VCE Algorithmics (HESS) study plan
VCE Algorithmics (HESS) · Give each week a clear focus.
8 weeks · About 6 hours per week
Unit 3
Define the characteristics of an algorithm (finiteness, definiteness, input, output, effectiveness) and test three sample procedures against them
Distinguish between algorithmic and heuristic solutions to a problem, giving two examples of each
Identify the inputs, outputs, and processing steps of a simple algorithm expressed in pseudocode
Trace the execution of a short iterative algorithm by hand, recording variable values at each step
Your checkpoint
A one-page reference sheet with the algorithm characteristics, a comparison table of algorithmic versus heuristic approaches, and a hand-traced execution table for two short pseudocode algorithms
Unit 3
Compare linear search and binary search by counting comparisons on data sets of 10, 100, and 1000 items
Explain why binary search requires sorted data and state the precondition explicitly
Implement linear search and binary search in a chosen programming language
Write a short argument explaining when a slower simple algorithm may still be preferable
Your checkpoint
A working code file containing both search algorithms plus a results table of comparison counts across the three data set sizes
Unit 3
Describe the properties of a graph including vertices, edges, directed and undirected edges, and weights
Represent the same small graph as an adjacency matrix and an adjacency list
Trace breadth-first search and depth-first search on a given graph, listing visit order
Compare the space requirements of adjacency matrix versus adjacency list representations
Your checkpoint
A hand-drawn graph with both representations plus written BFS and DFS traversal orders, checked against a code implementation
Unit 3 & Unit 4
Explain the difference between best-case, worst-case, and average-case analysis of an algorithm
Classify given functions into growth orders such as constant, logarithmic, linear, quadratic, and exponential
Derive the time complexity of nested loops and simple recursive functions by counting operations
Implement a naive recursive Fibonacci function and measure its run time for increasing inputs
Your checkpoint
A complexity analysis report covering five short code snippets, each with a justified Big-O classification and a brief explanation of the dominant operation
Unit 4
Explain the divide-and-conquer strategy and identify its three stages in merge sort and quicksort
Trace quicksort partitioning on a small list, showing the pivot and the state after each swap
Trace merge sort on a small list, showing the splitting and merging stages
Compare the worst-case time complexity of merge sort and quicksort and explain the causes
Your checkpoint
A step-by-step trace of both sorting algorithms on the same eight-element list, with the number of comparisons counted for each
Unit 4
Describe the structure and properties of a binary search tree, including the ordering rule
Insert and delete nodes in a binary search tree by hand, including a node with two children
Explain why a balanced tree gives logarithmic search time and how an unbalanced tree degrades to linear time
Implement insertion and search operations for a binary search tree
Your checkpoint
A code implementation of a binary search tree with insert and search, plus a hand-drawn diagram showing the tree built from a given insertion sequence and the result of one deletion
Unit 4
Identify problems that are intractable in practice and explain why brute-force enumeration becomes infeasible
Describe the idea of a heuristic approach to an intractable problem and give two concrete examples
Explain what it means for a problem to be verifiable quickly even when solving it is hard
Compare the growth of polynomial and exponential functions numerically for increasing input sizes
Your checkpoint
A written explanation of intractability with a numerical table showing exponential growth, plus two heuristic strategies described for a chosen hard problem
Unit 3 & Unit 4
Solve a set of timed practice problems covering search, graph traversal, sorting, trees, and complexity analysis
Redo every previously missed question type from weeks 1 to 7 and record the corrected reasoning
Summarise all complexity results from the plan on a single sheet for quick recall
Explain aloud, without notes, the key ideas of each major algorithm studied in the plan
Your checkpoint
A completed timed practice set with a scored results log and a one-page master summary sheet of all algorithms and their complexities
Milestones
Week 2: Can implement and trace both linear and binary search, and can state the sorted-data precondition for binary search without notes
Week 4: Can classify five unseen code snippets by growth order and justify each classification in one sentence
Week 6: Can trace quicksort and merge sort by hand on an unseen list and can insert and delete nodes in a binary search tree correctly
Week 8: Scores at least 80 percent on the timed practice set and can explain every algorithm's complexity from memory