Arrays

Initializing

Arrays are initialized by default:
- int[] array = new int[10] gives an array full of ten 0s
- What does boolean[] array = new boolean[15] give?
- How about String[] array = new String[22]?

How would you write a method daysInMonth(int month, int year)?
- How could an array help?
How would you write ordinalDate()?
How could a DAYS_IN_MONTH array help?
How could a different array let you remove the loop?

Look at a standard description of tax brackets: https://www.debt.org/tax/brackets/
- How could you write a calculateTax(income) method without using a loop (or explicitly calculating the tax for each bracket)?
  - 970 + .12 (income - 9700); 4543 + .22*(income - 39475)
  - https://turbotax.intuit.com/tax-tips/irs-tax-return/current-federal-tax-rate-schedules/L7Bjs1EAD
- We could create a Tax object with max and rate fields. Or we can just have two parallel arrays.
Sometimes having two arrays is easier than creating separate objects.

Write a method int mode(int[] nums) that returns the number that occurs most frequently.
How many loops does your code have?
Can you use only one loop?

A matrix (2D grid) can be represented as a 2D array:
- int[][] matrix = new int[5][7] generates a grid with 5 rows and 7 columns.
- Just use both indices to access: matrix[3][4] = 14
That’s the easy case. We need to peek under the hood:

A 2D array is an array of arrays. Saying new int[rows][cols] is really a short-cut for

int[][] matrix = new int[numRows]
for (int row = 0; row < numRows; ++row) {
     int[row] = new int[numCols];
}  

Each row in an array is a complete, separate Java object.
With this “array of array” model, we can access the dimensions of the array like this:
- int numRows = matrix.length;
- int numCols = matrix[0].length (this works if all rows have the same number of columns)
Because each row is a separate Java object, rows don’t have to all have the same number of columns.
- This is called a “jagged” array.
- Jagged arrays aren’t terribly common.
- Most common scenario is probably representing only half of a symmetric matrix.
  - Consider a matrix representing people in a room. friends[r][c] is true of person r and person c know each other. This matrix is symmetric. Thus, we need only store half of it.