### Algo.2013f-exam History

Hide minor edits - Show changes to output - Cancel

Changed lines 29-31 from:

# Q1: my construction of gadget II is wrong (why?). Can you find the correct construction?

to:

# Q1: my construction of gadget II is wrong (why?). Can you find the correct construction? \\

[SOLUTION: use 2 copies of gadget I as before. Their distinguished vertices are (A,B) and (A',B').\

Identify B with B'. Then introduce a new vertex C and form a triangle (A,A',C). Now A and C must have different color]

[SOLUTION: use 2 copies of gadget I as before. Their distinguished vertices are (A,B) and (A',B').\

Identify B with B'. Then introduce a new vertex C and form a triangle (A,A',C). Now A and C must have different color]

Added lines 28-32:

# Q1: my construction of gadget II is wrong (why?). Can you find the correct construction?

# Q2: The problem should say "AT MOST B" not "AT LEAST B". Reason? We want to force the \

path to go through as many clauses as possible.

Added lines 26-40:

COMMENTS ON SOLUTION:

# Q4: Claim C can be improved: v is a bottleneck iff it is a candidate. \

Thanks to Nguyen for pointing this out.

# Q5: The claim that we can find real bottlenecks in O(m+n) time is a bit subtle. \

We did not provide the details, but try to see if you can do this. Thanks to Nguyen for \

pointing this out.

# Q7: our solution actually uses this definition: An edge e=(i,j) is "essential" if C(e)=\delta(i,j). \

We do not actually ensure that there are no alternative paths from i to j with cost at most C(e). \

Doing this seems a bit tougher.

Added line 25:

Here is the [[(Attach:) StudyQuestions-sol.pdf]] (posted Dec 17).

Changed lines 17-19 from:

This will be on Thu, Dec 19, in usual classroom 312, from 3:30-7:30 pm. It is a closed-book exam.

to:

This will be on Thu, Dec 19, in usual classroom 312, from 3:30-7:30 pm.

It is a closed-book exam.

It is a closed-book exam.

Changed line 21 from:

We will collect ~~them~~ at the end of the exam.

to:

We will collect these sheets at the end of the exam.

Added lines 18-19:

But we will allow a 8"x11" sheet (2-sided) of notes which you prepare in advance.

We will collect them at the end of the exam.

We will collect them at the end of the exam.

Added lines 14-21:

!! Final Exam

This will be on Thu, Dec 19, in usual classroom 312, from 3:30-7:30 pm. It is a closed-book exam.

Here is a set of study questions [[(Attach:) StudyQuestions.pdf]]

Deleted lines 79-81:

This will be on Dec 19, in usual classroom 312, from 3:30-7:30 pm.

Added lines 63-64:

For AVL Trees, be familiar with the insert/delete as well as the Merge/Split \

algorithms (Split is described in solution of hw3) \\

algorithms (Split is described in solution of hw3) \\

Changed lines 66-67 from:

your rules for logarithms and exponentiations).

to:

your rules for logarithms and exponentiations). \

Changed lines 62-67 from:

Be sure you can do rotations and all the associated algorithms on actual trees.

to:

Be sure you can do rotations and all the associated algorithms on actual trees. \\

Since we disallow calculators, you are expected to do hand calculators (review \

your rules for logarithms and exponentiations).

Since we disallow calculators, you are expected to do hand calculators (review \

your rules for logarithms and exponentiations).

Changed lines 30-31 from:

# Here are ~~some technical~~ remarks, based on your questions (click to expand):

to:

# Here are more remarks, based on your questions (click to expand):

Changed lines 45-46 from:

: Homework 3, question 10~~: This is a question about %green%min-size AVL trees%%. %toggle% :\~~

It is our typo NOT to have said this. My intent is clear from the model answer. \

It is our

to:

: Homework 3, question 10 on height of AVL tree with 100 nodes: \

This is a question about %green%min-size AVL trees%%. %toggle% :\

It is a typo NOT to have said this. My intent is clear from the model answer. \

This is a question about %green%min-size AVL trees%%. %toggle% :\

It is a typo NOT to have said this. My intent is clear from the model answer. \

Added lines 50-62:

: In proofs, can I quote your theorems? %toggle% :\

YES, you can (probably SHOULD). Unless I specifically forbid it. \\

E.g., I might say, \

prove from first principles and do not quote the Master Theorem, etc. \\

Note that there is STILL some work to do, even if you quote theorems. \\

E.g., when quoting the Master Theorem, you still need to show that a particular \

case applies. That may require showing regularity, etc. \\

E.g., in estimating sums using our Rules for Polynomial-type or Exponential-type, \

you may need to justify why they are polynomial- or exponential-type.

: Hand Simulations %toggle% :\

Be sure you can do rotations and all the associated algorithms on actual trees.

Added lines 37-47:

: Bug in Non-Recursive DFS %toggle% :\

Line 9-10 should be changed to: \\

%green% PREVISIT(v,u); If (v is unseen), then color v seen.%% \\

In short, you should ALWAYS do the PREVISIT. \\

This is clear, if you remember that PREVISIT amounts \

to processing the edge (u,v). Thanks to Huaisi for pointing this out.

: Homework 3, question 10: This is a question about %green%min-size AVL trees%%. %toggle% :\

It is our typo NOT to have said this. My intent is clear from the model answer. \

But you should answer the question without making this assumption! That is, you should \

always read a question literally. We will grade you accordingly.

Line 9-10 should be changed to: \\

%green% PREVISIT(v,u); If (v is unseen), then color v seen.%% \\

In short, you should ALWAYS do the PREVISIT. \\

This is clear, if you remember that PREVISIT amounts \

to processing the edge (u,v). Thanks to Huaisi for pointing this out.

: Homework 3, question 10: This is a question about %green%min-size AVL trees%%. %toggle% :\

It is our typo NOT to have said this. My intent is clear from the model answer. \

But you should answer the question without making this assumption! That is, you should \

always read a question literally. We will grade you accordingly.

Changed line 30 from:

# Here are some technical remarks, based on your questions:

to:

# Here are some technical remarks, based on your questions (click to expand):

Changed line 32 from:

Does "double rotation" just mean "rotate^2(u)"? %toggle% :\

to:

: Does "double rotation" just mean "rotate^2(u)"? %toggle% :\

Changed line 20 from:

# This is an open-book exam, but not open-computer or electronic devices (or calculators).

to:

# This is an open-book exam, but not open-computer or electronic devices (or calculators). \

Changed lines 23-25 from:

# In terms of topics, you are technically responsible for everything up to

~~the~~ lecture on Oct 8. That means the first 6 Lectures.

~~But~~ the first 3 Lectures will be emphasized, especially on ~~topics~~

to:

# In terms of topics, you are technically responsible for everything up to \

the lecture on Oct 8. That means the first 6 Lectures. \

But the first 3 Lectures will be emphasized, especially on topics \

the lecture on Oct 8. That means the first 6 Lectures. \

But the first 3 Lectures will be emphasized, especially on topics \

Changed lines 32-33 from:

to:

Does "double rotation" just mean "rotate^2(u)"? %toggle% :\

No, it is not the same thing. According to p.17 of Lect.III, it must be \

No, it is not the same thing. According to p.17 of Lect.III, it must be \

Changed line 20 from:

This is an open-book exam, but not open-computer or electronic devices (or calculators).

to:

# This is an open-book exam, but not open-computer or electronic devices (or calculators).

Changed line 23 from:

In terms of topics, you are technically responsible for everything up to

to:

# In terms of topics, you are technically responsible for everything up to

Changed lines 28-36 from:

To ensure adequate coverage, we will have a section of short questions.

to:

# To ensure adequate coverage, we will have a section of short questions.

# Here are some technical remarks, based on your questions:

'''What is a 'double rotation'?''' %toggle% :\

It does just mean to 'rotate^2(u)'. According to p.17 of Lect.III, it must be \

either zig-zag or zag-zig. But zig-zig or zag-zag do not count as 'double rotation'. \

Of course, all four cases comes under 'rotate^2(u)'.

# Here are some technical remarks, based on your questions:

'''What is a 'double rotation'?''' %toggle% :\

It does just mean to 'rotate^2(u)'. According to p.17 of Lect.III, it must be \

either zig-zag or zag-zig. But zig-zig or zag-zag do not count as 'double rotation'. \

Of course, all four cases comes under 'rotate^2(u)'.

Changed lines 16-18 from:

This will be in class, on Oct 10.

Get a sample copy of a past midterm exam from NYU Classes, under resources.

Get a sample copy of a past midterm exam from NYU Classes, under resources.

to:

# This will be in class, on Oct 10.

# Get a sample copy of a past midterm exam from NYU Classes, under resources.

# Get a sample copy of a past midterm exam from NYU Classes, under resources.

Added line 28:

To ensure adequate coverage, we will have a section of short questions.

Changed lines 20-27 from:

to:

This is an open-book exam, but not open-computer or electronic devices (or calculators).

Sorry, if you want the lecture notes, you must print a copy.

In terms of topics, you are technically responsible for everything up to

the lecture on Oct 8. That means the first 6 Lectures.

But the first 3 Lectures will be emphasized, especially on topics

in the lecture and in the homework.

Sorry, if you want the lecture notes, you must print a copy.

In terms of topics, you are technically responsible for everything up to

the lecture on Oct 8. That means the first 6 Lectures.

But the first 3 Lectures will be emphasized, especially on topics

in the lecture and in the homework.

Added lines 17-18:

Get a sample copy of a past midterm exam from NYU Classes, under resources.

Changed lines 18-22 from:

We will give you more guidance soon.

to:

We will give you more guidance soon.

!! Final Exam

This will be on Dec 19, in usual classroom 312, from 3:30-7:30 pm.

!! Final Exam

This will be on Dec 19, in usual classroom 312, from 3:30-7:30 pm.

Changed lines 1-5 from:

(:title ~~Assignment~~ Page :)

Assignments are either Homework Assignments or Reading Assignments.

!! Exam Page

Assignments are either Homework Assignments or Reading Assignments.

!! Exam Page

to:

(:title Exam Page :)

Added lines 1-21:

(:title Assignment Page :)

Assignments are either Homework Assignments or Reading Assignments.

!! Exam Page

(:if false:)

Your homework assignments are found in the following pdf file:

* Homework assignment file: [[(Attach:) coming-soon.pdf]].

* Homework solution file: [[(Attach:) hw_sol.pdf]].

(:if end:)

!! Midterm Exam

This will be in class, on Oct 10.

We will give you more guidance soon.

Assignments are either Homework Assignments or Reading Assignments.

!! Exam Page

(:if false:)

Your homework assignments are found in the following pdf file:

* Homework assignment file: [[(Attach:) coming-soon.pdf]].

* Homework solution file: [[(Attach:) hw_sol.pdf]].

(:if end:)

!! Midterm Exam

This will be in class, on Oct 10.

We will give you more guidance soon.