Data StructuresMore List Methods

Our first encodingMatrix

CQ:Are these programs equivalent?

b = [‘h’,’e’,’l’,’l’,’o’]b.insert(len(b), “w”)print(b)

b = [‘h’,’e’,’l’,’l’,’o’]b.append(“w”)print(b)

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A: yes

B: no

Advanced List OperationsL = [0, 1, 2, 0]

L.reverse()print(L) will print: [0, 2, 1, 0]

L.remove(0)print(L) will print: [2, 1, 0]

L.remove(0)print(L) will print: [2, 1]

print (L.index(2)) will print 0

Why are Lists useful?They provide a mechanism for creating a

collection of items

def doubleList(b): i = 0 while i < len(b): b[i] = 2 * b[i] i = i +1 return (b)

print(doubleList([1,2,3]))

Using Lists to Create Our Own Encodings

Python provides a number of encodings for us:Binary, ASCII, Unicode, RGB, Pictures etc.

We know the basic building blocks, but we are still missing something …We need to be able to create our own encodings

What if I want to write a program that operates on proteins?

Under the hood: what is a matrix?

A matrix is not “pre defined” in python

We “construct” a way to encode a matrix through the use of listsWe will see how to do so using a single list (not

ideal)We will see how to do so using a list of lists

Two different ways Row by Row Column by Column 1 2

3 4( )

ListsSuppose we wanted to extract the value 3

The first set of [] get the array in position 1 of y. The second [] is selecting the element in position 2 of that array. This is equiv. to:

y = [“ABCD”, [1,2,3] , ”CD”, ”D”]y[1][2]

z = y[1]z[2]

Lets make it more concrete!

Lets revisit encoding a matrix

Lets try something simple:A = [1, -1, 0, 2]B = [1, 0, 0, 0.5, 3, 4, -1, -3, 6]

Does this work?We lose a bit of information in this encoding

Which numbers correspond to which row

We can explicitly keep track of rows through a row length variable

B = [1, 0, 0, 0.5, 3, 4, -1, -3, 6]rowLength = 3B[rowLength*y +x]

Lets convince ourselves

x = 0y = 0B[3*0 + 0]

B = [1, 0, 0, 0.5, 3, 4, -1, -3, 6]rowLength = 3B[rowLength*y +x]

x = 1y = 1B[3*1 + 1]

x = 2y = 1B[3*1 + 2]

Can we encode it another way?

We can encode column by column, but we lose some information againWhich numbers correspond to which column

We can explicitly keep track of columns through a column length variable

B = [1, 0.5, -1, 0, 3, -3, 0, 4, 6]columnLength = 3B[columnLength*x + y]

Lets convince ourselves

x = 0y = 0B[3*0 + 0]

x = 1y = 1B[3*1 + 1]

x = 2y = 1B[3*2 + 1]

B = [1, 0.5, -1, 0, 3, -3, 0, 4, 6]columnLength = 3B[columnLength*x + y]

Lists of ListsRecall that when we had a string in our list

B = [“ABCD”, 0, 1, 3]

We could utilize the bracket syntax multiple timesprint B[0][1] would print B

Lists can store other ListsB = [[0, 1, 3], 4, 5, 6]

Another way to encode a Matrix

Lets take a look at our example matrix

What about this?B= [[1, 0, 0], [0.5, 3, 4], [-1, -3, 6]]

Why is this important?We can now write code that more closely

resembles mathematical notation i.e., we can use x and y to index into our matrix

B = [[1, 0, 0], [0.5, 3, 4], [-1, -3, 6]]for x in range(3): for y in range(3): print (B[x][y])

…but first some more notation

We can use the “*” to create a multi element sequence6 * [0] results in a sequence of 6 0’s[0, 0, 0, 0, 0, 0]3 * [0, 0] results in a sequence of 6 0’s[0, 0, 0, 0, 0, 0]10 * [0, 1, 2] results in what?

What is going on under the hood?

Lets leverage some algebraic properties3 * [0, 0] is another way to write[0, 0] + [0, 0] + [0, 0]

We know that “+” concatenates two sequences together

What about lists of lists?We have another syntax for creating lists

[ X for i in range(y)]This creates a list with y elements of X

Example: [ 0 for i in range(6)] ≡ [0]*6[0, 0 ,0 ,0 ,0 ,0]

Example: [[0, 0] for i in range(3)] ≡ [[0,0]]*3[[0, 0], [0, 0], [0, 0]]

What does this does: [2*[0] for i in range(3)]?

Lets put it all together

m1 = [ [1, 2, 3, 0], [4, 5, 6, 0], [7, 8, 9, 0] ]m2 = [ [2, 4, 6, 0], [1, 3, 5, 0], [0, -1, -2, 0] ]m3= [ 4*[0] for i in range(3) ]

for x in range(3): for y in range(4): m3[x][y]= m1[x][y]+m2[x][y]

Data structuresWe have constructed our first data structure!

As the name implies, we have given structure to the dataThe data corresponds to the elements in the matrixThe structure is a list of lists

The structure allows us to utilize math-like notation

Clicker Question: did we encode the same matrix

in both programs?

[[1, 2], [3, 4]] [[1, 3], [2, 4]]

21

A: yes

B: no

C: maybe

Lets explore why it depends

1 23 4

1 32 4

[[1, 3], [2, 4]]

2[[1, 2], [3, 4]]

1

( () )

Both lists of lists can either be a row by row or acolumn by column encoding

Let us encode something else using lists!

We call this structure a tree

Root

Root

How might we encode such a structure?

What structures do we know of in python?Strings, Ranges, Lists

We know that lists allow us to encode complex structures via sub listsWe used sub list to encode either a row or a

column in the matrixWe used an ‘outer’ list of rows or columns as a

matrix

Can we use the same strategy?

How might we encode a simple tree?

Root

Leaf1 Leaf2 Leaf3

Tree = [‘Leaf1’, ‘Leaf2’, ‘Leaf3’]

Trees can be more complex

Root

Leaf1 Leaf2

Leaf3 Leaf4 Leaf5

Tree = [‘Leaf1’, ‘Leaf2’, [‘Leaf3’, ‘Leaf4’, ‘Leaf5’]]

Trees can be more complex

Root

Leaf1

Leaf2

Leaf3 Leaf4 Leaf5

Tree = [[‘Leaf0’,‘Leaf1’], ‘Leaf2’, [‘Leaf3’, ‘Leaf4’, ‘Leaf5’]]

Leaf0

Trees can be more complex

Root

Leaf1

Leaf2

Leaf3 Leaf4

Leaf6

Tree = [[‘Leaf0’,‘Leaf1’], ‘Leaf2’, [‘Leaf3’, ‘Leaf4’, [‘Leaf5’, ‘Leaf6’]]]

Leaf0

Leaf5

What is the intuitionEach sub list encodes the ‘branches’ of the tree

We can think of each sub list as a ‘sub tree’

We can use indexes (the bracket notation []) to select out elements or ‘sub trees’

How can we select out the leaves?

Root

Leaf1

Tree[0]

Leaf2

Tree[1]

Leaf3

Tree[2]

Tree = [‘Leaf1’, ‘Leaf2’, ‘Leaf3’]

Indexes provide us a way to “traverse” the tree

Root

Leaf1

Leaf2

Leaf3 Leaf4

Leaf6

Tree = [[‘Leaf0’,‘Leaf1’], ‘Leaf2’, [‘Leaf3’, ‘Leaf4’, [‘Leaf5’, ‘Leaf6’]]]

Leaf0

Leaf5

0

0

0

0 1

1

1

1

2

2

Indexes provide us a way to “traverse” the tree

Root

Leaf1

Leaf2

Leaf3 Leaf4

Leaf6

Tree = [[‘Leaf0’,‘Leaf1’], ‘Leaf2’, [‘Leaf3’, ‘Leaf4’, [‘Leaf5’, ‘Leaf6’]]]Tree[2]

Leaf0

Leaf5

0

0

0

0 1

1

1

1

2

2

Indexes provide us a way to “traverse” the tree

Root

Leaf1

Leaf2

Leaf3 Leaf4

Leaf6

Tree = [[‘Leaf0’,‘Leaf1’], ‘Leaf2’, [‘Leaf3’, ‘Leaf4’, [‘Leaf5’, ‘Leaf6’]]]Tree[2][2]

Leaf0

Leaf5

0

0

0

0 1

1

1

1

2

2

Indexes provide us a way to “traverse” the tree

Root

Leaf1

Leaf2

Leaf3 Leaf4

Leaf6

Tree = [[‘Leaf0’,‘Leaf1’], ‘Leaf2’, [‘Leaf3’, ‘Leaf4’, [‘Leaf5’, ‘Leaf6’]]]Tree[2][2][1]

Leaf0

Leaf5

0

0

0

0 1

1

1

1

2

2

CQ: How do we select ‘Leaf4’ from the Tree?

Tree = [[‘Leaf0’,‘Leaf1’], ‘Leaf2’, [‘Leaf3’, ‘Leaf4’, [‘Leaf5’, ‘Leaf6’]]]

A: Tree[2][1]

B: Tree[3][2]

C: Tree[1][2]

Operations on TreesTrees, since they are encoded via lists support

the same operations lists supportWe can “+” two treesWe can embedded two trees within a list

This creates a larger tree with each of the smaller trees as sub trees

Example: Tree1 = [‘Leaf1’, ‘Leaf2’] Tree2 = [‘Leaf3’, ‘Leaf4’] Tree = [Tree1, Tree2]

“+” two trees

Leaf1

Leaf2

Leaf3 Leaf4Leaf0

Leaf6Leaf5Tree1 = [[‘Leaf0’, ‘Leaf1’]]Tree2 = [‘Leaf2’]Tree3 = [[‘Leaf3’, ‘Leaf4’, [‘Leaf5’, ‘Leaf6’]]]

“+” two trees

Leaf1

Leaf2

Leaf3 Leaf4Leaf0

Leaf6Leaf5Tree1 = [[‘Leaf0’, ‘Leaf1’]]Tree2 = [‘Leaf2’]Tree4 = Tree1+Tree2 [[‘Leaf0’, ‘Leaf1’], ‘Leaf2’]

“+” two trees

Leaf1

Leaf2

Leaf3 Leaf4Leaf0

Leaf6Leaf5Tree4 = [[‘Leaf0’, ‘Leaf1’], ‘Leaf2’]Tree3 = [[‘Leaf3’, ‘Leaf4’, [‘Leaf5’, ‘Leaf6’]]]Tree = Tree4+Tree3

Why are trees important?They are a fundamental structure in computer

science

They enable us to search very quicklyWe will revisit trees later in the course

What have we covered so far:Given a tree diagram we can write a list of lists Given a complex list we can select elements