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  1. APriority Queue ranks its elements by key with a total order relation • Keys: - Every element has its own key - Keys are not necessarily unique • Total Order Relation - Denoted by≤ -Reflexive: k ≤k -Antisymetric: if k1≤k2and k2≤k1, then k1≤k2. -Transitive: if k1≤k2and k2≤k3, then k1≤k3.

  2. Heaps and Priority Queues • Heap can be used to implement a priority queue • store a (key, element) item at each internal node • keep track of the last node (2, Chomu) (5, Ram) (6, Sohan) (9, Shyam) (7, Anna)

  3. Priority queues are used in a number of applications. We name three: In event-driven simulations, events can be kept in a priority queue, with the priority being the time at which an event is to take place. Events are removed from the queue in chronological order and processed.

  4. 26 Νοε 2024 · PriorityQueue (Comparator<E> comparator): Creates a PriorityQueue with the default initial capacity and whose elements are ordered according to the specified comparator. Example: The example below explains the following basic operations of the priority queue.

  5. Use a priority queue. public UnorderedPQ(int maxN) { pq = (Item[]) new Comparable[maxN]; } public boolean isEmpty() { return N == 0; } public void insert(Item x) { pq[N++] = x; } public Item delMax() { int max = 0; for (int i = 1; i < N; i++) if (less(max, i)) max = i; exch(max, N-1); return pq[--N]; } } Challenge.

  6. Priority Queue A priority queue (PQ for short) is a data structure that allows us to process keys in order, without storing them in full sorted order all at once

  7. Priority Queue Client Example Problem: Find the largest M of a stream of N elements. Ex 1: Fraud detection - isolate $$ transactions. Ex 2: File maintenance – find biggest files or directories. Possible constraint: may not have enough memory to store N elements. Solution: Use a priority queue. Ex: top 10,000 in a stream of 1 billion.

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