=
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
=
HW6 P2 (Total: 25 points)
=
(partial points available)
10
Homework #6
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, March 24th, 11.59pm
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Homework #3
Solutions
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
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Solutions
Homework #1
Introduction to Algorithms/Algorithms 1
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Spring 2016
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Homework #5
Introduction to Algorithms/Algorithms 1
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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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Pl
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 device.
Name
Signature
Date
1
Problem 1 (20 points)
In
Homework #8
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.
Where to submit: On blackboard, under student assessm
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 new page.
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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.
Where to submit: On blackboard, under student assessm
Homework #2
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, February 11th, 11.59pm
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Format: Please start each problem on a new page.
Where to submit: On blackboard, under student asse
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 page.
Where to submit: On blackboard, under student asse
Homework #1
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, February 4rd, 5pm
Late submissions: will NOT be accepted
Format: Please start each problem on a new page.
Where to submit: On blackboard, under student assessmen
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 case, only specific cases
-8 Incomplete Proof (did not pro
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 induction
8.0 the rest of the induction
2.2, 15.0 pts
1, 3.0
Homework #7
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Apr 4th, 11:59pm Late submissions: will NOT be accepted
Format: Please start each problem on a new page.
Where to submit: On blackboard, under student assessment
Please ty
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
Format: Please start each problem on a new page.
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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 are larger than the pivot.
Suppose Bob knows a secret wa
Homework #3
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 new page.
Where to submit: On blackboard, under student assessmen
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.
Where to submit: On blackboard, under student assessm
Solutions
Homework #2
Introduction to Algorithms/Algorithms 1
600.363/463
Spring 2016
Due on: Thursday, February 11th, 5pm
Late submissions: will NOT be accepted
Format: Please start each problem on a new page.
Where to submit: On blackboard, under studen
Quiz #2
Introduction to Algorithms/Algorithms 1
600.363/463
April 7th, 9:00-10:15am
Ethics Statement
I agree to complete this exam without unauthorized assistance from any person, materials, or device.
Signature
Date
1
Problem 1 (20 points)
Define a stron
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
theorem part 3, T (n) = (n2.1 )
2 a = 25, b = 5, logb a = l
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 on the two possible operators.)
The optimal substructure
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 nodes in both of its subtrees should be at least 1/5 o
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 common subsequence. Let c[i, j, a] be the length 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 only once. Since the loop starts from the smallest value o
600.363/463 Algorithms
Mid Semester Examination 1
October 11, 2013
1 hr 10 mins; closed book
I. Specify whether the following equations hold or not. Give an intuitive juscation for your
answer. Formal proofs are not needed.
1. 3n2 + 5n = O(n2 log n)
2. 2n