Welcome to CS 1!
Professor Tom Cormen, 204 Sudikoff Lab
www.cs.dartmouth.edu/~cs1
Graduate TA: Shruti Agarwal
Undergraduate course staff:
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Michael Aaberg
Mazen Ammar
Ross Bower
Andre Chen
Daniel Chen
Kyle Dotterrer
Ella Dzenitis
Irene Feng
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Isabella Florissi
Emily Greene
Vivian Hu
Mahina Kaholokula
Jaki Kimball
Gabrielle Kirlew
Joshua Lang
Justine Lee
Courtney Ligh
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Annie Ma
Andrew Meier
Lauren Mitchell
Tim Rizvanov
Anya Rosen
Brophy Tyree
Kristen Vondrak
Lily Xu
Problem 1: Who has my Gumby?
Algorithm: A precise sequence of simple steps to
solve a problem
Algorithm 1
Step 1: Ask someone new if he or she has my
Gumby.
Step 2: If the answer is yes, then stop: I have found
my Gumby.
Step 3: If the answer is no and everyone has been
asked, then stop: nobody has my Gumby.
Step 4: Otherwise (the answer is no but there is
someone new to ask), go back to step 1.
Evaluating an algorithm
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Is our algorithm correct? If it gives an answer,
are we sure that the answer is right?
Is our algorithm complete? Does it always find
the answer, if the answer exists?
Is our algorithm efficient? How much time will it
take to run? In the best case? In the worst case?
Could we implement the algorithm as a
computer program?
Problem 2: What is my friend’s phone number?
Algorithm 2: Linear search
Step 1: Read a new name in the phone book.
Step 2: If it’s my friend’s name, then stop: we found
my friend’s name and home phone number.
Step 3: If not my friend’s name and all names have
been read, then stop: my friend’s phone
number is unlisted.
Step 4: Otherwise (not my friend’s name but there is
a new name to read), then go back to step 1.
Problem 2: What is my friend’s phone number?
Algorithm 3: Binary search
Step 1: Rip the phone book in half.
Step 2: Choose the half containing my friend’s
name. Discard the other half.
Step 3: If what remains is just one page, then search
for my friend’s name on that page.
Step 4: If what remains is more than just one page,
then go back to step 1.
Properties of binary search
• Would binary search work if the phone book
were not sorted by name?
• How efficient is this algorithm?
 How many rips would we need if the phone book
contained 2 pages?
 4 pages?
 8 pages?
 16 pages?
 32 pages?
 256 pages? (Hint: 256 = 28)
 1024 pages? (Hint: 1024= 210)
 1,048,576 pages? (Hint: 1,048,576= 10242 = 220)
Problem 3: How many students shall I
tell my colleagues attended CS 1 today?
Algorithm 4: Counting in parallel
Step 1: Everyone stand up. Think of the number 1.
Step 2: Everyone who is standing: find a partner. If an odd number of
people are standing, then one person will remain without a partner.
Step 3: If you have a partner, then one of you will sit down. Decide
between you on who will sit. The one who sits should tell the one
who remains standing the number he or she is thinking.
Step 4: If you are standing and were told a number, add it to the
number you were thinking, and think about this new number.
Step 5: If you are the last person standing, report the number you are
thinking.
Step 6: Otherwise (more than one person is standing), then go back to
step 2.
Properties of counting in parallel
• How many rounds would it take if only 2
people were in the class?
• 4 people?
• 8 people?
• 16 people?
• How many rounds did it take? Why?