1. Traversing an array 1.Definition 2.Use the for loop 3.Some new functions 4.Use the while loop 1

2. Definition Traversing (verb): Travel across or through: "he traversed the forest". (Google) – With respect to arrays (vectors AND matrices), it means look at each element of the array Why would traversing an array be useful? – To find the minimum, maximum – To add up all the elements together – To add up only certain elements – To multiply all the elements together – To filter some elements out – To copy elements that match a criteria – To count how many elements fit a criteria – To delete elements that match a criteria 2

3. Most practical loop The loop used to traverse an array: for Applied to a vector for k = 1:__ %code end Applied to a matrix for r = 1:__ for c = 1:__ %code end 3 Number of elements Number of rows Number of columns NEVER hardcode these values. Keep the code flexible, ready to work for any size of arrays.

4. Helpful functions How many elements are in the array? 4 FunctionReturn value length(vector) Number of elements in the vector length(matrix) Highest dimension size(matrix,1) Number of rows in the matrix size(matrix,2) Number of columns in the matrix size(matrix,n) Size in the n th dimension numel(array) Number of elements total in the array

5. Example1 5 Find the minimum (in a vector) INDEX: (1) (2) (3) (4) length(array) kkkkkk

6. Example2 6 Find the minimum (in a matrix)

7. Example2 7 Find the minimum (in a matrix) Nested loops (1) (2) (3) (4) (5) (1) (2) (3) (4) (5) (6) (7) r ccccccc r

8. Example3 8 Count the number of elements (vector) Assume this array of dices (values 1 through 6 only) Task: Count how many times each number came out 31366336341 numbercount II 0 IIII I 0 III 123456123456 Brainstorm Question: -Loops? -Counting? -Traversing the array?

9. Example3 9 Count the number of elements (vector) Assume this array of dices (values 1 through 6 only) 31366336341 numbercount I dieNb kkkkk INDEX: (1) (2) (3) (4) length(array) k 123456123456 I 0 dieNb II How many times did we “traverse the array”? How many times will we loop? Which loop will we use? Will there be nested loops? How does counting works?

10. Example3 10 Count the number of elements (vector)

11. Traversing up till a condition is met The for loop is great if the entire array needs to be traversed What if… – Traverse only until a condition is met? – Traverse only until an item is found? – Of course the _________ loop is used! For example – Linear search: search 1 by 1 – Binary search: items are sorted, jump around (i.e. phone book) 11

12. Example4 12 Linear Search(Vector) Assume this array of dices (values 1 through 6 only) Have I rolled at least one 5?

13. Lessons Learned New functions – length() – size() – numel() To traverse an entire array: use the for loop To traverse an array up till a condition is met: use the while loop, though each criteria are still present – Start at index 1 (or at r=1, c=1) – Increment to the next index/indices (somewhere) – Indicate where to stop if search criteria not met – You may have to nest two while loops is array is a matrix! 13