CS62 - Spring 2020 - Class 7
Example code in this lecture
BinarySearchExamples
ArrayList
Lecture notes
admin
- Darwin part 1 (World and Species) due tonight
- Thursday mentor hours 7-9pm
Readings
- Chapter 1.3 (Page 136–137)
packages
- a package is a collection of classes
- two ways packages are indicated (both are required):
1) the .java files occur in the same directory
2) the package is indicated at the top of the file:
package darwin;
- For example, all of the files for the second assignment are in the darwin package
- by convention, packages are lowercase
- All classes within a package can utilize the other class functionality (i.e., public methods) without importing
- we often have a package hierarchy, e.g.
- "java" is a built-in package
- within that, there is the io package, i.e., "java.io"
- if you want to utilize a class outside of your package, you need to import it
- when we import files, you can either import a specific class in a package:
import java.io.BufferedReader
- or you can import all the files in the package:
import java.io.*
package private
- what are the access modifiers we've seen so far:
- private: only accessible within the class
- public: anyone can access it
- protected: only subclasses can access it
- there's one last modifier: no modifier (often call package private)
- accessible within the package
- generally this is not a preferred modifier
- We'll use it once or twice in this class, but generally you should avoid it
look at search2 method in
BinarySearchExamples code
- what does this method do?
- uses a helper method
- does the same thing as the previous, but using recursion
- which version is better?
- what is the running time, using Big-O notation?
- same as for the iterative version
can we do better than either of these procedures?
- without any preprocessing of the data, no
Last time we played the number guessing game. How were you able to find the number without just listing a bunch of random numbers?
- When we guessed a number, we were told larger or smaller which allowed us to eliminate a bunch of numbers
what if I told you the data was in sorted order?
- how do you find information in a phonebook (where the data is in essence, sorted)?
show binarySearch method in
BinarySearchExamples code
- what does the code do?
- keeps a low and a high value
- we know that if findMe is in the array, then nums[low] <= findMe <= nums[high]
- picks the middle element between low and high
- compares that middle element to our value and then either finds the data or DISCARDS HALF OF THE REMAINING DATA
- an example
- 1, 3, 7, 15, 16, 18, 21, 40, 45, 50
- what's the running-time?
- best case: O(1) it's the midpoint in the array
- worst case: not found
- how many times do we iterate through the while loop?
- let's consider the case where the number of elements is a power of 2
- we could always pad it up do the next largest power of 2
- at each iteration we throw away half of the data, n/2, n/4, n/8
- when will it be done?
- when n/2^i = 1
log n/2^i = log 1
log n - log 2^i = 0
log n - 2 log i = 0
log n = 2 log i
i = log_2 n
- runtime is O(log_2 n)
- average case: half as many iterations through the while loop... still O(log_2 n)
how would we write a recursive version?
- we'd need a helper method
- rather than keeping low and high as variables, they'll be parameters
- then, rather than adjust them, we just call recursively call our method with smaller values
show binarySearchRecursive in
BinarySearchExamples code
Last comments on binary search
- It‚ is easy to get indices wrong, so be careful!
- "Although the basic idea of binary search is comparatively straightforward, the details can be surprisingly tricky... Professor Donald Knuth (taken from
http://en.wikipedia.org/wiki/Binary_search_algorithm
)
-
http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html
- How hard is it?
http://portal.acm.org/citation.cfm?doid=358476.358484,
only accessible on campus
- What if we wanted to return the first one in the list?
Lists
- lists are general structures that store sequential data
- the key operations are that we can get and set values at indices, but other operations will be useful.
- the BasicList interface in
ArrayList code
defines a very basic interface for lists
- get/set
- add (add to the end)
- size
ArrayLists
- Java has a List interface for data structures that store data sequentially:
-
https://docs.oracle.com/javase/8/docs/api/java/util/List.html
- lots of methods, but key: get and set and particular indices
- The ArrayList class implements this interface
- Why do you think its called "ArrayList"?
- the underlying structure that it stores the data in is an array
look at the BasicArraylist class in
ArrayList code
- keep track of two instance variables
- data (the actual data)
- size (the number of elements in the data)
- note this is different than the size of the data array
- Anything new/unusual in the constructor?
- we cannot create new arrays of type E (or of any type variable)
- this has to do with how Java implemented generics
- instead, we create a new array of Objects and type cast it to an E[]
- look at get and set
- what do you think the rangeCheck method does?
- checks to see that the index is within a valid range
- look at rangeCheck
- if we want to have a method raise an exception, we use the keyword "throw"
- remember, exceptions are just classes so we need to create a new instance
what are the run times of get, set, and size?
- Assuming array index operations are O(1), then O(1)
adding to an ArrayList
- so far, we haven't added any functionality over arrays
- what was the main functionality that ArrayLists added over arrays?
- add/extend
- how do you think this is done?
- we allocate some initial array
- we fill it in as we go
- what happens when it fills up?
- we have to create a bigger array!
- copy over the old values
what does the resize method do in the BasicArrayList class in
ArrayList code
?
- creates a new array of type E
- copies the existing value
- then sets data to be that new array!
- look at add method
- check to see if we're out of space
- if so, resize
- we can choose any size that's larger than the existing
- we'll talk more about how different sizes might affect things
look at ArrayList slides