| Contents [0/2] |
| Homework [1/2] |
| HW Answers [2/2] |
(Click here for one slide per page)
| Homework [1/2] |
Read Algorithms 3.4.
Complete the quiz on D2L.
hw3a: Section 3.3 Problems
You should do the following problems on paper. The problems are all quite easy, and will give you practice with balanced trees. You will hand in your answers in on d2l in the folder labeled hw3a - Balanced Tree Problems. Make sure you submit to the correct folder! You must submit a word, pdf or text file. You can write out your answers on paper and upload a scan. If you hand in a text file, be sure to used a fixed-width font like Courier.
2-3 Trees:
3.3.1
3.3.2
3.3.3
3.3.5 --- structurally different means that they are different even
if all you ignore the values (take all values to be equal)
and you also ignore the order of the children
Red-Black Trees:
3.3.9
3.3.10
3.3.11
3.3.14
3.3.15
Complete all remaining methods in MyIntSET.java. These methods are the mutator methods. Hand in your MyIntSET.java file in the hw3b folder.
NB: If you did extra work last week and already completed the mutator methods when you submitted Homework 2, you must resubmit your file! The grading process is semi-automated and I don't have time to hunt around for last week's submission.
Complete your design document for the Term Project.
The section on Assessment Criteria in the assignment should give you enough information to understand what I'm looking for.
If I asked you for more detail in my feedback to your project proposal, please be sure to include it. Be sure to ask questions if anything I said in the feedback is confusing or if you want more information. I'm usually pretty quick to respond on Discord!
Hand your design document in using the appropriate folder in D2L.
| HW Answers [2/2] |
3.3.1
AES => E
/ \
A S
E E S
/ \ => / | \
A QSY A Q Y
E S E S U S
/ | \ => / | | \ => / \
A Q TUY A Q T Y E U
/ \ / \
A Q T Y
S S
/ \ / \
E U => E O U
/ \ / \ / | \ / \
A IOQ T Y A I Q T Y
S
/ \
E O U
/ | \ / \
A IN Q T Y
===========================================================
3.3.2
LPY => P
/ \
L Y
P L P
/ \ => / | \
HLM XY H M XY
L P L P X P
/ | \ => / | | \ => / \
CH M RXY CH M R Y L X
/ \ / \
CH M R Y
P P
/ \ / \
L X => C L X
/ \ / \ / | \ / \
ACH M R Y A H M R Y
P
/ \
C L X
/ | \ / \
A EH M RS Y
===========================================================
3.3.3
Tree is:
E R
/ | \
AC HM SX
Here's one class of solution:
Insert order:
+ first three inserted must include one of E,R and one from a leaf on either side.
+ next two include other of E,R + one from the leaf not included before.
+ the three remaining, which are from three different leaves
These are
AEH, RX
AEX, HR
ARX, EH
HRX, AE
where order within the groups doesn't matter
A could be C
H could be M
X could be S
But it's also possible:
AER, (C)HX
ERX, (S)AH
===========================================================
3.3.5
1:
*
2:
* *
3:
*
/ \
* *
4:
*
/ \
* **
5a:
*
/ \
* * **
5b:
* *
/ | \
* * *
6:
* *
/ | \
* * **
7a (add to 3-node of 6):
*
/ \
* *
/ \ / \
* * * *
7b (add to 2-node of 6):
* *
/ | \
** * **
8a (add to 2-node of 7a or 3-node of 7b):
*
/ \
* *
/ \ / \
* * * **
8b (add to 2-node of 7b):
* *
/ | \
** ** **
9a (add to 2-node of 8a or 3-node of 8b)
*
/ \
* *
/ \ / \
* * ** **
9b (add to 2-node of 8a or 3-node of 8b)
*
/ \
* *
/ \ / \
* ** * **
9c (add to 3-node of 8a)
*
/ \
* * *
/ \ / | \
* * * * *
10a (add to 2-node of 9a or 9b)
*
/ \
* *
/ \ / \
* ** ** **
10b (add to 3-node of 9a or 2-node of 9c)
*
/ \
* * *
/ \ / | \
* * * * **
10c (add to 3-node of 9b or 2-node of 9c)
*
/ \
* * *
/ \ / | \
* ** * * *
===========================================================
3.3.9
i) no - not balanced
ii) no - not balanced
iii) yes
iv) yes
===========================================================
3.3.10
S S
/ \ / \
E O U == O U
/ | \ / \ // \ / \
A IN Q T Y E Q T Y
/ \
A N
//
I
===========================================================
3.3.11
P P
/ \ / \
C L X == L X
/ | \ / \ // \ / \
A EH M RS Y C M S Y
/ \ //
A H R
//
E
===========================================================
3.3.14
A B
\\ => //
B A
B B
// \\ => / \
A C A C
B B
/ \ / \
A C ==> A D
\\ //
D C
B B D
/ \ / \\ // \
A D ==> A D ==> B E
// \\ / \ / \
C E C E A C
D D
// \ // \
B E ==> B F
/ \ \\ / \ //
A C F A C E
D D D
// \ // \\ / \
B F ==> B F ==> B F
/ \ // \\ / \ / \ / \ / \
A C E G A C E G A C E G
D D
/ \ / \
B F B F
/ \ / \ ==> / \ / \
A C E G A C E H
\\ //
H G
D D D
/ \ / \ / \
B F B F B H
/ \ / \ ==> / \ / \\ ==> / \ // \
A C E H A C E H A C F I
// \\ / \ / \
G I G I E G
D D
/ \ / \
B H B H
/ \ // \ ==> / \ // \
A C F I A C F J
/ \ \\ / \ //
E G J E G I
D D D H
/ \ / \ / \\ // \
B H B H B H D J
/ \ // \ ==> / \ // \\ ==> / \ / \ ==> / \ / \
A C F J A C F J A C F J B F I K
/ \ // \\ / \ / \ / \ / \ / \ / \
E G I K E G I K E G I K A C E G
On 2-3 threes:
ABC => B
/ \
A C
B B D
/ \ => / | \
A CDE A C E
B D B D F D
/ | \ => / | | \ => / \
A C EFG A C E G B F
/ \ / \
A C E G
D D
/ \ / \
B F => B F H
/ \ / \ / \ / | \
A C E GHI A C E G I
D D D H
/ \ / \ / | \
B F H => B F H J => B F J
/ \ / | \ / \ / | | \ / \ / \ / \
A C E G IJK A C E G I K A C E G I K
3-nodes pile up on the right in intermediate states.
At most one red link from root to leaf.
===========================================================
3.3.15
On 2-3 threes:
IJK => J
/ \
I K
J H J
/ \ => / | \
GHI K G I K
H J F H J H
/ | \ => / | | \ => / \
EFG I K E G I K F J
/ \ / \
E G I K
H H
/ \ / \
F J => D F J
/ \ / \ / | \ / \
CDE G I K C E G I K
H H D H
/ \ / \ / | \
D F J => B D F J => B F J
/ | \ / \ / | | \ / \ / \ / \ / \
ABC E G I K A C E G I K A C E G I K
3-nodes pile up on the left in intermediate states.
All red links on path from root to least node.