We've provided a set of starter files with skeleton code for the exercises in the lab. You can get them in the following places:

Consider the following code:

```
class Animal(object):
def __init__(self):
self.is_alive = True # It's alive!!
class Pet(Animal):
def __init__(self, name, year_of_birth, owner=None):
Animal.__init__(self) # call the parent's constructor
self.name = name
self.age = CURRENT_YEAR - year_of_birth
self.owner = owner
def eat(self, thing):
self.talk()
if thing == "poison":
self.lose_life()
print(self.name + " ate a " + str(thing) + "!")
def talk(self):
print("..")
```

What would python print if the following is typed into the interpreter, after the first two class definitions?

```
>>> a = Animal()
>>> a.is_alive
________
>>> a.talk()
________
>>> hamster = Pet("Hamster", 2014)
>>> hamster.talk()
________
>>> hamster.eat("seed")
________
>>> hamster.eat("poison")
________
```

Implement a `Cat`

class that inherits from `Pet`

. Use superclass methods wherever possible.

```
class Cat(Pet):
"""
>>> my_cat = Cat("Furball", 2011, "Me", lives=2)
>>> my_cat.talk()
Meow!
>>> my_cat.name
'Furball'
>>> my_cat.lose_life()
>>> my_cat.is_alive
True
>>> my_cat.eat("poison")
Meow!
Furball ate a poison!
>>> my_cat.is_alive
False
>>> my_cat.lose_life()
'Cat is dead x_x'
"""
def __init__(self, name, year_of_birth, owner, lives=9):
assert type(lives) == int and lives > 0
"*** YOUR CODE HERE ***"
def talk(self):
"""A cat says 'Meow!' when asked to talk."""
"*** YOUR CODE HERE ***"
def lose_life(self):
"""A cat can only lose a life if they have at least one
life. When there are zero lives left, the 'is_alive'
variable becomes False.
"""
"*** YOUR CODE HERE ***"
```

Now implement a `NoisyCat`

class, which inherits from `Cat`

. A `NoisyCat`

is
just like a normal `Cat`

except, when asked to talk, it says what a normal `Cat`

says twice.

```
class NoisyCat(Cat):
"""
>>> my_cat = NoisyCat("Noisy Kitty", 2011, "Me", lives=1)
>>> my_cat.talk()
Meow!
Meow!
>>> my_cat.name
'Noisy Kitty'
>>> my_cat.lose_life()
>>> my_cat.lose_life()
'Cat is dead x_x'
"""
def __init__(self, name, year_of_birth, owner, lives=9):
"*** YOUR CODE HERE ***"
# hint: do you need to write another __init__?
def talk(self):
"""A NoisyCat will always repeat what he/she said
twice."""
"*** YOUR CODE HERE ***"
```

In lecture, we introduced the OOP version of an `Rlist`

:

```
class Rlist:
"""A recursive list consisting of a first element and the rest.
>>> s = Rlist(1, Rlist(2, Rlist(3)))
>>> print(rlist_expression(s.rest))
Rlist(2, Rlist(3))
>>> len(s)
3
>>> s[1]
2
"""
class EmptyList:
def __len__(self):
return 0
empty = EmptyList()
def __init__(self, first, rest=empty):
self.first = first
self.rest = rest
```

Just like before, these `Rlists`

have a first and a rest. The
difference is that, now, the `Rlists`

are *mutable*.

To check if an `Rlist`

is empty, compare it against the class variable
`Rlist.empty`

:

```
if rlist is Rlist.empty:
return 'This rlist is empty!'
```

Don't construct another `EmptyList`

!

Predict what Python will display when the following lines are typed into the interpreter:

```
>>> print(Rlist(1, Rlist(2)))
_____
>>> Rlist()
_____
>>> rlist = Rlist(1, Rlist(2, Rlist(3)))
>>> rlist.first
_____
>>> rlist.rest.first
_____
>>> rlist.rest.rest.rest is Rlist.empty
_____
>>> rlist.first = 9001
>>> rlist.first
_____
>>> rlist.rest = rlist.rest.rest
>>> rlist.rest.first
_____
>>> rlist = Rlist(1)
>>> rlist.rest = rlist
>>> rlist.rest.rest.rest.rest.first
_____
```

In lecture, we learned about the special "underscore" methods for
classes, two of which were `__len__`

, which allows you to call the
builtin function `len`

on the object, and `__getitem__`

, which allows
you to use index notation on the object. Implement both of them for
the `Rlist`

class. Afterwards, the doctests for the `Rlist`

class
should pass.

```
class Rlist(object):
"""A mutable rlist class.
>>> r = Rlist(3, Rlist(2, Rlist(1)))
>>> len(r)
3
>>> len(r.rest)
2
>>> r[0]
3
>>> r[1]
2
"""
# previous stuff here
def __len__(self):
"*** YOUR CODE HERE ***"
def __getitem__(self, index):
"*** YOUR CODE HERE ***"
```

When we write recursive functions acting on `rlists`

, we often find that they
have the following form:

```
def func(rlist):
if rlist == Rlist.empty:
return <Base case>
else:
return <Expression involving func(rlist.rest)>
```

In the spirit of abstraction, we want to factor out this commonly seen pattern. It turns out that we can define an abstraction called `fold`

that do this.

A recursive list can be represented as a series of `Rlist`

constructors, where
`Rlist.rest`

is either another recursive list or the empty list.

We represent such a list in the diagram below:

In this diagram, the recursive list

```
Rlist(1, Rlist(2, Rlist(3, Rlist(4,Rlist(5)))))
```

is represented with `:`

as the constructor and `[]`

as the empty list.

We define a function `foldr`

that takes in a function `f`

which takes two
arguments, and a value `z`

. `foldr`

essentially replaces the `Rlist`

constructor
with f, and the empty list with `z`

. It then evaluates the expression and
returns the result. This is equivalent to:

```
f(1, f(2, f(3, f(4, f(5, z)))))
```

We call this operation a right fold.

Similarily we can define a left fold `foldl`

that folds a list starting from the
beginning, such that the function `f`

will be applied this way:

```
f(f(f(f(f(z, 1), 2), 3), 4), 5)
```

Also notice that a left fold is equivilant to python's `reduce`

with a starting value.

Write the left fold function by filling in the blanks.

```
def foldl(rlist, fn, z):
""" Left fold
>>> lst = Rlist(3, Rlist(2, Rlist(1)))
>>> foldl(lst, sub, 0) # (((0 - 3) - 2) - 1)
-6
>>> foldl(lst, add, 0) # (((0 + 3) + 2) + 1)
6
>>> foldl(lst, mul, 1) # (((1 * 3) * 2) * 1)
6
"""
if rlist is Rlist.empty:
return z
return foldl(______, ______, ______)
```

Now write the right fold function.

```
def foldr(rlist, fn, z):
""" Right fold
>>> lst = Rlist(3, Rlist(2, Rlist(1)))
>>> foldr(lst, sub, 0) # (3 - (2 - (1 - 0)))
2
>>> foldr(lst, add, 0) # (3 + (2 + (1 + 0)))
6
>>> foldr(lst, mul, 1) # (3 * (2 * (1 * 1)))
6
"""
"*** YOUR CODE HERE ***"
```

Now that we've written the fold functions, let's write some useful functions using list folding!

Write the `mapl`

function, which takes in a Rlist `lst`

and a
function `fn`

, and returns a new Rlist where every element is the function
applied to every element of the original list. Use either `foldl`

or
`foldr`

. Hint: it is much easier to write with one of them than the other!

```
def mapl(lst, fn):
""" Maps FN on LST
>>> lst = Rlist(3, Rlist(2, Rlist(1)))
>>> mapped = mapl(lst, lambda x: x*x)
>>> print(rlist_expression(mapped))
Rlist(9, Rlist(4, Rlist(1)))
"""
"*** YOUR CODE HERE ***"
```

Write the `filterl`

function, using either `foldl`

or `foldr`

.

```
def filterl(lst, pred):
""" Filters LST based on PRED
>>> list = Rlist(4, Rlist(3, Rlist(2, Rlist(1))))
>>> filtered = filterl(lst, lambda x: x % 2 == 0)
>>> print(rlist_expression(filtered))
Rlist(4, Rlist(2))
"""
"*** YOUR CODE HERE ***"
```

Notice that `mapl`

and `filterl`

are not recursive anymore! We used the
implementation of `foldl`

and `foldr`

to implement the actual recursion: we only
need to provide the recursive step and the base case to `fold`

.

Use `foldl`

to write `reverse`

, which takes in a recursive list and
reverses it. Hint: It only takes one line!

```
def reverse(lst):
""" Reverses LST with foldl
>>> reversed = reverse(Rlist(3, Rlist(2, Rlist(1))))
>>> print(rlist_expression(reversed))
Rlist(1, Rlist(2, Rlist(3)))
>>> reversed = reverse(Rlist(1))
>>> print(rlist_expression(reversed))
Rlist(1)
>>> reversed = reverse(Rlist.empty)
>>> reversed == Rlist.empty
True
"""
"*** YOUR CODE HERE ***"
```

**Extra for experts**: Write a version of reverse that do not use the
`Rlist`

constructor. You do not have to use `foldl`

or `foldr`

.

**Extra for Experts**: Write foldl using foldr! You only need to fill
in the `step`

function.

```
def foldl2(rlist, fn, z):
""" Write foldl using foldr
>>> list = Rlist(3, Rlist(2, Rlist(1)))
>>> foldl2(list, sub, 0) # (((0 - 3) - 2) - 1)
-6
>>> foldl2(list, add, 0) # (((0 + 3) + 2) + 1)
6
>>> foldl2(list, mul, 1) # (((1 * 3) * 2) * 1)
6
"""
def step(x, g):
"*** YOUR CODE HERE ***"
return foldr(rlist, step, identity)(z)
```

Trees are a way we have of representing a hierarchy of information. A family tree is a good example of something with a tree structure. You have a matriarch and a patriarch followed by all the descendants. Alternately, we may want to organize a series of information geographically. At the very top, we have the world, but below that we have countries, then states, then cities. We can also decompose arithmetic operations into something much the same way.

The name "tree" comes from the branching structure of the pictures, like real trees in nature except that they're drawn with the root at the top and the leaves at the bottom.

**Terminology**:

**node**: a point in the tree. In these pictures, each node includes a label (value at each node)**root**: the node at the top. Every tree has one root node children the nodes directly beneath it. Arity is the number of children that node has.**leaf**: a node that has no children. (Arity of 0!)

In this course, we will only be working with binary trees, where each node as at most two children. For a general binary tree, order does not matter. Additionally, the tree does not have to be balanced. It can be as lopsided as one long chain.

Our implementation of binary trees can be found in `trees.py`

:

```
class Tree:
def __init__(self, entry, left=None, right=None):
self.entry = entry
self.left = left
self.right = right
def copy(self):
left = self.left.copy() if self.left else None
right = self.right.copy() if self.right else None
return Tree(self.entry, left, right)
```

We also included a function `tree_string`

, which prints out a string
representation of a tree:

```
>>> print(tree_string(Tree(1, Tree(3, None, Tree(2)), Tree(4, Tree(5), Tree(6)))))
-1-
/ \
3 4
\ / \
2 5 6
```

Define the function `size_of_tree`

which takes in a tree as an
argument and returns the number of non-empty nodes in the tree.

```
def size_of_tree(tree):
r""" Return the number of non-empty nodes in TREE
>>> print(tree_string(t)) # doctest: +NORMALIZE_WHITESPACE
-4--
/ \
2 1-
/ \ / \
8 3 5 3
/ / \ / \
7 1 6 2 9
>>> size_of_tree(t)
12
"""
"*** YOUR CODE HERE ***"
```

Define the function `deep_tree_reverse`

, which takes a tree and
reverses the given order.

```
def deep_tree_reverse(tree):
r""" Reverses the order of a tree
>>> a = t.copy()
>>> deep_tree_reverse(a)
>>> print(tree_string(a)) # doctest: +NORMALIZE_WHITESPACE
--4---
/ \
1- 2-
/ \ / \
3 5 3 8
/ \ / \ \
9 2 6 1 7
"""
"*** YOUR CODE HERE ***"
```

Define the function `filter_tree`

which takes in a tree as an argument
and returns the same tree, but with items included or excluded based
on the pred argument.

Note that there is ambiguity about what excluding a tree means. For this function, when you exclude a subtree, you exclude all of its children as well.

```
def filter_tree(tree, pred):
r""" Removes TREE if entry of TREE satisfies PRED
>>> a = t.copy()
>>> filtered = filter_tree(a, lambda x: x % 2 == 0)
>>> print(tree_string(filtered)) # doctest: +NORMALIZE_WHITESPACE
4
/
2
/
8
>>> a = t.copy()
>>> filtered = filter_tree(a, lambda x : x > 2)
>>> print(tree_string(filtered))
4
"""
"*** YOUR CODE HERE ***"
```

Define the function `max_of_tree`

which takes in a `tree`

as an
argument and returns the max of all of the values of each node in the
tree.

```
def max_of_tree(tree):
r""" Returns the max of all the values of each node in TREE
>>> print(tree_string(t)) # doctest: +NORMALIZE_WHITESPACE
-4--
/ \
2 1-
/ \ / \
8 3 5 3
/ / \ / \
7 1 6 2 9
>>> max_of_tree(t)
9
"""
"*** YOUR CODE HERE ***"
```