Scala algorithm: Compute nth row of Pascal's triangle

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Algorithm goal

In a Pascal's triangle, a number in a row is created by adding the two numbers directly above it; the first row is contains only 1, and the second row contains 1 and another 1.

This is a Pascal's triangle to its 5th row:

     1
    1 1
   1 2 1
  1 3 3 1
 1 4 6 4 1

The goal is to compute the nth row of the triangle.

Test cases in Scala

assert(nextRow(List(1, 1)) == List(1, 2, 1))
assert(pascalsTriangle(0) == List(1))
assert(pascalsTriangle(1) == List(1, 1))
assert(pascalsTriangle(2) == List(1, 2, 1))
assert(pascalsTriangle(3) == List(1, 3, 3, 1))
assert(pascalsTriangle(4) == List(1, 4, 6, 4, 1))

Algorithm in Scala

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Explanation

Breaking down the problem to its constituent part, we need to compute the next row from a previous row. Noticing the fact that the next row's items are really a sum of pairs of previous row's items, combined with previous row's items slightly shifted, notice that to go from row [1,2,1], we produce a new row which is [1, 2 + 1, 1 + 2, 1], which is [0 + 1, 1 + 2, 2 + 1, 1 + 0], which is [0, 1, 2, 1] + [ 1, 2, 1, 0 ].

Effectively, we just need to sum the original row with the original row slightly shifted (0 added). (this is © from www.scala-algorithms.com)

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Scala concepts & Hints

  1. Lazy List

    The 'LazyList' type (previously known as 'Stream' in Scala) is used to describe a potentially infinite list that evaluates only when necessary ('lazily').

  2. 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")
    
  3. Zip

    'zip' allows you to combine two lists pair-wise (meaning turn a pair of lists, into a list of pairs)

    It can be used over Arrays, Lists, Views, Iterators and other collections.

    assert(List(1, 2, 3).zip(List(5, 6, 7)) == List(1 -> 5, 2 -> 6, 3 -> 7))
    
    assert(List(1, 2).zip(List(5, 6, 7)) == List(1 -> 5, 2 -> 6))
    
    assert(List(5, 6).zipWithIndex == List(5 -> 0, 6 -> 1))
    
    assert(List(5, 6).zipAll(List('A'), 9, 'Z') == List(5 -> 'A', 6 -> 'Z'))
    
    assert(List(5).zipAll(List('A', 'B'), 1, 'Z') == List(5 -> 'A', 1 -> 'B'))
    

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Explore the 21 most useful Scala concepts

To save you going through various tutorials, we cherry-picked the most useful Scala concepts in a consistent form.

  1. Class Inside Class
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  4. Def Inside Def
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