Tower Building Activity
UNIT 2 DAYS 13-14
Standard 2: Problem Solving
Objective 1: Students will become "computational
thinkers" by applying a variety of problem-solving
techniques as they create solutions to problems that
are situated in a variety of contexts.
e. Create algorithms that meet specified objectives.
f. Compare the tradeoffs between different algorithms
for solving the same problem.
Standard 2: Problem Solving
Objective 2: Students will be introduced to selected
topics in discrete mathematics including Boolean logic,
functions, graphs and the binary number system.
b. Explore algorithms for fundamental practical
problems, such as searching, sorting and finding paths
in graphs.
Vocabulary
Iteration: The completion and repetition of a task
Linear Search:
In computer science, linear search or sequential search is a method for
finding a particular value in a list that checks each element in sequence until the desired
element is found or the list is exhausted. The list need not be ordered.
Binary Search:
A binary search algorithm (or binary chop) is a technique for finding a
particular value in a linear array, by ruling out half of the data at each step. A binary search
finds the median, makes a comparison to determine whether the desired value comes before or
after it, and then searches the remaining half in the same manner. A binary search is an example
of a divide and conquer algorithm (more specifically a decrease and conquer algorithm) and a
dichotomic search (more at Search algorithm).
Tower Building Activity
Donald Trump wants to build a 100 meter high tower as quickly
as possible. He has unlimited resources and an unlimited budget
and is willing to spend any amount to get the job done.
He has chosen to build the tower with blocks that are 100 meters
long and 100 meters wide, but only 1 meter tall. The blocks
interlock on top and bottom (like Legos). They cannot be stacked
sideways.
Using special lifters, putting one stack on top of another stack
takes one week regardless of how high the stacks are.
Journal: Tower Building Activity
What is the shortest amount of time
that it will take to build the tower?
(Write down your thoughts, and draw
an illustration, chart, or graph in your
journal.)
Planning - 10 meter tower
Week #
# of Stacks
# of Blocks in
Stack
Remainder
Example – 10 Meter Tower
Week 1
Week 1
Week 2
Week 2
Week 2
Week 3
Week 3
Week 3
Week 3
Week 4
Week 4
Week 4
SAMPLE SOLUTIONS
SAMPLE SOLUTIONS
1000 meter tower
SAMPLE SOLUTIONS
In general: The number of weeks is the smallest n such that the height of the tower is less than 2n.
Linear Search
Linear—start at the beginning, look at each
item until you find it or there is no more
data. Data DOES NOT have to be sorted first
Dictionary – look at each page until you
find the word “seize.” How many searches?
Binary Search
Binary—look at middle item, eliminate the
half where the value is not located. Find the
new middle element and continue the
process until you find it, or there is no more
data. Data DOES have to be sorted first
(put in some order, like alphabetical order.)
Binary Search
Binary— Searching for the word “Word.”
Open to the middle of the dictionary.
Eliminate the half where the value is not located.
 Find the new middle element
 Continue the process until you find it, or there is no
more data.
(HOW MANY SEARCHES DID IT TAKE????)
Key to Binary Search
Data DOES have to be sorted first (put in
some order, like alphabetical order.)
CREDITS
Exploring Computer Science, 2013 - www.exploringcs.org
How Binary Search Works, by Matt – https://www.youtube.com/channel/UCMxz5sSOwG2ZWLNbspdZ4GA
Created and compiled by Jeff Hinton 2014
Modified by Dawnene Young 2015