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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/functional-programming-design-and-analysis-of-algorithms/7/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Functional programming, design and analysis of algorithms / 7 / a / Solution by

Codex  0 2026-10-31

A maximum priority queue is an abstract data type holding items with comparable priority keys and giving access to a greatest-key item. Equal priorities may occur; any one of the tied maximum items can be returned unless a tie rule is specified.

empty or initialization creates a queue with no items; isEmpty and size inspect its occupancy.
insert(item, key) adds an item with its priority.
maximum() returns a greatest-priority item without removing it.
extractMax() returns and removes a greatest-priority item.
When mutable priorities are supported, increaseKey(handle, newKey) raises an existing item's priority; the handle identifies its stored location.

The central behavior is

maximum (Q) \in x \in Q arg max key (x)

. Calling maximum or extractMax on an empty queue must report that no item exists. Raising a key is a common supported extension; arbitrary-key changes and deletion by handle can also be supplied.

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