Scala algorithm: Binary search in a rotated sorted array

Published

Algorithm goal

This is a variation of BinarySearch, where the input array is rotated (RotateArrayRight).

For example, an input of [1,2,3,4], rotated could become [3,4,1,2].

Binary search runs in $$O(\log{n})$$, which is faster than a linear search ($$O(n)$$).

Test cases in Scala

assert(searchIn(Array.empty, 7) == None)
assert(searchIn(Array(7, 1), 7) == Some(0))
assert(searchIn(Array(9, 1, 7), 7) == Some(2))
assert(searchIn(Array(7, 9, 1), 7) == Some(0))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 7) == Some(1))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 1) == Some(4))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 10) == None)
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 9) == Some(3))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 4) == Some(7))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 5), 5) == Some(7))


Algorithm in Scala

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

Explanation

The Scala implementation uses the Range concept in order to achieve a more terse solution, in particular by defining the range for the next iteration in terms of the previous range, rather than dealing with raw indices.

This is a very powerful concept because you notice that in Scala, algorithms can be quite self-explanatory whereas in some C/Python algorithm implementations one would have to refer to documentation and comments for an explanation. Documentability is crucial in sharing knowledge. (this is © from www.scala-algorithms.com)

The variation requires us to capture the case where our range is still uneven. In this case, the code explains the story

Scala concepts & Hints

1. Def Inside Def

A great aspect of Scala is being able to declare functions inside functions, making it possible to reduce repetition.

def exampleDef(input: String): String = {
def surroundInputWith(char: Char): String = s"$char$input\$char"
surroundInputWith('-')
}

assert(exampleDef("test") == "-test-")


It is also frequently used in combination with Tail Recursion.

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. Range

The (1 to n) syntax produces a "Range" which is a representation of a sequence of numbers.

assert((1 to 5).toString == "Range 1 to 5")

assert((1 to 5).reverse.toString() == "Range 5 to 1 by -1")

assert((1 to 5).toList == List(1, 2, 3, 4, 5))

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. 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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