# Scala algorithm: Single-elimination tournament tree

Published

## Algorithm goal

The single-elimination tournament is popular in team games. Represent a tournament tree which enables us to know what games to expect next, and who the overall winner of the tournament is, once the wins have been submitted. Here is a visual representation:

## Test cases in Scala

``````assert(
tourney.nextGames == Set(Drakas -> Lucas),
"The first iteration has a specific next game"
)
assert(tourney.winner.isEmpty, "The first iteration does not have a winner")
assert(
tourney.win(Sanzo).nextGames == tourney.nextGames,
"A win by an unscheduled player does nothing to affect next games"
)
assert(
tourney.win(Sanzo).winner.isEmpty,
"A win by an unscheduled player does not give a new winner"
)
assert(
tourney.win(Drakas).nextGames == Set(Drakas -> Sanzo),
"A Drakas win pushes the next game to be Drakas v Sanzo"
)
assert(
tourney.win(Drakas).winner.isEmpty,
"A Drakas win still does not yield an overall winner"
)
assert(
tourney.win(Drakas).win(Drakas).nextGames.isEmpty,
"Drakas win 2x means final stage has no more expected games"
)
assert(
tourney.win(Drakas).win(Drakas).winner.contains(Drakas),
"Drakas win 2x means he is now set a winner of the tournament"
)
``````

## Algorithm in Scala

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

## Explanation

There are two aspects of this algorithm: first is to build the tree in-memory, the second is to process inputs in each iteration.

In building the tree, we take every 2 sibling players, and create a sub-tournament. Then each sibling sub-tournament gets combined with the next; we repeat until we are left with no siblings, and that becomes the root of our tournament tree. (this is Â© from www.scala-algorithms.com)

The leaf nodes are filled in, so they are 'DefinedPlayer', and those games that were not played yet are 'UndefinedPlayer'. Each 'UndefinedPlayer' has a left and a right, which represent the sub-trees that are either defined or not defined by themselves. When both children of an Undefined are defined, it means we now expect a face-off.

## Scala concepts & Hints

1. ### Collect

'collect' allows you to use Pattern Matching, to filter and map items.

``````assert("Hello World".collect {
case character if Character.isUpperCase(character) => character.toLower
} == "hw")
``````
2. ### 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)
``````
3. ### 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")
``````
4. ### 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)
``````
5. ### State machine

A state machine is the use of `sealed trait` to represent all the possible states (and transitions) of a 'machine' in a hierarchical form.

6. ### 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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