In this post, we will solve **John and Fences HackerRank Solution**. This problem **(John and Fences)** is a part of **HackerRank Functional Programming** series.

**Task**

John’s house has bizarre fencing. There areÂ *N*Â fences. Though the contiguous fences have the constant width of 1 unit but their height varies. Height of these fences is represented by arrayÂ *H = [h _{1}, h_{2}… h_{N}]*.John’s house has bizarre fencing. There areÂ

*N*Â fences. Though the contiguous fences have the constant width of 1 unit but their height varies. Height of these fences is represented by arrayÂ

*H = [h*.

_{1}, h_{2}… h_{N}]John loves his fences but has to finally bow down to his wife’s repeated requests of replacing them with the regular fences. Before taking them down, John wants to keep some part of the fences as souvenir. He decides to carve out the largest rectangular area possible where the largest rectangle can be made of a number of contiguous fence. Note that sides of the rectangle should be parallel to *X* and *Y* axis.

Let’s say there are 6 fences, and their height is,Â *H*Â =Â *[2, 5, 7, 4, 1, 8]*. Then they can be represented as

```
__
8 __ | |
7 | | | |
6 __| | | |
5 | | |__ | |
4 | | | | | |
3 __| | | | | |
2 | | | | |__| |
1 |__|__|__|__|__|__|
h1 h2 h3 h4 h5 h6
```

Some possible carvings are as follow:

- If we carve rectangle fromÂ
*h1, h2 and h3*Â then we can get the max area of 2×3 = 6 units. - If we carve rectangle fromÂ
*h3, h4, h5 and h6*, then max area is 4×1 = 4 units. - If we carve rectangle fromÂ
*h2, h3 and h4*, then max area is 4×3 = 12, which is also the most optimal solution for this case.

**Input**

First line will contain an integerÂ *N*Â denoting the number of fences. It will be followed by a line containingÂ *N*Â space separated integers,Â *h _{1}Â h_{2}Â … h_{N}*, which represents the height of each fence.

**Output**

Print the maximum area of rectangle which can be carved out.

**Constraints**

- 1 â‰¤Â
*N*Â â‰¤ 10^{5} - 1 â‰¤Â
*h*Â â‰¤ 10_{i}^{4}

**Sample Input**

```
6
2 5 7 4 1 8
```

**Sample Output**

`12`

**Explanation**

John can carve a rectangle of height 4 from fence #2, #3 and #4, whose respective heights are 5, 7 and 4. So this will lead to a rectangle of area 3×4 = 12 units.

**Solution – John and Fences – HackerRank Solution**

**Scala**

import java.util.Scanner import scala.collection.immutable.TreeMap object Solution { def main(args: Array[String]): Unit = { val sc = new Scanner(System.in) val n = sc.nextInt val h = (0 until n).map(_ => sc.nextInt) sc.close() case class Fence(height: Int, pos: Int) val fences = h.indices.map(i => Fence(h(i), i)).sortBy(_.height).toList case class Accumulator(tree: TreeMap[Int, Int], bestSquare: Int) println( fences.foldLeft(Accumulator(TreeMap(0 -> n), 0))((acc, x) => { val (left, right) = acc.tree.rangeTo(x.pos).last Accumulator(acc.tree - left + (left -> x.pos) + (x.pos + 1 -> right), math.max(acc.bestSquare, (right - left) * x.height)) }).bestSquare ) } }

**Note: **This problem **(John and Fences)** is generated by **HackerRank** but the solution is provided by **CodingBroz**. This tutorial is only for **Educational** and **Learning** purpose.