Functional programming examples using Scala

Recursion

Pascal's Triangle

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

Calculates Pascal's Triangle given a valid column and row. A Test Suite is also included.

Parentheses Balancing

A recursive function ( Test Suite) that tests whether the parentheses in a string are balanced. Valid cases include:

• hello(world())
• `some text with (some content in brackets).

Invalid cases:

• :-(
• )(()

Calculating Change (as in for money)

Given a set of possible coin denominations, count all (Test Suite) the possible ways to give change for a given amount x.

Example:
denominations: 1,2
change amount: 4
solutions: [1+1+1+1, 2+2, 1+1+2]
function return value: 3 - (3 possible solutions)

Functional Sets

Sets can be defined as a function. In other words you could write a function that represents the values included in a set, this is called a characteristic function. For example an integer set can be defined by a function that returns a boolean value based on whether a given integer exists in the set.

type Set = Int => Boolean

The first step is to define a set (Test Suite ) that can only contain 1 integer a singletonSet then define functions to build larger sets from the singletonSet namely: union, intersect and diff. Finally implement the ability to query the set and to transform it via a forall and map function.