Topic 2 - 2 Dimensional Arrays

2D Arrays in Java Arrays with multiple dimensions may be declared and used int[][] mat = new int[3][4]; the number of pairs of square brackets indicates the dimension of the array. could have an array of 3 dimensions, or 4 or more, but AP only covers arrays of 1 or 2 dimensions Topic 2 - 2D Arrays

Number of Rows and Columns Once 2D array created access elements with 2 subscripts int[][] mat = new int[3][4]; by convention, in a 2D array the first subscript indicates the row number and the second the column number mat has 3 rows and 4 columns per row Topic 2 - 2D Arrays

Coordinates of a Cell When accessing elements 2 subscripts are needed the first subscript indicates the row the second subscript indicates the column int[][] mat = new int[3][4]; mat[2][3] = 12; column row Topic 2 - 2D Arrays

2 Dimensional Arrays row 0 1 2 3 column 0 0 0 0 1 0 0 0 0 2 1 2 0 0 0 0 0 0 0 0 This is our abstract picture of the 2D array mat[2][1] = 12; Topic 2 - 2D Arrays

The Real Picture 0 1 2 3 0 0 0 0 1 2 0 1 2 3 0 0 0 0 mat 0 1 2 3 0 0 0 0 mat holds the memory address of an array with 3 elements. Each element holds the memory address of an array of 4 ints Topic 2 - 2D Arrays

Arrays of Multiple Dimension because multiple dimensional arrays are treated as arrays of arrays of arrays……multiple dimensional arrays can be ragged each row does not have to have the same number of columns each row array has its own length variable this is rarely used and is not tested on APCS int[][] raggedMat = new int[5][]; for(int i = 0; i < raggedMat.length; i++) raggedMat[i] = new int[i + 1]; Topic 2 - 2D Arrays

Rectangular 2D Arrays Ragged arrays are sometime useful, but normally we deal with rectangular 2D arrays each row has the same number of columns as every other row use this a lot as precondition to methods that work on matrices given int[][] mat mat.length refers to the number of rows in the 2D array mat[0].length refers to the number of columns per row Topic 2 - 2D Arrays

Working with 2D Arrays It is very common to have to access all elements of a 2D array Simplest way to do this is with a nested for loop. Topic 2 - 2D Arrays

Example of nested for Loops String temp; for(int i = 0; i < 4; i++) { for(int j = 0; j < 3; j++) { temp = "[" + i + "," + j + "] "; System.out.print( temp ); } System.out.println(); What is the output? outer loop inner loop Topic 2 - 2D Arrays

Output of Example [0,0] [0,1] [0,2] [1,0] [1,1] [1,2] [2,0] [2,1] [2,2] [3,0] [3,1] [3,2] What would out be if the println statement were removed? Topic 2 - 2D Arrays

2D Array Example Find the maximum value in a 2D array of ints must search every element public int findMax(int[][] mat) { /* pre: mat != null, mat.length > 0, mat[0].length > 0, mat is rectangular post: return maximum element in mat */ Topic 2 - 2D Arrays

findMax Implemented public int findMax(int[][] mat) { int max = mat[0][0]; for(int r = 0; r < mat.length; r++) { for(int c = 0; c < mat[0].length; c++) { if( mat[r][c] > max ) { max = mat[r][c]; } return max; Topic 2 - 2D Arrays

Conway' Game of Life A more complicated 2D Array problem Conway's Game of Life www.math.com/students/wonders/life/life.html cells are either occupied by an organism or empty next generation depends on the current status (occupied or empty) and your 8 neighboring cells occupied cell 0 - 1 neighbors, organism dies (loneliness) 2 - 3 neighbors, organism lives >= 4 neighbors, organism dies (over crowding) empty cell 3 neighbors birth, organism born Topic 2 - 2D Arrays

Game of Life Example 0 1 2 3 4 5 1 2 3 4 5 . . . . . . . * * . . . . . * . * . . * . * . . . . . * . . "*" -> occupied, "." -> empty, generation 0 Topic 2 - 2D Arrays

Game of Life 0 1 2 3 4 5 1 2 3 4 5 . 1 . 2 . 2 . 1 . 0 . 0 . 1 * 2 * 2 . 3 . 1 . 1 . 1 . 4 * 4 . 4 * 1 . 1 . 1 * 2 . 4 * 4 . 3 . 2 . 1 . 2 * 2 . 4 * 2 . 1 . 0 . 1 . 2 * 2 . 2 . 1 added number of neighboring cells that are occupied Topic 2 - 2D Arrays

Game of Life 0 1 2 3 4 5 1 2 3 4 5 . . . . . . . * * * . . . * . . * . . . * . * . . . . * . . apply all changes simultaneously, generation 1 Topic 2 - 2D Arrays

Game of Life 0 1 2 3 4 5 1 2 3 4 5 . . * . . . . * . * . . . . . * . . . . * . * . apply all changes simultaneously, generation 2 Topic 2 - 2D Arrays

Game of Life 0 1 2 3 4 5 1 2 3 4 5 . . . . . . . * * * . . . . . * . . . . . * * . . . * . * . apply all changes simultaneously, generation 3 Topic 2 - 2D Arrays

Game of Life 0 1 2 3 4 5 1 2 3 4 5 . . * . . . . . * * . . . . . . . . . . * . * . . . . * . . apply all changes simultaneously, generation 4 Topic 2 - 2D Arrays

Game of Life 0 1 2 3 4 5 1 2 3 4 5 . . * * . . . . * . . . . . . . . . . . * . * . . . . * . . apply all changes simultaneously, generation 5 (and so forth…) Topic 2 - 2D Arrays

Game of Life nextGen method Write a method that returns a 2D array of booleans that represents the next generation based on the current generation public boolean[][] nextGen(boolean[][] world) { /* pre: world != null, mat.length > 0, mat[0].length > 0, world is rectangular post: return next generation of world based on rules of Game of Life */ Topic 2 - 2D Arrays

nextGen source code public boolean[][] nextGen(int[][] world) { final int ROWS = world.length; final int COLS = world[0].length; boolean[][] result = new boolean[ROWS][COLS]; int num; for(int r = 0; r < ROWS; r++) { for(int c = 0; c < COLS; c++) { num = getNumNeighbors(world, r, c); //check for alive and survives if( world[row][col] && ( num == 2 || num == 3) result[row][col] = true; // check for birth else if( !world[row][col] && num == 3) } Topic 2 - 2D Arrays

2D Array in the MBCS The AP Marine Biology Case Study uses a 2D array in its BoundedEnv class the BoundedEnv class represents an area of water in which the fish in the MBCS are located instance variables for BoundedEnv private Locatable[][] theGrid; private int objectCount; Topic 2 - 2D Arrays

the allObjects method a method in the BoundedEnv class returns an array with a reference to everything in the BoundedEnv typical 2D array processing (nested loop) makes use of helper methods instead of accessing length variables directly (numRows, numCols) Topic 2 - 2D Arrays

the allObjects source code /** pre: none * Returns all the objects in this environment. * @return an array of all the environment objects **/ public Locatable[] allObjects() { Locatable[] theObjects = new Locatable[numObjects()]; int tempObjectCount = 0;   // Look at all grid locations. for ( int r = 0; r < numRows(); r++ ) { for ( int c = 0; c < numCols(); c++ ) { // If there's an object at this location, // put it in the array. Locatable obj = theGrid[r][c]; if ( obj != null ) { theObjects[tempObjectCount] = obj; tempObjectCount++; } return theObjects; Topic 2 - 2D Arrays