1. Section 9.2b
Adding and Removing from a Heap

2. The add method Concept: the heap is implemented as an ArrayList
Pseudocode:
add(element): returns element
add element to end of ArrayList // to maintain heap shape property
call reheapUp(element) // to re-establish heap order property
return element
Note: reheapUp is outlined on the next two slides

4. reheapUp operation Concept:
element to be moved up is at end of ArrayList
finds proper heap location for element
Pseudocode:
reheapUp(element)
set an index variable (hole) to the end of the arraylist
while(hole is not root and element > hole’s parent)
move the hole’s parent element down (to hole)
move the hole index up
place element into final location (hole)
Note that the formula for finding the index of the parent of any child is
parentIndex = (childIndex – 1) / 2

5. The remove method Concept:
removes the object at the front (root) of the priority queue (heap)
Pseudocode:
remove: returns element: throws PQUnderflowException
get (and store) the root element
remove (and store) the last element in the ArrayList
if(ArrayList is not empty) // make sure its not the last removal
call reheapDown(last element)
return root element
Note: reheapDown is outlined on the next two slides

7. reheapDown operation Concept:
the current heap root position is “empty”
move last item in ArrayList up
move the empty hole down
stop when the two locations meet
Pseudocode:
reheapDown(element)
set hole index to zero // root location
call newHole to find new hole location
while(newHole not equal to hole)
set the ArrayList element at hole location to element at new hole location
set hole to new hole location
set ArrayList element at hole location to element
Note: newHole is outlined on the next slide

8. newHole method Concept:
Given a hole location, determine if the new hole location should be
either in the left child, right child, or stay at the present location.
Pseudocode:
newHole(int hole, element): return index
if either child of hole is larger than element
return the index of the larger child
else
return the index of the current hole
Note that the formula for the index of the left and right children is as follows
int left = (hole * 2) + 1; // index for left child
int right = (hole * 2) + 2; // index for right child

9. Heaps Versus Other Representations of Priority Queues
add
remove