Recursive Data Structures

Read this page. In the previous unit of our course we studied recursive algorithms. Recursion is a concept that also applies to data. Here we look at recursive data structures - lists, trees, and sets. A list is a structure that consists of elements linked together. If an element is linked to more than one element, the structure is a tree. If each element is linked to two (sub) elements, it is called a binary tree. Trees can be implemented using lists, as shown in the resource for this unit. Several examples of the wide applicability of lists are presented. A link points to all the remaining links, i.e. the rest of the list or the rest of the tree; thus, a link points to a list or to a tree - this is data recursion.

The efficiency of the programming process includes both running time and size of data. This page discusses the latter for recursive lists and trees.

Lastly, why read the last section on sets? Sets are another recursive data structure and the last section 2.7.6, indicates their connection with trees, namely, a set data type can be implemented in several different ways using a list or a tree data type. Thus, the programming process includes implementation decisions, in addition, to design or algorithm decisions. Each of these types of decisions is constrained by the features of the programming language used. The decision choices, such as which data structure to use, will impact efficiency and effectiveness of the program's satisfaction of the program's requirements.

Note: You will notice an unusual use of C++ here. What the author is doing is showing how to pass a fixed-value data-structure as a calling argument.

8. Recursive operations on pairs of quadtrees

We can use multirec to superimpose one quadtree on top of another: Our function will take a pair of quadtrees, using destructuring to extract one called left and the other called right:

const superimposeQuadTrees = multirec({
  indivisible: ({ left, right }) => isString(left),
  value: ({ left, right }) => right ==='⚫️'
                              ? right
                              : left,
  divide: ({ left, right }) => [
      { left: left.ul, right: right.ul },
      { left: left.ur, right: right.ur },
      { left: left.lr, right: right.lr },
      { left: left.ll, right: right.ll }
    ],
  combine: ([ul, ur, lr, ll]) => ({  ul, ur, lr, ll })
});

quadTreeToArray(
  superimposeQuadTrees({
    left: arrayToQuadTree(canvas),
    right: arrayToQuadTree(glider)
  })
)
  //=>
    ([
      ['⚪️', '⚪️', '⚪️', '⚪️'],
      ['⚪️', '⚫️', '⚪️', '⚪️'],
      ['⚫️', '⚪️', '⚪️', '⚫️'],
      ['⚫️', '⚫️', '⚫️', '⚫️']
    ])

Again, this feels like faffing about just so we can be recursive. But we are in position to do something interesting!