueue("C"))
.flatMap(_.dequeue)
.map(_._1)
.contains("B")
)
assert(
Queue.empty
.enqueue("A")
.enqueue("B")
.dequeue
.map(_._2.enqueue("C"))
.flatMap(_.dequeue)
.map(_._2)
.flatMap(_.dequeue)
.map(_._1)
.contains("C")
)
assert(
Queue.empty
.enqueue("A")
.enqueue("B")
.dequeue
.map(_._2.enqueue("C"))
.flatMap(_.dequeue)
.map(_._2)
.flatMap(_.dequeue)
.map(_._2)
.flatMap(_.dequeue)
.isEmpty
)


## Algorithm in Scala

20 lines of Scala (compatible versions 2.13 & 3.0), showing how concise Scala can be!

## Explanation

The most straightforward implementation of a Queue would contain a single List, however in this case, we would have to choose between making enqueue fast, or making dequeue fast, because with a List, to get the tail element is an $$O(n)$$ operation.

However, there is a more efficient way, which is to use an 'incoming' and an 'outgoing' List: so long as 'outgoing' is not empty, we can destructure it at O(1) cost, and we can enqueue to 'incoming' at O(1) cost. The only time where we would face a cost would be when 'outgoing' is empty, and 'incoming' is non-empty: then, we would have to convert the 'incoming' to 'outgoing' by reversal, which is an O(n) operation. However, amortized, it would be more efficient than the biased approach. (this is © from www.scala-algorithms.com)

## Scala concepts & Hints

1. ### Option Type

The 'Option' type is used to describe a computation that either has a result or does not. In Scala, you can 'chain' Option processing, combine with lists and other data structures. For example, you can also turn a pattern-match into a function that return an Option, and vice-versa!

assert(Option(1).flatMap(x => Option(x + 2)) == Option(3))

assert(Option(1).flatMap(x => None) == None)

2. ### Pattern Matching

Pattern matching in Scala lets you quickly identify what you are looking for in a data, and also extract it.

assert("Hello World".collect {
case character if Character.isUpperCase(character) => character.toLower
} == "hw")

3. ### Stack Safety

Stack safety is present where a function cannot crash due to overflowing the limit of number of recursive calls.

This function will work for n = 5, but will not work for n = 2000 (crash with java.lang.StackOverflowError) - however there is a way to fix it :-)

In Scala Algorithms, we try to write the algorithms in a stack-safe way, where possible, so that when you use the algorithms, they will not crash on large inputs. However, stack-safe implementations are often more complex, and in some cases, overly complex, for the task at hand.

def sum(from: Int, until: Int): Int =
if (from == until) until else from + sum(from + 1, until)

def thisWillSucceed: Int = sum(1, 5)

def thisWillFail: Int = sum(1, 300)

4. ### Tail Recursion

In Scala, tail recursion enables you to rewrite a mutable structure such as a while-loop, into an immutable algorithm.

def fibonacci(n: Int): Int = {
@scala.annotation.tailrec
def go(i: Int, previous: Int, beforePrevious: Int): Int =
if (i >= n) previous else go(i + 1, previous + beforePrevious, previous)

go(i = 1, previous = 1, beforePrevious = 0)
}

assert(fibonacci(8) == 21)


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