Standard Methods Of A Solution

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Notes

Linear Search

A **linear search** checks every value in a dataset one by one from the start.
It works on **unsorted** data.
Algorithm: check first value; if match → stop; else move to next; repeat until found or end.
Uses a **boolean flag** (e.g., `found`) to track if the target is located.
In pseudocode, a `FOR` loop iterates through the array; `IF` compares each element to the target.
If found, set flag to `TRUE` and output message; after loop, if flag still `FALSE`, output 'not found'.

Bubble Sort

A **bubble sort** repeatedly passes through a list, comparing adjacent pairs and swapping if out of order.
Each full pass is called a **pass**; the algorithm may need multiple passes.
After each pass, the largest (or smallest) element 'bubbles' to its correct position at the end.
The algorithm stops when a complete pass makes **no swaps**.
In pseudocode, a `WHILE` loop runs while `swaps = TRUE`; inner `FOR` loop compares `nums[y]` and `nums[y+1]`.
Swap uses a temporary variable; after each pass, the range decreases by 1.
In exams, you only need to show the state after each pass, not every individual swap.

Totalling

**Totalling** accumulates a running total of values as they are input or processed.
Initialise total to 0, then in a loop add each value: `Total ← Total + ItemValue`.
Example: summing item prices on a receipt.

Counting

**Counting** increments (or decrements) a counter by a fixed amount (usually 1) each iteration.
Used to track the number of times an action occurs, e.g., loop iterations.
Increment example: `Count ← Count + 1`; decrement: `Count ← Count - 1`.
Often used with `DO...UNTIL` or `WHILE` loops to control repetition.

Maximum, Minimum & Average

**Maximum** and **minimum** find the largest and smallest values in a dataset.
In pseudocode, use built-in functions: `Highest ← max(Scores)`, `Lowest ← min(Scores)`.
**Average** (mean) is calculated by summing all values and dividing by the count.
Sum via loop: `Total ← Total + Scores[Count]`; then `Average ← Total / LENGTH(Scores)`.
These methods are commonly used for grades, scores, or any numeric data.

Linear search through an array checking each element; target 11 not found.

Bubble sort passes on [5,2,4,1,6,3] showing final sorted order after 4 passes.

Illustration of totalling and counting methods.

Practice questions

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1.What is a linear search?
Easy
- AAn algorithm that starts at the first value and checks every value one at a time
- BAn algorithm that divides the dataset in half repeatedly to find a value
- CAn algorithm that sorts data by comparing adjacent pairs and swapping them
- DAn algorithm that uses a hash table to locate data quickly
2.Which of the following is true about a bubble sort?
Easy
- AIt compares adjacent values and swaps them if they are in the wrong order
- BIt selects the smallest value and moves it to the beginning
- CIt requires the dataset to be already sorted to work
- DIt only works on numeric data
3.What does the 'found' variable represent in a linear search algorithm?
Easy
- AWhether the target value has been found in the dataset
- BThe index of the current element being checked
- CThe total number of comparisons made
- DThe value of the target being searched for
4.A linear search is performed on the list [5, 2, 8, 1, 9] to find the value 8. How many comparisons are made before the value is found?
Medium
- A3
- B2
- C5
- D4
5.What is the purpose of the 'swaps' variable in a bubble sort algorithm?
Medium
- ATo indicate whether any swaps were made during a pass
- BTo count the number of passes completed
- CTo store the temporary value during a swap
- DTo determine the length of the array
6.After one pass of a bubble sort on the list [5, 2, 4, 1, 6, 3], what is the order of the list?
Medium
- A[2, 4, 1, 5, 3, 6]
- B[2, 5, 4, 1, 6, 3]
- C[2, 1, 4, 3, 5, 6]
- D[1, 2, 3, 4, 5, 6]
7.Which of the following is a valid advantage of a linear search?
Medium
- AIt can be performed on unsorted data
- BIt is the fastest search algorithm for large datasets
- CIt uses divide and conquer to reduce search time
- DIt requires the data to be sorted first
8.In the context of standard methods of a solution, what is 'totalling'?
Medium
- AKeeping a running total of values entered into the algorithm
- BCounting the number of times a loop iterates
- CFinding the largest value in a list
- DSorting a list into ascending order

Slides

Standard Methods of a Solution

Standard methods are common algorithmic techniques used to solve problems.
They include linear search, bubble sort, totalling, counting, and finding max/min/average.
These methods are building blocks for more complex algorithms.

Linear Search

A linear search checks each item in a list one by one from the start.
It works on unsorted data and stops when the target is found or the list ends.
It uses a flag (e.g., found) to indicate success.

What is the main advantage of a linear search?

It is the fastest search algorithm
It works on unsorted data
It requires the data to be sorted
It uses a divide-and-conquer approach

Bubble Sort

Bubble sort repeatedly passes through a list, comparing adjacent items and swapping them if they are in the wrong order.
Each pass moves the largest unsorted item to its correct position at the end.
The algorithm stops when a pass completes with no swaps.

In bubble sort, each full run of comparisons from beginning to end is called a ____. The algorithm stops when no ____ are made in a pass.

Totalling and Counting

Totalling adds up values as they are processed (e.g., sum of items on a receipt).
Counting increments or decrements a variable by a fixed amount (usually 1) to track occurrences.
Both are used in many algorithms, like linear search counting index positions.

Which pseudocode correctly implements totalling?

Total ← 0; FOR each item: Total ← Total + item
Total ← 1; FOR each item: Total ← Total×item
Total ← 0; FOR each item: Total ← item
Total ← 0; WHILE condition: Total ← Total - 1

Maximum, Minimum and Average

The maximum is the largest value in a dataset; the minimum is the smallest.
The average (mean) is the sum of all values divided by the number of values.
These can be computed using built-in functions (max, min) or by iterating through the list.

To find the average of a list, you first calculate the ____ of all values, then divide by the ____ of values.

Which of these are true about standard methods?

Linear search can be used on unsorted data.
Bubble sort requires only one pass to sort any list.
Counting is used to track how many times an action occurs.
The average is found by multiplying all values together.

Linear Search Pseudocode

Set found ← FALSE before the loop.
Loop through each index from 1 to length of array.
If data[index] = target, set found ← TRUE and output message.
After loop, if found is still FALSE, output 'Target not found'.

In the linear search pseudocode, what is the purpose of the boolean variable 'found'?

To count the number of comparisons
To indicate whether the target has been located
To store the target value
To control the loop index

Bubble Sort Pseudocode

Use a WHILE loop with a swaps flag set to TRUE initially.
Inside, set swaps ← FALSE, then FOR y ← 1 TO numlength-1.
If nums[y] > nums[y+1], swap them and set swaps ← TRUE.
After each pass, decrement numlength because the last element is sorted.

In bubble sort pseudocode, after each pass the variable ____ is decreased by 1 because the last element is in its correct position.

Example: Bubble Sort on Words

Sort the list: Milk, Eggs, Bananas, Cheese, Potatoes, Grapes.
Use first letters: M, E, B, C, P, G.
Pass 1: E, B, C, M, G, P.
Pass 2: B, C, E, G, M, P (sorted).

After the first pass of a bubble sort on [5,2,4,1,6,3], what is the order?

[2,4,1,5,3,6]
[2,5,4,1,6,3]
[1,2,3,4,5,6]
[5,2,4,1,6,3]

Totalling Example

Pseudocode: Total ← 0; FOR Count ← 1 TO ReceiptLength; INPUT ItemValue; Total ← Total + ItemValue; NEXT Count; OUTPUT Total.
This sums all item values entered by the user.

Which of these are examples of standard methods?

Linear search
Binary search
Bubble sort
Quick sort

Counting Example

Counting can increment or decrement by 1 each iteration.
Example: Count ← 0; DO OUTPUT Count; Count ← Count + 1; UNTIL Count ≥ 50.
This outputs pass numbers from 0 to 49.

What will the following pseudocode output? Count ← 50; DO OUTPUT Count; Count ← Count - 1; UNTIL Count ≤ 0

50, 49, 48, ..., 0
50, 49, 48, ..., 1
49, 48, ..., 0
50, 49, 48, ..., 1, 0

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