cs10 final review by glenn sugden is licensed under a creative commons...
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CS10 Final Review by Glenn Sugden is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
CS10 Final Review
Programming
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Concept Review
• Loops & Variables
•Conditionals
• Lists
• Algorithms & Complexity
•Concurrency
•Recursion
•Data Structures
•Hash Tables
• Lamdas & HOFs
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Loops & Variables
Correct?
Multiplying operand1 by operand2
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Loops & Variables
No! Why?
Multiplying operand1 by operand2
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Loops & Variables
Uninitialized Variable
Multiplying operand1 by operand2
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Loops & Variables
Initialized Variable!
Multiplying operand1 by operand2
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Loops & Variables
Be sure that yourvariables are initialized to a correct / known / sane value!
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Loops & Variables
Correct now?
Multiplying operand1 by operand2
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Loops & Variables
What if operand1 is negative? Or a “real”
number like 2.3?
Multiplying operand1 by operand2
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Loops & Variables
Be sure that yourlooping conditions
are valid!
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Reports “+” for positive numbers, “-” for negative
numbers.
Correct?
Conditionals
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Reports “+” for positive numbers, “-” for negative
numbers.
No! Why?
Conditionals
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Conditionals
Reports “+” for positive numbers, “-” for negative
numbers.
What aboutnumber = 0?
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Conditionals
Loops & Variables
•Be sure that your conditionals handle all possible cases!
•Double-check edge cases, or inputs that fall on either side of your predicate.
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Lists
Duplicate wordsbeginning with ‘c’
Does this correctly loop over list?
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Lists
No! Why?
Duplicate wordsbeginning with ‘c’
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Lists
Index within conditional!
Duplicate wordsbeginning with ‘c’
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Duplicate wordsbeginning with ‘c’
Lists
Correct now?
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Lists
No! Why?
Duplicate wordsbeginning with ‘c’
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Lists
Off by 1!
Duplicate wordsbeginning with ‘c’
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Lists
Correct now?
Duplicate wordsbeginning with ‘c’
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Lists
No! Why?
Duplicate wordsbeginning with ‘c’
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Duplicate wordsbeginning with ‘c’
Lists
The list keeps changing size!
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Lists
The list keeps changing size!
Duplicate wordsbeginning with ‘c’
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Lists
How do you correct it?Here is one solution...
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Duplicate wordsbeginning with ‘c’
Lists
Push the index past the inserted item...
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Lists
Seems pretty “kludgy” though...Here is a much, much better solution...
http://en.wikipedia.org/wiki/Kludge
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Duplicate wordsbeginning with ‘c’
Lists
Make a new, resulting list!
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Lists
Much better! And our original list is
still intact!
Duplicate wordsbeginning with ‘c’
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•Be sure indexes are correct during the entire loop.
•BYOB starts list indexing at 1
•If the input list changes size during the loop, your index will be off!
Check-Lists
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Algorithms & Complexity
Order of growth?
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Constant: O(c)Reason: No matter what “n” is, the loop always repeats
1000 times.
Algorithms & Complexity
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Algorithms & Complexity
Order of growth?
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Still Constant: O(c)Reason: No matter what the
list is, the loop always repeats 1000 times.
Algorithms & Complexity
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Algorithms & Complexity
Order of growth?
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Linear: O(n)Reason: Number of operations proportional to the input size
(n)
Algorithms & Complexity
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Algorithms & Complexity
Order of growth?
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Still Linear: O(n)Reason: Number of operations proportional to the input size
(length)
Algorithms & Complexity
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Algorithms & Complexity
Order of growth?
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Reason: Number of operations proportional to the square of the size of the input data (n)
Algorithms & Complexity
Quadratic: O(n2)
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Algorithms & Complexity
Quadratic: O(n2)
Input size
# of operations
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Algorithms & Complexity
Order of growth?
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Algorithms & Complexity
Still Quadratic: O(n2)Reason: Number of operations proportional to
the square of the size of the input data (length)
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Algorithms & Complexity
Order of growth?
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Algorithms & Complexity
Reason: the recursive call is run twice for each value of n.
Exponential: O(cn)
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Algorithms & Complexity
Exponential: O(2n)
Input size
# of operations
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Algorithms & Complexity
Order of growth?
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Algorithms & Complexity
Reason: the number of times the loop runs grows far more slowly
(square root) than “n”
Logarithmic: O(Logcn)
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# of operations
Algorithms & Complexity
2
Input size
Note that
these have
traded places!
Logarithmic: O(Log n)
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Algorithms & Complexity
2
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Compare!
Note that linear growth doesn’t even register on this graph!
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Consider the number of times the calculation repeats, rather than
specific inputs.
Algorithms & Complexity
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Algorithms & ComplexityExamples
Constant
Linear
Quadratic
Exponential
Logarithmic
Hash Table Lookup
Text or List Length
Square Matrix
Calcs.(Naïve) Sorting
Recursive Fractals
Binary Searches
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Concurrency
List adds upto 200?
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Concurrency
List adds upto 200?
No! Why?
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Concurrency
List adds upto 200?
No! Why?
These might choose
the same number at the same
time!
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Concurrency
List adds upto 200?
Anything else?
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No “wait” here means these might access
the same indexes (or not access them at
all), by interrupting a
broadcast script that is already
running!
Concurrency
List adds upto 200?
No! Why?
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Recursion
n=0
n=1
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n=4
n=∞
n=2
n=3
Recursion
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n=4
n=∞
n=2
n=3
Recursion
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RecursionAn algorithmic technique where a function, in order to accomplish a task, calls itself with some part of the task.
•Recursive solutions involve two major parts:1.Base case(s), in which the problem is simple enough to be solved directly,2.Recursive case(s). A recursive case has three components:
1.Divide the problem into one or more simpler or smaller parts of the problems,
2.Invoke the function (recursively) on each part, and3.Combine the solutions of the parts into a solution for the
problem.
•Depending on the problem, any of these may be trivial or complex.
http://inst.eecs/~cs3l/sp09/lectures/L06/2009SpCS3L06.html
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Data Structure : Hash Tables
Can we use “MapReduce” to build a
hash table?
(we’ll come back to that...)
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Lambdas & HOFs
•What is a Lambda?
•What is a Higher-Order Function (HOF)?
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Lambdas & HOFs
•A “First Class” Procedure
•“Function as Data”
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Lambdas & HOFs•What is a Higher-Order Function
(HOF)?
•In mathematics and computer science, higher-order functions, functional forms, or functionals are functions which do at least one of the following:
■ take one or more functions as an input■ output a function
http://en.wikipedia.org/wiki/Higher-order_function
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Lambdas & HOFs Useful HOFs (you can build your own!) map Reporter over List
Report a new list, every element E of List becoming Reporter(E)
keep items such that Predicate from ListReport a new list, keeping only elements E of List if Predicate(E)
combine with Reporter over ListCombine all the elements of List with Reporter(E)This is also known as “reduce”
Acronym example keep map combine
http://inst.eecs.berkeley.edu/~cs10/sp11/lec/17/src/2011-03-30-CS10-L17-DG-HOF-I.pptx
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Data Structure : Hash Tables
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Data Structure : Hash Tables
•Determine size of hash table.
•Hashing function (algorithm) to generate keys (index) from values (items).
•Modulo key (index) by hash table size.
•Store key and value in hash table at the resulting index.
•Find key in table using above algorithms (reading value instead of storing it).
http://en.wikipedia.org/wiki/Hash_table
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Data Structure : HOF/Hash Tables
Can we use “MapReduce” to
build a hash table?
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•Try to program one on your own... it’s great practice with HOFs, Lists, etc.!
•I will post the solution to Piazzza...
Yes!
Data Structure : HOF/Hash Tables