1. Section 6.6 discusses a very “non-intuitive”, but powerful list/array-based approach to implement a priority queue,
call a binary heap. The list/array is used to store a complete binary tree (a full tree with any additional leaves as far left
as possible) with the items being arranges by heap-order property, i.e., each node is ≤ either of its children. An
example of a min heap “viewed” an a complete binary tree would be:
6
15 10
114 20 50
20
300 125 117
[1]
[2] [3]
[4] [5] [6] [7]
[8] [9] [10]
1 23456789100
not
used 6 15 10 114 20 20 50 300 125 117
Python List actually used
to store heap items
a) For the above heap, the list/array indexes are indicated in [ ]'s. For a node at index i, what is the index of:
its left child if it exists:
its right child if it exists:
its parent if it exists:
b) What would the above heap look like after inserting 13 and then 3? (show the changes on above tree)
General Idea of insert(newItem):
append newItem to the end of the list (easy to do, but violates heap-order property)
restore the heap-order property by repeatedly swapping the newItem with its parent until it percolates to correct spot
c) What is the big-oh notation for inserting a new item in the heap?
d) Complete the code for the percUp method used by insert.
class BinHeap:
def __init__(self):
self.heapList = [0]
self.currentSize = 0
def percUp(self,currentIndex):
paraentIndex =
while
def insert(self,k):
self.heapList.append(k)
self.currentSize = self.currentSize + 1
self.percUp(self.currentSize)
Data Structures (CS 1520) Lecture 7 Name:_________________
L
ecture 7
- Page
1
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