1. Arrays An Array is an ordered collection of variables
One of our first “data structures”
Gives some relationships between different data
Usage: “store the grades of everybody in this class”
Without arrays: one variable for each student 
With arrays: one variable for the whole class! It just stores one entry for each student

2. Arrays Arrays have a “Base Type”
E.g. “An array of ints”
E.g. “An array of doubles”
E.g. ”An array of Strings”
Can be any built-in Java type, or a user-defined one (later)
Each object inside the array is called an element

3. Arrays Declared by adding [ ] to the type: General syntax:
double[] testScores; // Only declares, does not create space
testScores = new double[100]; // Allocates space in memeory
// Now we can start using it!
General syntax:
⟨array-variable ⟩ = new ⟨base-type ⟩[⟨array-length ⟩];

4. Arrays
An array in memory is like a “list” of particular length
int[] a = new int[5]; // Creates 5 elements in memory A
A[0]
A[1]
A[2]
A[3]
A[4]
The whole array is called A but individual elements are referenced with the [ ] operator
The array has an attribute called “length” which returns the number of elements:
A.length == 5 // will be true

5. Arrays
To access individual elements of an array variable, use the [ ] operator:
testScores[0] = 100.0; // Counting starts at 0
testScores[7] = 95.5; // Assigns 95 to the 8’th element
We can use an int variable to index:
int i = 10;
testScores[i] = 80;

6. Default values Every variable gets set to a default when it is created
However, usually shouldn’t be relied on

7. Arrays and For-Loops
We can use a for-loop to very easily traverse an array:
int[] myArray = new int[100];
// Assigns each element random between 1 and 10
for( int i = 0; i < myArray.length; i++ ){
myArray[i] = (int) (10.0*Math.random() + 1); }

8. Arrays and For-loops Calculate the average of our random array:
double avg;
double sum = 0;
for( int = 0; i < myArray.length; i++ ){
sum = sum + myArray[i]; // OR sum += myArray[i]; }
avg = sum / myArray.length;

9. Largest Array element
Use linear search: check one-by-one, remember the biggest so far
int biggest = myArray[0];
for( int i = 0; i<myArray.length; i++ ){
if ( myArray[i] > biggest ){
biggest = myArray[i]; }
System.out.println(”The largest element is: “ + biggest);

10. Array Access Using a for-loop is an example of sequential access
Access elements one-by-one
Another common way to access is by random access
Can’t predict which will be used next
Has hardware and memory implications

11. Example: Birthday paradox
How many people do you need to select at random until two have the same birthday?
Internal bias: we only typically consider our own birthday, but there are hundreds of comparisons to be checked in a room of ~20 people!
In pure statistics: with 23 randomly selected birthdays, there is a 50% chance that two of them are the same!
Program goal: simulate drawing random birthdays until you get a match. Count the number of draws until a collision happens.

12. Multidimensional Arrays
Can be used to hold many “dimensions” of data
E.g. Can think of an “array of arrays”
Acts like a matrix or a table:
int[][] myMatrix = new int[5][10]; // Declares 2-d, 5-by-10 array
// with 50 int elements myMatrix[3][2] = 100; // Access like a matrix, each dimension at a time

13. Multidimensional Arrays
Example task:
create a 2-d array to hold test scores of multiple students at once
Print the average of each student
Method: use a matrix where each student is a row and each column is an exam score

14. Example: Input Reverse
Algorithm
Ask the user for up to 100 positive integers, enter a 0 to stop
Store them each in an array
Count how many the user entered
Print the integers back to the user, in reverse order of how they were entered

15. Example: Finding the Mode
Algorithm:
Generate an array of 100 random numbers from 1 to 10
Use a length 10 array to count how many times each number appears in the array
Report the one that appears the most, or multiple if there are ties