# Counting valleys traversed below sea level, given elevation changes

Gary is an avid hiker. He tracks his hikes meticulously, paying close attention to small details like topography. During his last hike he took exactly steps. For every step he took, he noted if it was an uphill, or a downhill, step. Gary's hikes start and end at sea level and each step up or down represents a unit change in altitude. We define the following terms:

A mountain is a sequence of consecutive steps above sea level, starting with a step up from sea level and ending with a step down to sea level. A valley is a sequence of consecutive steps below sea level, starting with a step down from sea level and ending with a step up to sea level. Given Gary's sequence of up and down steps during his last hike, find and print the number of valleys he walked through.

For example, if Gary's path is, he first enters a valley units deep. Then he climbs out an up onto a mountain units high. Finally, he returns to sea level and ends his hike.

### Function Description

Complete the countingValleys function in the editor below. It must return an integer that denotes the number of valleys Gary traversed.

countingValleys has the following parameter(s):

• n: the number of steps Gary takes
• s: a string describing his path

### Input Format

The first line contains an integer, the number of steps in Gary's hike. The second line contains a single string, of characters that describe his path.

### Output Format

Print a single integer that denotes the number of valleys Gary walked through during his hike.

My solution goes like this :

def countingValleys(n: Int, s: String): Int = {
def rec(path: List[Char], counter: Int, valleys: Int): Int = {
path match  {
case Nil => valleys
case x::xs if (x == 'U') && ((counter + 1) == 0) =>
rec(xs, counter+1, valleys+1 )
case x::xs if x == 'U' => rec(xs, counter +1, valleys)
case x::xs if x == 'D' => rec(xs, counter -1, valleys)
}
}
rec(s.toList, 0, 0)
}


Sample Input:

8
UDDDUDUU


Sample Output:

1


I wonder if there is a more idiomatic solution in functional programming style.

• Side question about the problem - is the number of steps (n) redundant information? Won't that always be s.length? Jul 14 '19 at 19:10
• Yes, you are absolutely correct. Function was provided this way. I will report the question on Hacker-Rank. Jul 15 '19 at 5:10
• @Sandio adding n as an additional information is necessary for languages like C++ that don't perform the same level of behind-the-scenes memory management as other languages Jul 16 '19 at 10:08
• Oh. That makes sense. @Vogel612 Thank you for the information. Jul 16 '19 at 21:02

Your counter is a cumulative sum of elevation changes; elevation would be a more precise name for it.

Ultimately, the goal is to count the number of times the elevation changes from -1 to 0. To do that:

1. Translate the 'U' and 'D' steps into +1 and -1, respectively.
2. Obtain a sequence representing the elevation profile of the hike using Seq.scan.
3. Count the number of times -1 is followed by 0 in the elevation profile, using Seq.sliding(2) and Iterator.count.
def countingValleys(n: Int, s: String): Int = s
.map(_ match {case 'U' => +1; case 'D' => -1})
.scan(0)(_+_)
.sliding(2)
.count(_ == Vector(-1, 0))

• This is so out of the box. Thank you. Jul 15 '19 at 7:27

There's nothing wrong with or "not functional" about your approach. This might be opinion territory, but personally I would consider using foldLeft as it might be more readable and you can potentially eliminate some of the complexity of your cases.

(also I got rid of n here as it is completely irrelevant, I know it's a problem from a website so you have to follow the format they gave you)

def countingValleys (steps: String): Int = steps
.foldLeft((0, 0)) {
case ((valleys, elevation), 'D') => (valleys, elevation - 1)
case ((valleys, -1), 'U') => (valleys + 1, 0)
case ((valleys, elevation), _) => (valleys, elevation + 1)
}
._1

• Thank you for your solution. It is helpful. Jul 15 '19 at 7:29
• Note that the original code's counter is what you call depth. That's a bit confusing, since positive depth represents higher elevation. Also, the original code's valleys is what you call counter. I think valleys was a clearer name. Jul 16 '19 at 5:40
• @200_success good point on the naming, updated. Jul 16 '19 at 12:13