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Traversing an array

1. Definition2. Use the for loop3. Some new functions4. Use the while loop

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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

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Most practical loop

• The loop used to traverse an array: for

• Applied to a vectorfor k = 1:__

%codeend

• Applied to a matrixfor r = 1:__

for c = 1:__ %codeend

end

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.

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Helpful functions

• How many elements are in the array?

Function Return 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 nth dimension

numel(array) Number of elements total in the array

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Example1 Find the minimum (in a vector)

INDEX: (1) (2) (3) (4) length(array)

k k k k k k

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Example2 Find the minimum (in a matrix)

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Example2 Find the minimum (in a matrix)

• Nested loops

(1)

(2)

(3)

(4)

(5)

(1) (2) (3) (4) (5) (6) (7)

r

c c c c c c c

r

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Example3 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

3 1 3 6 6 3 3 6 3 4 1

number count

II0IIIII0III

123456

Brainstorm Question:-Loops?-Counting?-Traversing the array?

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Example3 Count the number of elements (vector)

• Assume this array of dices (values 1 through 6 only)

3 1 3 6 6 3 3 6 3 4 1

number count

IdieNbdieNb

k k k k k

INDEX: (1) (2) (3) (4) length(array)

k

123456

I0

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?

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Example3 Count the number of elements (vector)

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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)

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Example4 Linear Search (Vector)

• Assume this array of dices (values 1 through 6 only)

• Have I rolled at least one 5?

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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!