1. Two dimensional arrays.
More arrays
Two dimensional arrays.

2. But our hotel reservation system has a limitation.
What if our hotel has more than one floor and each floor can have hundreds of rooms?

3. Maybe matrices from mathematics can help us.
Arrays (so far) are one dimensional.
Matrices are two dimensional.
(from wikipedia)

4. Maybe matrices from mathematics can help us.
So the row can be the floor of the hotel and the column can be the particular room # on that floor!

5. Introducing 2D arrays.

6. 2D arrays Declare (and allocate) a 1D array
int N = 100; //number of rooms
boolean rooms[] = new boolean [ N+1 ];
Declare (and allocate) a 2D array
int Floors = 10; //number of floors
int Rooms = 100; //rooms on a floor
boolean rooms2D[][] = new boolean[Floors+1][Rooms+1];

7. 2D arrays Initialize a 1D array Initialize a 2D array
for (int i=0; i<=N; i++)
rooms[i] = false; //initially unoccupied
Initialize a 2D array
int Floors = 10; //number of floors
int Rooms = 100; //rooms on a floor
boolean rooms2D[][] = new boolean[Floors+1][Rooms+1];
Looks like we’ll need a for loop for the floor and another for loop for the rooms. But first, how would we initialize all of the rooms on floor 0?

8. 2D arrays Initialize a 1D array Initialize a 2D array
for (int i=0; i<=N; i++)
rooms[i] = false; //initially unoccupied
Initialize a 2D array
int Floors = 10; //number of floors
int Rooms = 100; //rooms on a floor
boolean rooms2D[][] = new boolean[Floors+1][Rooms+1];
But first, how would we initialize all of the rooms on floor 0?
for (int rm=0; rm<=Rooms; rm++)
rooms2D[0][rm] = false;

9. 2D arrays
But first, how would we initialize all of the rooms on floor 0?
for (int rm=0; rm<=Rooms; rm++)
rooms2D[0][rm] = false;
Or…
int f = 0;
rooms2D[f][rm] = false;
Can we initialize the next floor?

10. 2D arrays Can we initialize the next floor? int f = 0;
for (int rm=0; rm<=Rooms; rm++)
rooms2D[f][rm] = false;
f = 1;
How about the next?

11. 2D arrays How about the next? int f = 0;
for (int rm=0; rm<=Rooms; rm++)
rooms2D[f][rm] = false;
f = 1;
f = 2; …
So f starts at 0 and then increments to the next floor and so on.

12. 2D arrays Initialization with nested for loops.
for (int f=0; f<=Floors; f++) {
for (int rm=0; rm<=Rooms; rm++) {
rooms2D[f][rm] = false; }

13. Recall from our 1D hotel reservation system…
//function that determines how many rooms
// are occupied in our hotel
static int occupiedCount ( boolean rooms[], int N ) {
int count = 0;
for (int i=1; i<=N; i++) {
if (rooms[i])
++count; }
return count;
Now, how can we make a similar function that works for our 2D hotel?

14. Recall from our 1D hotel reservation system…
//function that determines how many rooms
// are occupied in our 2D hotel
static int occupiedCount ( boolean rooms2d[][],
int Floors, int Rooms ) {
int count = 0;
for (int i=1; i<=N; i++) {
if (rooms[i])
++count; }
return count;
This still needs “adjustment.”

15. Recall from our 1D hotel reservation system…
//function that determines how many rooms
// are occupied in our 2D hotel
static int occupiedCount ( boolean rooms2d[][],
int Floors, int Rooms ) {
int count = 0;
int f = 1;
for (int i=1; i<=Rooms; i++) {
if (rooms[f][i])
++count; }
return count;
This is better but it still needs “adjustment.”

16. Recall from our 1D hotel reservation system…
//function that determines how many rooms
// are occupied in our 2D hotel
static int occupiedCount ( boolean rooms2d[][],
int Floors, int Rooms ) {
int count = 0;
for (int f=1; f<=Floors; f++) {
for (int i=1; i<=Rooms; i++) {
if (rooms[f][i])
++count; }
return count;
Done!

17. Back to matrices from mathematics.
In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e.,
(from wikipedia)

18. Practice with 2D arrays Calculate the trace of a 2D array.
Calculate the sum of all of the elements in a 2D array.
Calculate the sum of a particular row in a 2D array.
Calculate the sum of a particular column in a 2D array.
Calculate means (averages) for 1-4 above. Calculate mean for 3x3.

19. Recap Pass by value Pass by reference 1D arrays and 2D arrays
Arrays and functions