【CS 61a study notes 4】Tree & Iterator & Generator

Tree

We often use recursion to solve Tree problem .The main idea is , we peel off the label of the tree to find the base case , and then use for-statement to apply the function to all branches.

Tree data abstraction

# Tree ADT

def tree(label, branches=[]):
    """Construct a tree with the given label value and a list of branches."""
    for branch in branches:
        assert is_tree(branch), 'branches must be trees'
    return [label] + list(branches)

def label(tree):
    """Return the label value of a tree."""
    return tree[0]

def branches(tree):
    """Return the list of branches of the given tree."""
    return tree[1:]

def is_tree(tree):
    """Returns True if the given tree is a tree, and False otherwise."""
    if type(tree) != list or len(tree) < 1:
        return False
    for branch in branches(tree):
        if not is_tree(branch):
            return False
    return True

def is_leaf(tree):
    """Returns True if the given tree's list of branches is empty, and False
    otherwise.
    """
    return not branches(tree)

def print_tree(t, indent=0):
    """Print a representation of this tree in which each node is
    indented by two spaces times its depth from the root.

    >>> print_tree(tree(1))
    1
    >>> print_tree(tree(1, [tree(2)]))
    1
      2
    >>> numbers = tree(1, [tree(2), tree(3, [tree(4), tree(5)]), tree(6, [tree(7)])])
    >>> print_tree(numbers)
    1
      2
      3
        4
        5
      6
        7
    """
    print('  ' * indent + str(label(t)))
    for b in branches(t):
        print_tree(b, indent + 1)

def copy_tree(t):
    """Returns a copy of t. Only for testing purposes.

    >>> t = tree(5)
    >>> copy = copy_tree(t)
    >>> t = tree(6)
    >>> print_tree(copy)
    5
    """
    return tree(label(t), [copy_tree(b) for b in branches(t)])

class Tree

class Tree:
    """
    >>> t = Tree(3, [Tree(2, [Tree(5)]), Tree(4)])
    >>> t.label
    3
    >>> t.branches[0].label
    2
    >>> t.branches[1].is_leaf()
    True
    """
    def __init__(self, label, branches=[]):
        for b in branches:
            assert isinstance(b, Tree)
        self.label = label
        self.branches = list(branches)

    def is_leaf(self):
        return not self.branches

    def map(self, fn):
        """
        Apply a function `fn` to each node in the tree and mutate the tree.

        >>> t1 = Tree(1)
        >>> t1.map(lambda x: x + 2)
        >>> t1.map(lambda x : x * 4)
        >>> t1.label
        12
        >>> t2 = Tree(3, [Tree(2, [Tree(5)]), Tree(4)])
        >>> t2.map(lambda x: x * x)
        >>> t2
        Tree(9, [Tree(4, [Tree(25)]), Tree(16)])
        """
        self.label = fn(self.label)
        for b in self.branches:
            b.map(fn)

    def __contains__(self, e):
        """
        Determine whether an element exists in the tree.

        >>> t1 = Tree(1)
        >>> 1 in t1
        True
        >>> 8 in t1
        False
        >>> t2 = Tree(3, [Tree(2, [Tree(5)]), Tree(4)])
        >>> 6 in t2
        False
        >>> 5 in t2
        True
        """
        if self.label == e:
            return True
        for b in self.branches:
            if e in b:
                return True
        return False

    def __repr__(self):
        if self.branches:
            branch_str = ', ' + repr(self.branches)
        else:
            branch_str = ''
        return 'Tree({0}{1})'.format(self.label, branch_str)

    def __str__(self):
        def print_tree(t, indent=0):
            tree_str = '  ' * indent + str(t.label) + "\n"
            for b in t.branches:
                tree_str += print_tree(b, indent + 1)
            return tree_str
        return print_tree(self).rstrip()

hw03

mobile data abstraction

'''
We are making a planetarium mobile.
A mobile is a type of hanging sculpture.A binary mobile consists of two arms.Each arm is a rod of a certain length, from which hangs either a planet or another mibile.

We will represent a binary mobile using data abstructions below:
    A mobile must have both a left arm and a right arm
    An arm has a positive length and must have something hanging at the end ,either a mobile or a planet
    A planet has a positive size ,and nothing hanging from it 
    
Arms-length recursion(sidenote)
def min_depth(t):
    """ A simple function to return the distance between t's root and its closest leaf"""
    if is_leaf(t):
        return 0 # Base case--the distance between a node and itself is 0
    h = float('inf') #Python's version of infinity
    for b in branches(t):
        if is_leaf(b):
            return 1 #!!!
        h = min(h,1+min_depth(b))
    return h
    
The line flagged with !!! is an "arms-length" recursion violation.
Although our code works correctly when it is present,by performing this check we are doing work that should be done by the next level of recursion -- we already have an if-statement that handles any inputs to min_depth that are leaves, so we should not include this line to eliminate redundancy in our code.


def min_depth(t):
    if is_leaf(t):
        return 0
    
    h = float('inf')
    
    for b in branches(t):
        h = min(h,1 +min_depth(b))
    return h
    
Arm-length recursion is not only redundant but often complicates our code and obscures the functionality of the recursive functions,making writing recursive functions much more difficult.     
   
'''

def mobile(left, right):
    """Construct a mobile from a left arm and a right arm."""
    assert is_arm(left), "left must be a arm"
    assert is_arm(right), "right must be a arm"
    return ['mobile', left, right]

def is_mobile(m):
    """Return whether m is a mobile."""
    return type(m) == list and len(m) == 3 and m[0] == 'mobile'

def left(m):
    """Select the left arm of a mobile."""
    assert is_mobile(m), "must call left on a mobile"
    return m[1]

def right(m):
    """Select the right arm of a mobile."""
    assert is_mobile(m), "must call right on a mobile"
    return m[2]

def arm(length, mobile_or_planet):
    """Construct a arm: a length of rod with a mobile or planet at the end."""
    assert is_mobile(mobile_or_planet) or is_planet(mobile_or_planet)
    return ['arm', length, mobile_or_planet]

def is_arm(s):
    """Return whether s is a arm."""
    return type(s) == list and len(s) == 3 and s[0] == 'arm'

def length(s):
    """Select the length of a arm."""
    assert is_arm(s), "must call length on a arm"
    return s[1]

def end(s):
    """Select the mobile or planet hanging at the end of a arm."""
    assert is_arm(s), "must call end on a arm"
    return s[2]

def planet(size):
    """Construct a planet of some size.
    Implementing the planet data abstraction by completing the planet constructor and the size selector so that the plant is represented using a two element list where the first element is the string 'planet' and the second element is the size.
    The total_weight example is provided to demonstrate use of the mobile,arm,and planet abstraction
    """
    assert size > 0
    "*** YOUR CODE HERE ***"
    return ['planet',size]
    

def size(w):
    """Select the size of a planet."""
    assert is_planet(w), 'must call size on a planet'
    "*** YOUR CODE HERE ***"
    return w[1]
    

def is_planet