Algorithms Worksheet - A-Level - Intermediate
Algorithms worksheet for A-Level / Vocational (Ages 16-18). Intermediate level computing practice, aligned to the UK National Curriculum. Print-ready with answer key included.
Exploring Algorithms in Computing
A-Level / Vocational (Ages 16-18) - Intermediate
Instructions: This worksheet is designed to deepen your understanding of algorithms, a fundamental concept in computing. You will encounter a variety of activities that require you to analyse, evaluate, and apply different algorithmic approaches.
Understanding Big O Notation
For each algorithm described below, identify the Big O notation that best represents its time complexity. Provide a brief explanation for your choice.
1. A simple for loop iterating over an array of n elements.
2. A nested loop where each loop runs n times.
3. A binary search algorithm on a sorted array.
4. A recursive function that splits the input in half each time.
Sorting Algorithm Comparison
Compare the following sorting algorithms in terms of time complexity and space complexity. Provide examples to illustrate your points.
1. Bubble Sort
2. Quick Sort
3. Merge Sort
4. Insertion Sort
Graph Traversal Techniques
Discuss the differences between depth-first search (DFS) and breadth-first search (BFS) in graph traversal. Include scenarios where each is most effective.
1. Depth-First Search (DFS)
2. Breadth-First Search (BFS)
Algorithm Design Task
Design an algorithm to solve the following problem. Describe your approach, including pseudocode, and analyse its efficiency.
Problem: Design an algorithm to find the shortest path in a weighted graph using Dijkstra's algorithm.
Exploring Search Algorithms
For each search algorithm, explain how it works and discuss its efficiency. Provide examples where applicable.
1. Linear Search
2. Binary Search
Critical Evaluation of Algorithm Efficiency
Write a critical essay evaluating the role of algorithm efficiency in modern computing. Discuss the implications of inefficient algorithms on system performance.
Evaluate the importance of algorithm efficiency in computing and its impact on system performance. Use examples to support your argument. [25 marks]
Activity 1: O(n) ; O(n^2) ; O(log n) ; O(log n)
Activity 2: Bubble Sort: O(n^2), O(1) ; Quick Sort: O(n log n), O(log n) ; Merge Sort: O(n log n), O(n) ; Insertion Sort: O(n^2), O(1)
Activity 3: DFS: Uses stack, good for deep traversal ; BFS: Uses queue, good for shortest path in unweighted graphs
Activity 4: Dijkstra's algorithm involves priority queue, complexity: O(V^2) or O(V + E log V) with heap
Activity 5: Linear Search: O(n), works on unsorted data ; Binary Search: O(log n), requires sorted data
Activity 6: Efficiency is crucial for performance, affects speed, resource usage; inefficient algorithms can lead to bottlenecks
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