Keep the top three: shift safely and handle ties

Keeping one maximum needs one remembered value. Keeping three needs three ordered places: First ≥ Second ≥ Third. When a new maximum arrives, save the old values before overwriting them.

The four update cases #

Use mutually exclusive cases, such as if / else if, or explicit disjoint conditions. Independent tests that reuse a just-updated value can accidentally process one card twice. The order of assignments matters: writing First = v too early loses the old First.

Two meanings of top three #

The strict inequalities in the lecture’s TopThreeMarks code keep distinct score levels: repeated 97 does not create another mark level. A ranking of three students instead counts two different students with 97 separately. The walkthrough uses distinct levels and lets you change the field parameter.

Procedure TopThreeMarks(Rows, Field)
    First = -1; Second = -1; Third = -1
    for each row X in Rows {
        v = X[Field]
        if (v > First) {
            Third = Second
            Second = First
            First = v
        } else if (First > v and v > Second) {
            Third = Second
            Second = v
        } else if (Second > v and v > Third) {
            Third = v
        }
    }
    if (Third == -1) { report "Fewer than 3 distinct values" }
    else { return Third }
End Procedure

The source initializes marks to 0 because these marks are nonnegative. Here −1 marks an empty slot explicitly, so a valid zero is not confused with a filled slot. This bound is for marks, not arbitrary data. If fewer than three different values exist, do not return a placeholder as a genuine cutoff.