# Scala algorithm: Find the contiguous slice with the minimum average

Published , last updated

## Algorithm goal

In an array, find the contiguous slice that has the minimum average.

For example, $$[3, 1, 9, 1, 2]$$ has slices:

1. $$[3, 1]$$, average $$2$$.
2. $$[3, 1, 9]$$, average $$4.33$$.
3. $$[3, 1, 9, 1]$$, average $$3.5$$.
4. $$[3, 1, 9, 1, 2]$$, average $$3.2$$.
5. $$[1, 9]$$, average $$5$$.
6. $$[1, 9, 1]$$, average $$3.67$$.
7. $$[1, 9, 1, 2]$$, average $$3.25$$.
8. $$[9, 1]$$, average $$5$$.
9. $$[9, 1, 2]$$, average $$4$$.
10. $$[1, 2]$$, average $$1.5$$.

The slice with the minimum average is $$[1, 2]$$ because it has minimum average of $$1.5$$.

This is similar to Codility's MinAvgTwoSlice problem.

## Test cases in Scala

assert(findMinAvgSlice() == None)
assert(findMinAvgSlice(1) == None)
assert(findMinAvgSlice(1, 2) == Some(SubSlice(startIndex = 0, List(1, 2))))
assert(
findMinAvgSlice(3, 1, 2) == Some(SubSlice(startIndex = 1, List(1, 2)))
)
assert(
findMinAvgSlice(3, 1, 1, 2) == Some(SubSlice(startIndex = 1, List(1, 1)))
)
assert(
findMinAvgSlice(3, 1, 2, 1, 2) ==
Some(SubSlice(startIndex = 1, List(1, 2, 1)))
)
assert(
findMinAvgSlice(3, 1, 9, 1, 2) ==
Some(SubSlice(startIndex = 3, List(1, 2)))
)
assert(
findMinAvgSlice(Int.MaxValue, Int.MaxValue, 1, 2) ==
Some(SubSlice(startIndex = 2, List(1, 2)))
)
assert(
findMinAvgSlice(3, 4, Int.MinValue, Int.MinValue, 1, 2) ==
Some(SubSlice(startIndex = 2, List(Int.MinValue, Int.MinValue)))
)


## Algorithm in Scala

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## Explanation

We could find the solution using a brute-force search which would be computationally expensive because it means for every starting element, we have to consider nearly N other elements, so our complexity would be at least $$O(n^2)$$.

However, this (and similar problems like MaximumProfitStockPrices), are often mathematical in nature, and it is wise to have some mathematics in your toolbox to find a more optimal algorithm, which you will find here: (this is © from www.scala-algorithms.com)

### Mathematics

Suppose $$V(p, l)$$ is the average of $$l$$ numbers starting at position $$p$$. For example, $$V(3, 2)$$ is $$(A_3 + A_4) \div 2$$, where $$A_i$$ is the $$i$$th element of the input array.

Consider that a slice is of minimum length 2. If the next number decreases our average, then we get a slice of length $$3$$.

However, if we extend it by 2, and it decreases our average, we get the following equation:

$$V(p, 4) < V(p, 2) \implies 2 (A_p + A_{p+1} + A_{p+2} + A_{p+3}) < 4(A_p + A_{p+1})$$.

$$\implies 2(A_{p+2} + A_{p+3}) < 2(A_p + A_{p+1})$$, which would mean that we have just found a new and smaller slice of size 2.

## 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. ### Drop, Take, dropRight, takeRight

Scala's drop and take methods typically remove or select n items from a collection.

assert(List(1, 2, 3).drop(2) == List(3))

assert(List(1, 2, 3).take(2) == List(1, 2))

assert(List(1, 2, 3).dropRight(2) == List(1))

assert(List(1, 2, 3).takeRight(2) == List(2, 3))

assert((1 to 5).take(2) == (1 to 2))

3. ### 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)

4. ### 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")

5. ### Sliding / Sliding Window

Get fixed-length sliding sub-sequences (sliding windows) from another sequence

6. ### View

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

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