Algorithms - Basic

Elementary Data Structures Abstract Data Types Java provides many abstract data types, for example in the java.util package. This exam does not refer to the built-in collections, but to your own classes. Recursion

• Define recursion (note: to define recursion, you first need to define recursion - Anonymous)
• Identify obvious cases of false recursion (that could be implemented with a loop and no stack).
• Detect incorrect stop conditions that create never ending recursion.
• Implement recursion for solving problems.
  For example:
  • Compute a factorial
  • Euclid: find the greatest common divisor
  • Evaluate a prefix expression (simple example of recursive descent parser). e.g. +2,3 (which equals 5).
  • Find the greatest number of an array (false recursion)
  • Move towers of Hanoi.
  • Binary search in an ordered array.

Trees

• Define:
  • node, child/parent node, root, leaf,
  • path, height,
  • binary tree, ordered tree.
• Implement a tree representation
• Write an algorithm that:
  • Traverses a binary tree: preorder, inorder, postorder,
  • computes the height or the amount of nodes of a tree,
  • finds an element in a binary search tree,
  • constructs a tournament tree (from an array).

Sorting

• Define a stable sort.
• Identify and implement:
  • Selection sort.
  • Insertion sort.

Note: Java provides sorting algorithms, for example in the java.util package. This exam does not refer to these built-in algorithms, and require no knowledge about interfaces as Comparable.