Algorithms and Flowcharts

An algorithm is a finite list of exact steps; a flowchart draws it with standard symbols. Tracing follows the values step by step to find the output or a bug.

Key ideas

Each flowchart symbol has one job, and arrows show the order in which the steps are carried out.
To trace an algorithm, keep a table of every variable and update it after each step.
A loop goes back to a decision step; it stops the first time the condition sends it on, so check the condition every round.
Swapping two values needs a spare variable T, or the trick A = A + B, B = A − B, A = A − B.
Taking the last digit (N mod 10) and removing it (whole part of N ÷ 10) lets a loop add or reverse digits.
Debugging: run the algorithm on a small input, compare with the right answer, and find the first step that goes wrong.

Remember

Oval	start or stop
Parallelogram	input or output
Rectangle	a process, such as a calculation
Diamond	a decision with a yes or no answer
Arrow; small circle	direction of flow; connector
Swap with a spare	T = A, A = B, B = T
Reverse digits	R = R × 10 + last digit of N, then remove that digit (1234 → 4321)

Watch out

Using > where the algorithm says ≥ (or the other way): the loop runs one time more or less.
Starting a total at 1 instead of 0 (a product starts at 1).
Writing A = B, B = A to swap: both end up equal to the old B.

Worked example

Put the steps of an algorithm for charging a tablet in order. Write the letters in order.
(a) Find the charger
(b) Check that the charging sign appears
(c) Plug the charger into the socket
(d) Connect the cable to the tablet
(e) Switch on the socket

Working: Find the charger → Plug the charger into the socket → Connect the cable to the tablet → Switch on the socket → Check that the charging sign appears

Answer: a, c, d, e, b