1. Multidimensional Arrays

2. Array Conceptual: What if we want more than one index???
List of objects indexed by a number
What if we want more than one index???
Row / Col

3. Two-Dimensional Arrays
Logical matrix
Declare:
type identifier[rows][cols];
Rows then columns
int scores[5][3]; 1 2 76 82 83 84 94 88 93 3 91 98 4

4. Initialization Initialize as list of lists: Zero out entire array:
int nums[3][4] =  {{19,22,31,42},                   {50,61,32,83},                    {93,47,15,66}};
Zero out entire array:
int nums[3][4] =  {{0}};

5. 2D Access Access: scores[row][col] scores[4][0] = 10;
cout << scores[2][1];
//outputs 93 1 2 76 82 83 84 94 88 93 3 91 98 4 10

6. Storage 2D arrays stored internally in row major order scores[1][??]
First dimension is start address of row
scores[1][??] 1 2 76 82 83 84 94 88 93 1 2 3 4 5 6 7 8 76 82 83 84 94 88 93

7. Traversals Traverse with nested loops Row index/col index
Loop order matters

8. Loop Samples i, j aren't great, but get used to them
Use constants for loop conditions

9. Single Dimension Traversals
Traversing one row or column requires one loop, one hardcoded index

10. Sum all columns
Sum all columns:
Column is main loop, rows second:

11. Sum Rows And Columns
Use arrays of row totals / col totals to build all sums 1 4 2 5 9 7 1 2 1

12. Sum Rows And Columns
Use arrays of row totals / col totals to build all sums 1 4 2 5 9 7 1 2 4 1 4

13. Sum Rows And Columns
Use arrays of row totals / col totals to build all sums 1 4 2 5 9 7 1 2 6 1 4 2

14. Sum Rows And Columns
Use arrays of row totals / col totals to build all sums 1 4 2 5 9 7 1 2 6 5 1 9 2

15. Sum Rows And Columns
Use arrays of row totals / col totals to build all sums

16. Passing Arrays
Must specify each dimension after first when passed as parameter

17. Storage 2D arrays stored internally in row major order scores[1][??]
First dimension is start address of row
scores[1][??] 1 2 76 82 83 84 94 88 93 1 2 3 4 5 6 7 8 76 82 83 84 94 88 93

18. Passing Arrays
Compiles, but BAD

19. Passing Arrays
Specify columns using global constant:

20. Passing Arrays Same using defined global constants:
Don't need to pass number rows
Still need to specify array second dimension

21. Faking 2D Can fake 2D with a 1D array scores[1][2] scores[3*1 + 2]
[row][col]  [colwidth*row][col] 1 2 76 82 83 84 94 88 93
scores[1][2]
scores[3*1 + 2]
3*0 + 0
3*0 + 1
3*0 + 2
3*1 + 0
3*1 + 1
3*1 + 2
3*2 + 0
3*2 + 1
3*2 + 2 1 2 3 4 5 6 7 8 76 82 83 84 94 88 93

22. Multidimensional Arrays
Can have an arbitrary number of dimensions: