Homework 6: Hash Tables, etc
Due: Thursday, November 30, 8:59:59pm
Erratum: Question D.3 should say
max heap.
We are staying with the retro theme. Fill in your answers in the
following plain text file. Just use your favorite text editor to answer
the questions (e.g., emacs, vim, nano).
How to submit:
Here's the link for the file shown below: hw6.txt.
Edit the file and copy into the hw6 submission directory on GL
as usual.
<![CDATA[
Name:
Userid:
CMSC 341 Fall 2017 Homework 6
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Question A (15 points)
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Suppose we use the MAD method for hashing into a hash table with 13
slots with parameters a = 3 and b = 5. That is, key k is hashed into
slot number (3*k + 5) % 13.
Show the placement of the keys after inserting the following keys
in the given order into the hash table using separate chaining to
handle collisions.
Keys inserted (in order): 8 10 25 2 31 12 5 18
Type in each key on the same line as the index of the slot
where it is eventually inserted.
0:
1:
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Question B (15 points)
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Repeat Question A using linear probing to handle collisions.
Keys inserted (in order): 8 10 25 2 31 12 5 18
Type in each key on the same line as the index of the slot
where it is eventually inserted.
0:
1:
2:
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Question C (15 points)
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Repeat Question A using quadratic probing to handle collisions.
Keys inserted (in order): 8 10 25 2 31 12 5 18
Type in each key on the same line as the index of the slot
where it is eventually inserted.
0:
1:
2:
3:
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5:
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Question D (35 points total)
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We want to support the operations Insert(), Find() and Max() for
a program that uses n Insert(), n Find() and 15 Max() operations.
These operations can be performed in any order. The Max() operation
simply reports the maximum valued stored in the data structure
at the time of the call.
1. (5 points) Suppose that we use a red-black tree to support this
program. What is the asymptotic worst case running time for
n Insert(), n Find() and 15 Max() operations?
(a) O(n)
(b) O(n log n)
(c) O(n^2)
(d) O(n^2 log n)
(e) O(n^3)
Answer:
2. (5 points) BRIEFLY explain your choice above.
3. (5 points) Suppose that we use a binary max heap to support this
program. What is the asymptotic worst case running time for
n Insert(), n Find() and 15 Max() operations?
(a) O(n)
(b) O(n log n)
(c) O(n^2)
(d) O(n^2 log n)
(e) O(n^3)
Answer:
4. (5 points) BRIEFLY explain your choice above.
5. (5 points) Suppose that we use a hash table with a "good"
hash function to support this program. What is the asymptotic
"average" running time for n Insert(), n Find() and 15 Max()
operations?
(a) O(n)
(b) O(n log n)
(c) O(n^2)
(d) O(n^2 log n)
(e) O(n^3)
Answer:
6. (5 points) BRIEFLY explain your choice above.
7. (5 points) Which of these three data structures would you
pick to support n Insert(), n Find() and 15 Max() operations?
Briefly justify your answer.
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