# Scala algorithm: Maximum wait at a fuel station

Published

## Algorithm goal

Given a list of pump capacities, and a list of cars needing certain capacities (both in litres), determine the maximum waiting time for the cars at the gas station.

## Test cases in Scala

``````assert(Pump(1, Some(1)).consume == Pump(0))
assert(Pump(2, Some(2)).consume == Pump(1, Some(1)))
assert(maxWaitingTime(List(1), Vector(0)) == None)
assert(maxWaitingTime(List(1), Vector(1)) == Some(0))
assert(maxWaitingTime(List(1, 1), Vector(1)) == None)
assert(maxWaitingTime(List(1, 1), Vector(2)) == Some(1))
assert(
maxWaitingTime(List(1, 2, 1), Vector(2, 1)) == None,
"The sequence of cars cannot be fulfilled, as there is 1 litre extra needed"
)
assert(maxWaitingTime(List(1, 1, 2), Vector(4)) == Some(2))
assert(maxWaitingTime(List(1, 1, 1, 2), Vector(4)) == None)
assert(
maxWaitingTime(List(2, 8, 4, 3, 2), Vector(7, 11, 3)) == Some(8),
"Key example works"
)
assert(
Station(List(1), Vector(Pump(1))).tryCar
.contains(Station(Nil, Vector(Pump(1, Some(1))))),
"A car can be dequeued to an available pump"
)
assert(
Station(List(1), Vector(Pump(1))).tryCars ==
Station(Nil, Vector(Pump(1, Some(1)))),
"A car can be dequeued to an available pump for tryCars"
)
assert(
Station(List(1), Vector(Pump(1, Some(1)))).tryCar.isEmpty,
"A car cannot be dequeued when a pump is busy"
)
assert(
Station(List(2), Vector(Pump(1, None))).tryCar.isEmpty,
"A car cannot be dequeued when a pump does not have enough"
)
assert(
Station(List(1), Vector(Pump(1, Some(1)), Pump(1, None))).tryCar
.contains(Station(Nil, Vector(Pump(1, Some(1)), Pump(1, Some(1))))),
"A car be dequeued to another available pump"
)
``````

## Algorithm in Scala

50 lines of Scala (compatible versions 2.13 & 3.0).

## Explanation

We start test-first, by implement some basic expectations for 'maxWaitingTime'. Upon setting these up, we determine that this function is going to depend on the state of a 'Station' and the different 'Pumps' that are there.

'maxWaitingTime' assumes that cars will go to the first available fuel pump (they don't know how much is available, so try the first pump available). (this is Â© from www.scala-algorithms.com)

This algorithm is not so much a logical algorithm as it is a modeling problem, so it is highly recommended to go through each line of code, and then give it a go in implementing your own code against the unit tests for 'maxWaitingTime'.

## 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)
``````
5. ### View

The `.view` syntax creates a structure that mirrors another structure, until "forced" by an eager operation like .toList, .foreach, .forall, .count.

# Scala Algorithms: The most comprehensive library of algorithms in standard pure-functional Scala

## How our 100 algorithms look

1. A description/goal of the algorithm.
2. An explanation with both Scala and logical parts.
3. A proof or a derivation, where appropriate.
4. Links to Scala concepts used in this specific algorithm, also unit-tested.
5. An implementation in pure-functional immutable Scala, with efficiency in mind (for most algorithms, this is for paid subscribers only).
6. Unit tests, with a button to run them immediately in our in-browser IDE.

### Study our 100 Scala Algorithms: 6 fully free, 100 published & 0 upcoming

Fully unit-tested, with explanations and relevant concepts; new algorithms published about once a week.

### Explore the 22 most useful Scala concepts

To save you going through various tutorials, we cherry-picked the most useful Scala concepts in a consistent form.

## Subscribe to Scala Algorithms

Maximize your Scala with disciplined and consistently unit-tested solutions to 100+ algorithms.

Use it from improving your day-to-day data structures and Scala; all the way to interviewing.