601.433/633 Introduction to Algorithms
Homework #10
Fall 2017
Due: November 30, 2017, 1:30pm
Remember: you may work in groups of up to three people, but must write up your solution entirely
on your ow
Homework #2
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, February 11th, 11.59pm
Late submissions: will NOT be accepted
Format: Please start each problem on a new p
Homework #6
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, March 24th, 11.59pm
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Format: Please start each problem on a new page
Homework #6
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, March 24th, 11.59pm
Late submissions: will NOT be accepted
Format: Please start each problem on a new page
Homework #3
Solutions
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, Feb 18th, 11.59pm
Late submissions: will NOT be accepted
Format: Please start each problem on a
Solutions
Homework #1
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, February 4rd, 5pm
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Homework #5
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, March 3rd, 11.59pm
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Homework #9
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Friday, Apr 29, 11:59pm
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Format: Please start each problem on a new page.
Wher
Quiz #2
Introduction to Algorithms/Algorithms 1
600.363/463
Tuesday, April 2nd, 9-10.15am
Ethics Statement
I agree to complete this exam without unauthorized assistance from any person, materials, or
Homework #8
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, March 24th, 11.59pm
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Format: Please start each problem on a new page
Homework #2
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, February 11th, 11.59pm
Late submissions: will NOT be accepted
Format: Please start each problem on a new p
Homework #3
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, Feb 18th, 11.59pm
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Format: Please start each problem on a new page.
Homework #3
Sanghyun Choi (schoi60)
February 18th, 2016
1
Problem 1 (13 points)
Lets say that a pivot provides x|n x separation if x elements in an array are
smaller than the pivot, and n x elements a
Homework #9
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Friday, Apr 29, 11:59pm
Late submissions: will NOT be accepted
Format: Please start each problem on a new page.
Wher
Homework #5
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, March 3rd, 11.59pm
Late submissions: will NOT be accepted
Format: Please start each problem on a new page.
=
HW6 P1 (Total: 25 points)
=
(pick one)
0 Incorrect Proof
10 Not specifying the edge that we want to take instead of e (can't just pick any one from the cycle)
15 Almost correct proof
25 Correct
=
HW
Homework #1
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, February 4rd, 5pm
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Problem Points
1 (13 pts)
Breakdown
13 Full Correctness Proof
* Cannot have lower th
-1 Assumed QuickSort Partition is O(1)
-3 O(log_cfw_3/2 n )!= O(log_cfw_4/3 n )
-6 Does not consider asymptotic cas
Problem 1
1.1, 1.5 pts each
0.5 correct answer
1.0 correct argument
1.2, 10.0 pts
5.0 correctly proved big O
5.0 correctly proved big Omega
Problem 2
2.1, 10.0 pts
2.0 base case of inductio
Homework #7
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Apr 4th, 11:59pm Late submissions: will NOT be accepted
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Where to su
Homework #7 Solutions
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Apr 4th, 11:59pm Late submissions: will NOT be accepted
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W
Solutions
Homework #4
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, Feb 25th, 11.59pm
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Format: Please start each problem on a
Homework #6
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, March 24th, 11.59pm
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Format: Please start each problem on a new page
600.363/463 Algorithms - Fall 2013
Solution to Assignment 1
(110 points)
I (30 points) Tow possible solutions are shown below.
Solution 1:
i. Algorithm(10 points)
Input: Two arrays A and B, both of le
600.363/463 Algorithms - Fall 2013
Solution to Assignment 2
(90 points+20 bonus points)
I (30 points)
1 a = 25, b = 5, logb a = log5 25 = 2. Since f (n) = n2.1 = n2+0.1 = (n2+0.1 ), by the master
theo
600.363/463 Algorithms - Fall 2013
Solution to Assignment 3
(120 points)
I (30 points)
(Hint: This problem is similar to parenthesization in matrix-chain multiplication, except the
special treatment o
600.363/463 Algorithms - Fall 2013
Solution to Assignment 4
(30+20 points)
I (10 points)
This problem brings in an extra constraint on the optimal binary search tree - for every node
v , the number of
600.363/463 Algorithms - Fall 2013
Solution to Assignment 5
(20 points)
I (10 points)
Note that the optimal substructure of LCS holds. We introduce another variable to record
the ending symbol of the
600.363/463 Algorithms - Fall 2013
Solution to Assignment 6
(30 points)
I (10 points) 21-1 O-line minimum
a The values in the extracted array are 4, 3, 2, 6, 8, 1.
b Note that each key is inserted onl