Variables and iteration: remember your progress

A variable is a named place to keep a value while a procedure runs. Iteration means repeating a set of steps over the items. Together, they let you make progress without remembering everything in your head.

The two-pile method #

Put unvisited cards in Pile 1. Put visited cards in Pile 2. Start Count at 0. While Pile 1 has cards, pick one, move it to Pile 2 and add 1 to Count. When Pile 1 is empty, Count is the number of cards.

Count ← 0
While Pile 1 is not empty:
    Pick one card X from Pile 1
    Move X to Pile 2
    Count ← Count + 1
Report Count

Read an assignment correctly #

The arrow ← means “store the value on the right in the variable on the left”. Count ← Count + 1 first reads the old Count, adds 1, then replaces the stored value. It is an update instruction, not the algebra claim that a number equals itself plus one.

Three parts of every loop #

Initialization prepares the starting state. The repeated step processes one new item and updates the variables. The stopping condition tells you when no work remains. Initialize Count once before the loop; setting it to zero inside every repetition would erase earlier progress.

Why it works, even halfway through #

After k completed card visits, Count equals k. This statement stays true throughout the procedure. The original lecture counts 30 marks cards. The final answer does not depend on which unvisited card is chosen next, provided every card is counted once and only once.

During this procedure a card’s recorded marks are input values that we leave unchanged. The Count variable changes. “Constant during this computation” does not mean a field can never be edited in a different task.

Source: Lecture 1.2 — Concept of variables, iterators and filtering. Small teaching datasets and diagrams are prepared for these notes; lecture and tutorial totals are identified explicitly.