Topic 7 · Algorithm design and problem-solving

Searching, sorting, and the standard methods

Linear search, bubble sort, totalling, counting, and finding the maximum, minimum, and average, step by step.

Lesson 3 of 5Syllabus 7.4updated October 31, 2026

Linear search

A linear search checks each item in a list in order, from the first to the last, until it finds the target or reaches the end. The list does not need to be sorted.

Linear search for 23Interactive

114

331

423

617

742

Looking for 23. Start at item 1.

Step 1 / 5

Pseudocode

DECLARE Numbers : ARRAY[1:7] OF INTEGER
DECLARE Index : INTEGER
DECLARE Target : INTEGER
DECLARE Found : BOOLEAN
FOR Index <- 1 TO 7
    INPUT Numbers[Index]
NEXT Index
INPUT Target
Found <- FALSE
Index <- 1
WHILE Index <= 7 AND NOT Found DO
    IF Numbers[Index] = Target
      THEN
        Found <- TRUE
      ELSE
        Index <- Index + 1
    ENDIF
ENDWHILE
IF Found
  THEN
    OUTPUT "Found at position ", Index
  ELSE
    OUTPUT "Not found"
ENDIF

Bubble sort

A bubble sort goes through the list comparing each pair of neighbours and swapping them if they are in the wrong order. After each pass, the largest unsorted item has "bubbled" to the end. It stops when a pass makes no swaps.

Press Play and watch the orange pair being compared. Items that are in their final place are filled in.

Bubble sortInteractive

Pass 0Comparisons 0Swaps 0

Press Next to compare the first two items.

Step 1 / 19

Pseudocode

DECLARE Scores : ARRAY[1:6] OF INTEGER
DECLARE Top : INTEGER
DECLARE Index : INTEGER
DECLARE Temp : INTEGER
DECLARE Swap : BOOLEAN
FOR Index <- 1 TO 6
    INPUT Scores[Index]
NEXT Index
Top <- 6
REPEAT
    Swap <- FALSE
    FOR Index <- 1 TO Top - 1
        IF Scores[Index] > Scores[Index + 1]
          THEN
            Temp <- Scores[Index]
            Scores[Index] <- Scores[Index + 1]
            Scores[Index + 1] <- Temp
            Swap <- TRUE
        ENDIF
    NEXT Index
    Top <- Top - 1
UNTIL NOT Swap OR Top = 1

Exam tip. Swapping needs a temporary variable. Without Temp, the first assignment would overwrite one of the values.

Totalling and counting

Totalling keeps a running total: start at 0 and add each value. Counting adds 1 each time something happens. Both variables must be set to 0 before the loop.

Pseudocode

DECLARE Mark : INTEGER
DECLARE Total : INTEGER
DECLARE PassCount : INTEGER
DECLARE Student : INTEGER
Total <- 0
PassCount <- 0
FOR Student <- 1 TO 30
    INPUT Mark
    Total <- Total + Mark
    IF Mark >= 50
      THEN
        PassCount <- PassCount + 1
    ENDIF
NEXT Student
OUTPUT "Total: ", Total
OUTPUT "Passed: ", PassCount

Maximum, minimum, and average

To find the maximum, keep the largest value seen so far and replace it whenever a bigger value turns up. The minimum works the same way with smaller values. Start both with the first value (or with a value outside the possible range).

The average is the total divided by how many values there are.

Pseudocode

DECLARE Temps : ARRAY[1:7] OF REAL
DECLARE Day : INTEGER
DECLARE Highest : REAL
DECLARE Lowest : REAL
DECLARE Total : REAL
FOR Day <- 1 TO 7
    INPUT Temps[Day]
NEXT Day
Highest <- Temps[1]
Lowest <- Temps[1]
Total <- 0
FOR Day <- 1 TO 7
    IF Temps[Day] > Highest
      THEN
        Highest <- Temps[Day]
    ENDIF
    IF Temps[Day] < Lowest
      THEN
        Lowest <- Temps[Day]
    ENDIF
    Total <- Total + Temps[Day]
NEXT Day
OUTPUT "Highest: ", Highest
OUTPUT "Lowest: ", Lowest
OUTPUT "Average: ", Total / 7

Key terms

Linear search: Checking each item in turn until the target is found or the list ends.
Bubble sort: Repeatedly comparing and swapping neighbouring items until no swaps are needed.
Totalling: Adding each value to a running total.
Counting: Adding 1 to a counter each time something happens.

Check yourself

What is the most comparisons a linear search makes on a list of 50 items?Show answer

50, when the item is last or not in the list.

Why does the bubble sort use a Swap flag?Show answer

If a whole pass makes no swaps, the list is already sorted, so the algorithm can stop early.

Why must Total be set to 0 before the loop?Show answer

Otherwise it would start with an unknown value and the total would be wrong.

Try it in the editor Practice Open manual