Algorithms — Edexcel GCSE Computer Science

This criterion asks you to do two things with algorithms: follow one that already exists and write your own, in flowcharts, pseudocode or program code. Every algorithm you meet must combine the three control structures. Sequence means steps run in order, one after another. Selection means a condition chooses between paths, as in an IF statement. Repetition means a loop repeats a block: count-controlled loops run a set number of times, while condition-controlled loops run until a test changes. Iteration over every item in a data structure means visiting each element in turn, for example a FOR EACH loop over a list of scores. Input, processing and output must also be present: data is read in, transformed by calculation or comparison, then displayed or stored. To follow an algorithm, trace it line by line, recording variable values in a table.

This criterion has two parts: understanding why variables and constants are needed, and following and writing algorithms that use them alongside one- and two-dimensional data structures. A variable is a named store whose value can change while the algorithm runs, such as a running total. A constant is a named value fixed when it is declared and never changed, such as the maximum number of attempts or the value of pi; using a constant makes the algorithm easier to read and to update because the value appears once. Data structures hold related data. A string is a sequence of characters. A record groups fields of different types, for example a pupil record with name, age and score. A one-dimensional array is a list accessed by one index, such as scores[3]. A two-dimensional array is a table accessed by two indices, such as grid[row][column].

Algorithms need operators to turn stored data into decisions and results. Arithmetic operators compute values: addition combines, subtraction finds a difference, multiplication scales, division gives a quotient, modulus returns the remainder, integer division discards the fractional part, and exponentiation raises a base to a power such as 2³ = 8. Relational operators compare two values and yield true or false: equal to, less than, greater than, not equal to, less than or equal to, greater than or equal to. Logical operators combine or invert Boolean results: AND is true only when both inputs are true, OR is true when at least one is true, and NOT reverses a single Boolean. For example, a program accepts a score, then tests score ≥ 50 AND score ≤ 100 to decide whether the mark is valid.

To find an algorithm's output you execute it exactly as written with the supplied data. Work through each statement in order, updating every variable as its value changes, and respect sequence, selection and iteration. A trace table records this process: one column per variable, one row per step, so you can read off the value a variable holds at any chosen point. For example, given total ← 0 then a loop that adds 4 three times, the trace shows total becoming 4, then 8, then 12, so the output is 12. When a condition is tested, record the Boolean result and follow only the branch it selects. When a loop repeats, keep adding rows until the loop condition fails. The final row gives the output; an intermediate row gives the value at that point.

Programs can fail in three distinct ways. A syntax error breaks the rules of the language, so the translator cannot produce runnable code: for example, writing a loop header without its closing bracket, or misspelling a keyword. A logic error is grammatically valid code that produces the wrong result: for example, a total that adds a value before resetting the accumulator, or a condition that uses the wrong comparison operator. A runtime error occurs only while the program executes, such as dividing by zero, indexing an array outside its bounds, or converting non-numeric text to an integer. To identify a logic error in an algorithm, trace the variables step by step with a trace table, compare each intermediate value with the expected value, and locate the first step where they diverge.

Four standard algorithms must be understood. Bubble sort repeatedly compares adjacent items in a list and swaps them when they are in the wrong order, so large values move to the end on each pass; passes repeat until a complete pass makes no swaps. Merge sort splits a list into single-item sublists, then repeatedly merges pairs of sorted sublists in order until one sorted list remains. Linear search checks each item from the start of a list in turn until the target is found or the list ends, so it works on unsorted data. Binary search requires a sorted list: it examines the middle item, then discards the half that cannot contain the target and repeats on the remaining half until the target is found or the search space is empty.

Fitness for purpose means an algorithm produces correct output for every valid input, including boundary and edge cases; efficiency means it does so with acceptable execution time and storage. Compare counts quantify execution: a linear search on n items takes up to n compares, whereas a binary search on sorted data needs only about 10 compares for 1 000 items. Pass counts quantify loop behaviour: a single loop runs n passes, while nested loops run n² passes. Memory use measures extra storage: an in-place sort uses minimal extra memory for temporary variables, whereas creating a copy requires additional memory proportional to list size. Test data (normal, boundary, erroneous) verifies correctness before evaluating resource efficiency.