Maximum in one pass: keep the best so far

To find a maximum, remember the best value seen so far. Compare each new value with it. Replace the remembered value only when the new one is larger.

From keeping a card aside to keeping a variable #

The lecture first keeps the current best marks card in a separate place. Replacing it with a better card is the same idea as updating a Max variable. Keeping just the score saves the value but loses the identity of the card; a later lesson adds that information.

If the dataset is empty: report "No maximum"
Otherwise initialize Max from the first actual value
For every remaining value v {
    if (v > Max) {
        Max = v
    }
}
Report Max

Trace a short sequence #

A comparison with Max changes over time because Max changes. This differs from a fixed filter such as “score > 90”. It is also a replacement, not an accumulation: Max = Max + v would compute something else.

Results checked against the supplied dataset #

Use the stored LetterCount field for the word-length task: the comma on Vedanayagam, is not another letter. The shopping tutorial reports a maximum bill of Rs 4174; it is a maximum individual bill, not the total revenue of a store.

Why the final result is correct #

After each visit, Max is the maximum of the values already inspected. A new value either beats that maximum or cannot change it. After the last visit, the inspected set is the entire input. Card order can change the intermediate updates, but not the maximum value.

Source: Lecture 2.2; Tutorial 2.1. Small teaching datasets and diagrams are prepared for these notes; lecture and tutorial totals are identified explicitly.