#### Reading material

Pages 298-314 (Section 7.2.3-7.3.4 up to Implementing Heap-Sort In-Place),
pages 334-337 (Section 8.1.1)
#### Additional material

Proof of Proposition 7.5 in
PostScript and
PDF
Assume we have the following heap.

Removing the minimal element takes the following steps.

Inserting an element with key 8 takes the following steps.

Implementation of a priority queue with a heap in pseudocode:
PostScript and PDF

HeapPriorityQueue

PriorityQueueFullException

InPlaceHeapSorter

Dictionary

#### Question

Given a `Dictionary`

, find the keys which
occur more than once in the `Dictionary`

.