CS108L Computer Science for All
Week 11: Video Summaries
Search Algorithms
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Searching is what we when we want to find specific item among a group of items
Linear (Sequential) Search
 Simplest search method: Check every one of its elements, one at a time and in
sequence, until the desired one is found
 Psuedocode
 Specify the item you are looking for
 For each item in the list:
 Check list item to see if it is desired item
 YES  stop the search and return the item's location.
 NO  go to the next item on the list
 Pros
 Simple  easy to understand and implement
 Works well for
 Small lists
 Single searches of unsorted lists
 Cons
 More time consuming than other methods
 The worst case search  number items in the list
Binary Search
 Method:
 Start with a sorted list
 Repeat
 Divide list in half
 Check to see which half your item is in
 Select that half
 Pros
 Powerful
 Fast
 Relatively easy to understand
 Works well for large sorted data sets
 Cons
 Must sort your list first
 More difficult to implement
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Recursion
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What is Recursion?
▫ It is a concept/method used in computer science and mathematics
▫ Recursive problem: The problem can be described as a reduced or smaller
form of the same problem
▫ Sometimes the problem gets so small that the solution of the small problem
is trivial  can solved recursively or has a recursive implementation
▫ Recursion occurs in computer science when you use a recursive
implementation
Example
5! = 5 * 4 * 3 * 2 * 1
Or
5! = 5 * 4! Can be solved Recursively
• Or in general
n! = n * n-1 * n-2 * …* 3 * 2 * 1
Or
n! = n * (n-1)!
Implemented by calling a function or procedure in the body of that same function or
procedure. (must be prevented from consuming excessive computing resources)
Factorial Psuedocode
factorial N
if N <=1
(then factorial = 1)
(else factorial = N * factorial[N-1])
Pros
▫ Recursive description --- simple, elegant, and easy to explain and understand.
▫ Recursive implementation --- straightforward to build and verify.
Cons
▫ Can be difficult to understand at first.
▫ In some programming languages not as efficient as iteratively
▫ Can be difficult to program
 Circularity  infinite loop  MUST PUT IN A STOP
Why use recursion?
▫ The problem/program may be easier to understand, solve and program
using recursion
▫ When you have a recursive description  recursive solution is the most
direct solution path
▫ Usually creating an easy to verify code is more important than creating the
most efficient code
For every recursive algorithm, there is an equivalent iterative (looping) algorithm!!
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Algorithm Analysis
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What do we mean?
▫ Develop an understanding of the characteristics of the algorithm for different
input parameters.
Why?
▫ Predict performance/compare/choose algorithms
▫ Frequently more than one solution - Sorting
▫ Understand how it works  leads to improvement  shorter, simpler, and
more elegant algorithms
Use Computation Complexity
▫ A way to analyze an algorithm
▫ Takes into account how difficult and how efficient or fast the algorithm is.
Usually evaluate
▫ Amount of Time = Time Complexity
▫ Amount of Memory = Space Complexity
Time Complexity = Number of Operations
• Independent of programming language and computer used
• Algorithms are a sequence of steps or operations
• The more steps/operations, the longer the algorithm takes to run
• Measure of time = number of operations
▫ What is an operation? Anytime you ask the computer to do something
• Arithmetic operations
• Comparisons
• Swaps
• Copies or saves
• Accessing a list
• Number of times through a loop
▫ How do we do it?
• Calculation
• Look at the basic “loop’ that is used for each input
▫ Do not look at operations outside the “loop”
▫ Put a time value on each operation
• Look at how many times is the loop executed for each
type/amount of input!
• Look at how much input you have.
• Run the program
• Different types/amounts of inputs
▫ Look at Best/Worst/Average case
• Best-Case complexity: This is the complexity of solving the problem
for the best input of size n.
• Worst-case complexity: This is the complexity of solving the problem
for the worst input of size n. This is what we are really concerned
with.
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Average-case complexity: This is the complexity of solving the
problem on an average.
Space Complexity (Memory used0
▫ One algorithm may require more memory.
▫ If memory is a scarce resource, then Space Complexity (memory used) is
important
▫ Not as much of a problem as it used to be but data sets are getting huge.
There is often a time-space-tradeoff
▫ Want
 Low Computing time and
 Low Memory consumption.
▫ One then has to make a compromise
Usually look at Computational Complexity (efficiency)
▫ Time Complexity
▫ Space Complexity - Memory
▫ Other things may be important
 Difficulty
• Can we understand and implement it?
• Can we modify it?
 Validation
• Can we validate correctness of the code?
 Suitable
• Does the code suit the problem?
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