Searching and sorting
Cambridge IGCSE Computer Science (0478) · Unit 7: Algorithm design and problem solving · 10 flashcards
Searching and sorting is topic 7.2 in the Cambridge IGCSE Computer Science (0478) syllabus , positioned in Unit 7 — Algorithm design and problem solving , alongside Algorithm design and Testing and validation. In one line: Linear search sequentially checks each element in a list until the target is found or the end is reached. In the worst case (target is last or not present), it has a time complexity of O(n), where n is the number of elements.
This topic is examined in Paper 1 (computer systems theory) and Paper 2 (algorithms, programming and logic).
The deck below contains 10 flashcards — 6 definitions, 2 key concepts and 1 application card — covering the precise wording mark schemes reward. Use the 6 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
Describe the linear search algorithm and state its time complexity in the worst-case scenario
Linear search sequentially checks each element in a list until the target is found or the end is reached. In the worst case (target is last or not present), it has a time complexity of O(n), where n is the number of elements.
What the Cambridge 0478 syllabus says
2026-2028 syllabus, in our wordsWhat the syllabus expects you to be able to do in this topic, in plain English. Match the command word (Describe, Explain, State, etc.) in your answer to score full marks. For the exact wording, see the official syllabus (PDF).
- Understand Understand each stage of a program development life cycle: analysis, design, coding, then testing.
- Understand Understand that any computer system consists of smaller sub-systems, and that each of these can be broken into further sub-systems.
- Understand Understand how to break a problem down (decompose it) into its parts: inputs, outputs, processes and storage.
- Use Use structure diagrams, flowcharts and pseudocode to design and build solutions to problems.
- Explain Explain what a given algorithm is for: state its purpose and describe the processes it carries out.
- Understand Understand these standard ways of solving problems: totalling, counting, linear search, bubble sort, and finding the average, maximum and minimum values.
- Understand Understand why input data needs validation checks, and know the different types: presence, range, length, type and format checks, plus check digits.
- Understand Understand why input data needs verification checks, and know the different types: double entry check and visual check.
- Suggest Suggest appropriate test data of four kinds (normal, abnormal, extreme, boundary) and apply it.
- Complete Complete a trace table that records what happens when an algorithm is dry-run.
- Identify Identify the errors in a given algorithm and suggest how to correct them.
- Write Write algorithms, and amend existing ones, to solve a given problem or scenario using pseudocode, flowcharts and program code.
Describe the linear search algorithm and state its time complexity in the worst-case scenario.
Linear search sequentially checks each element in a list until the target is found or the end is reached. In the worst case (target is last or not present), it has a time complexity of O(n), where n is the number of elements.
Explain how the binary search algorithm works and state its pre-requisite for usage.
Binary search repeatedly divides the search interval in half. If the middle element matches the target, the search ends. Otherwise, the search continues in either the left or right half, depending on the target's value compared to the middle element. It requires a sorted list.
Outline the steps involved in the bubble sort algorithm.
Bubble sort repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. The largest element 'bubbles' to the end with each pass. This process is repeated until no more swaps are needed.
Describe the key principle behind the merge sort algorithm.
Merge sort is a divide-and-conquer algorithm. It recursively divides the list into smaller sublists, sorts each sublist, and then merges the sorted sublists back together to produce the final sorted list.
Explain how the insertion sort algorithm works.
Insertion sort builds the final sorted array one item at a time. It iterates through the input data, removes one element at each repetition, finds the location where that element belongs within the sorted array, and inserts it there.
Compare the efficiency of linear search and binary search in a sorted array.
Binary search (O(log n)) is significantly more efficient than linear search (O(n)) for sorted arrays, especially for large datasets. Linear search must check every element in the worst case, while binary search quickly narrows the search range.
Describe a situation where using a linear search would be more appropriate than a binary search.
Linear search is more appropriate when the dataset is small or unsorted. The overhead of sorting the data to use binary search might outweigh the benefits for small datasets.
Explain the concept of 'comparison' in the context of sorting algorithms.
Comparison refers to the operation of checking whether one element is greater than, less than, or equal to another element. Sorting algorithms like bubble sort, merge sort, and insertion sort use comparisons to determine the correct order of elements.
Compare the efficiency of bubble sort and merge sort.
Merge sort (O(n log n)) is significantly more efficient than bubble sort (O(n^2)) for larger datasets. Bubble sort's performance degrades rapidly as the input size increases, while merge sort scales much better.
If a list of 1024 items is to be sorted using binary search, what is the maximum number of comparisons to find if an item exists?
A binary search will take a maximum of 11 comparisons, since log base 2 of 1024 is 10. 2^10 = 1024. The question asks for the *number of comparisons*, not the number of splits.
Key Questions: Searching and sorting
Describe the linear search algorithm and state its time complexity in the worst-case scenario.
Linear search sequentially checks each element in a list until the target is found or the end is reached. In the worst case (target is last or not present), it has a time complexity of O(n), where n is the number of elements.
Explain how the binary search algorithm works and state its pre-requisite for usage.
Binary search repeatedly divides the search interval in half. If the middle element matches the target, the search ends. Otherwise, the search continues in either the left or right half, depending on the target's value compared to the middle element. It requires a sorted list.
Outline the steps involved in the bubble sort algorithm.
Bubble sort repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. The largest element 'bubbles' to the end with each pass. This process is repeated until no more swaps are needed.
Describe the key principle behind the merge sort algorithm.
Merge sort is a divide-and-conquer algorithm. It recursively divides the list into smaller sublists, sorts each sublist, and then merges the sorted sublists back together to produce the final sorted list.
Explain how the insertion sort algorithm works.
Insertion sort builds the final sorted array one item at a time. It iterates through the input data, removes one element at each repetition, finds the location where that element belongs within the sorted array, and inserts it there.
More topics in Unit 7 — Algorithm design and problem solving
Searching and sorting sits alongside these Computer Science decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0478 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Searching and sorting deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
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