Understanding Priority Queues (Heaps) in Computing: Operations and Implementation, Schemes and Mind Maps of Object Oriented Programming

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UNDER THE HOOD OF

PRIORITY QUEUES (HEAPS)

Problem Solving with Computers-II

Priority Queues or Heaps (Review)

• Clarification
  • heap , the data structure is not related to heap, the region of memory
• What are the operations supported?
• What are the running times?

Insert 50, then 35, then 8 6 10 40 12 32 43 47 45 41

Delete min

**- Replace the root with the rightmost node at the last level

• “Bubble down”- swap node with one of the children until the heap**

property is restored

6 10 40

32 12 47 45 41 50 35 43

Insert into a heap

**- Insert key(x) in the first open slot at the last level of tree (going from left to right)

• If the heap property is not violated - Done
• Else….**

Insert the elements {12, 41, 47, 45, 32} in a min-Heap using the vector

representation of the heap

6 10 40 12 32 43 47 45 41

For a node at index i, index of the parent is int(i/2)

Value 6 10 12 40 32 43 47 45 41 Index 0 1 2 3 4 5 6 7 8 Traversing up the “tree”

Insert 8 into a heap Value 6 10 12 40 32 43 47 45 41 50 35 Index 0 1 2 3 4 5 6 7 8 9 10 After inserting 8, which node is the parent of 8? A. Node 6 B. Node 12 C. None 43 D. None - Node 8 will be the root

Delete min

**- Replace the root with the rightmost node at the last level

• “Bubble down”- swap node with one of the children until the heap**

property is restored

6 10 40

32 12 47 45 41 50 35 43

std::priority_queue (STL’s version of heap)

A C++ priority_queue is a generic container, and can store any data type

on which an ordering can be defined: for example ints, structs (Card),

pointers etc.

#include

priority_queue pq;

Methods:

* push() //insert

* pop() //delete max priority item

* top() //get max priority item

* empty() //returns true if the priority queue is empty

• (^) You can extract object of highest priority in O(log N)
• (^) To determine priority: objects in a priority queue must be comparable to each other ! 13

Next lecture

* More on the STL priority_queue

* Applications of heaps and priority queues

! 14