1. ITEC324 Principle of CS III
Chapter 12 (Lafore’s Book)
Heaps
Hwajung Lee
ITEC324 Principle of CS III

2. Heaps Definition A heap is a binary tree with these characteristics:
It’s complete. This means it’s completely filled in, reading from left to right across each row, although the last row need not be full. (Example) fig12.1 in the page 580
Each node in a heap satisfies the heap condition, which states that every node’s key is larger than (or equal to) the keys of its descendants. (Example) fig12.2 in the page 581

3. Heaps: Removal Remove the root. Move the last node into the root.
Trickle (the terms bubble or percolate are also used) the last node down until it’s below a larger node and above a smaller one.
 See Remove method

4. Basic Operations & Key Change
See Trickle Down method
See Trickle Up method
See Key Change method

5. Insertion
the node to be inserted is placed in the first open position at the end of the array
Trickle the inserted node up until it’s below a larger node and above a smaller one.
 See Insert method

6. Heapsort
[Basic Idea]
insert all the unordered items into a heap using the normal insert() routine.
repeated application of the remove() routine will then remove the items in sorted order.
for (j = 0; j < size; j++)
theHeap.insert(anArray[j]); //from unsorted array
anArray[j] = theHeap.remove(); // to sorted array

7. Efficiency Efficiency of the heapsort cf. Quicksort
Expected case: O(N*logN)
Worst case: O(N*logN)
cf. Quicksort
Worst case: O(N2)

8. Recursive Approach [Recursive Approach]
Observation: Two correct subheaps make a correct heap.
(Example) fig12.8 in the page 602
See Heapify method
Transform array into heap