Heap Assignment Help

A heap is a binary tree in which the entries of the nodes can be compared with the less than operator of a strict weak ordering. In addition, two rules are usually implemented:

  • The entry contained by the node is NEVER less than the entries of the node's children
  • The tree is a COMPLETE tree.
Heap Sort

  • The total running time associated with heap sort is O(n lg n) + Build-Heap(A) time, that is O(n)
  • Heap sort runs on the heap data structure to enhance selection sort and make the running time asymptotically optimal
  • Running time is O(n log n) such as merge sort, but unlike selection, insertion, or even bubble sorts
  • Sorts in place such as insertion, selection or even bubble sorts, but unlike merge sort

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Heap Assignment Help

Definition in Data Structure

  • Heap: A special form of complete binary tree which key value associated with each node isn't any smaller (larger) than the key value of its children (if any).
  • Max-Heap: root node has the largest key.
    • A max tree is a tree in which the key value in each node is no smaller than the key values in its children. A max heap is a complete binary tree that is also a max tree.
      max heap
  • Min-Heap: root node has the smallest key.
    • A min tree is a tree in which the key value in each node is no larger than the key values in its children. A min heap is a complete binary tree that is also a min tree.
      min heap

Heap Implementation

  • Use binary_tree_node className
    • a) node implementation is for a general binary tree
    • b) but we may need to have doubly linked node
  • Use arrays
    • a) A heap is a complete binary tree
    • b) which can be implemented more easily with an array than with the node className
    • c) and do two-way links
  • Root at location [0]
  • Parent of the node in [i] is at [(i-1)/2]
  • Children of the node in [i] (if exist) is at [2i+1] and [2i+2]

Example For Implementing A Heap

Sorting Heap Example

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