Trees in python

The Tree class is defined as below.

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 __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()

Problem 3.2: Generate Paths (100 pts)

Define a generator function generate_paths which takes in a Tree t, a value value, and returns a generator object which yields each path from the root of t to a node that has label value.

t is implemented with a class, not as the function-based ADT.

Each path should be represented as a list of the labels along that path in the tree. You may yield the paths in any order.

def generate_paths(t, value):
    """Yields all possible paths from the root of t to a node with the label value
    as a list.

    >>> t1 = Tree(1, [Tree(2, [Tree(3), Tree(4, [Tree(6)]), Tree(5)]), Tree(5)])
    >>> print(t1)
    1
      2
        3
        4
          6
        5
      5
    >>> next(generate_paths(t1, 6))
    [1, 2, 4, 6]
    >>> path_to_5 = generate_paths(t1, 5)
    >>> sorted(list(path_to_5))
    [[1, 2, 5], [1, 5]]

    >>> t2 = Tree(0, [Tree(2, [t1])])
    >>> print(t2)
    0
      2
        1
          2
            3
            4
              6
            5
          5
    >>> path_to_2 = generate_paths(t2, 2)
    >>> sorted(list(path_to_2))
    [[0, 2], [0, 2, 1, 2]]
    """
    "*** YOUR CODE HERE ***"

solution dfs

def generate_paths(t, value):
    """Yields all possible paths from the root of t to a node with the label value
    as a list.
    >>> t1 = Tree(1, [Tree(2, [Tree(3), Tree(4, [Tree(6)]), Tree(5)]), Tree(5)])
    >>> print(t1)
    1
      2
        3
        4
          6
        5
      5
    >>> next(generate_paths(t1, 6))
    [1, 2, 4, 6]
    >>> path_to_5 = generate_paths(t1, 5)
    >>> sorted(list(path_to_5))
    [[1, 2, 5], [1, 5]]

    >>> t2 = Tree(0, [Tree(2, [t1])])
    >>> print(t2)
    0
      2
        1
          2
            3
            4
              6
            5
          5
    >>> path_to_2 = generate_paths(t2, 2)
    >>> sorted(list(path_to_2))
    [[0, 2], [0, 2, 1, 2]]
    """
    "*** YOUR CODE HERE ***"
    def helper(t,value,prev):
        #prev+=[t.label]
        if t.label==value:
            yield prev+[t.label]
        for b in t.branches:
            yield from helper(b,value,prev+[t.label])
    yield from helper(t,value,[])

a wrong solution

def generate_paths(t, value):
    """Yields all possible paths from the root of t to a node with the label value
    as a list.
    >>> t1 = Tree(1, [Tree(2, [Tree(3), Tree(4, [Tree(6)]), Tree(5)]), Tree(5)])
    >>> print(t1)
    1
      2
        3
        4
          6
        5
      5
    >>> next(generate_paths(t1, 6))
    [1, 2, 4, 6]
    >>> path_to_5 = generate_paths(t1, 5)
    >>> sorted(list(path_to_5))
    [[1, 2, 5], [1, 5]]

    >>> t2 = Tree(0, [Tree(2, [t1])])
    >>> print(t2)
    0
      2
        1
          2
            3
            4
              6
            5
          5
    >>> path_to_2 = generate_paths(t2, 2)
    >>> sorted(list(path_to_2))
    [[0, 2], [0, 2, 1, 2]]
    """
    "*** YOUR CODE HERE ***"
    def helper(t,value,prev):
        prev+=[t.label]
        if t.label==value:
            yield prev
        for b in t.branches:
            yield from helper(b,value,prev)
    yield from helper(t,value,[])
'''
错误原因：
在搜索完之后没有把变量prev还原成原来的模样，
在python中，list的赋值、传参都只是创造了一个引用关系，并不是一个copy，
因此在搜索branch1 的时候修改了prev的值会在 搜索branch2 的时候表现出来
'''

Problem 5: Decorate Christmas Tree (0 pts)

Christmas is coming soon. Isla bought a Christmas tree for Tsukasa. A Christmas tree is a Tree instance. There are some gifts on every nodes of the tree, and the label of each node is the number of gifts on it. Every gifts have the same weight.

We say a tree is balanced if it is a leaf or the total weight of its every branches are the same and all its branches are balanced. For example, the left tree is balanced but the right one is not.

3_2

Isla wants to buy more gifts and hang them on the tree to balance it. Please help her implement balance_tree, which takes in a tree t and hangs gifts as few as possible on it to balance it.

Note: For trees which have more than one ways to balance with the same minimum number of gifts, you can choose any one of them as result and it won't influence your score.

def balance_tree(t):
    """Balance a tree.

    >>> t1 = Tree(1, [Tree(2, [Tree(2), Tree(3), Tree(3)]), Tree(2, [Tree(4), Tree(4)])])
    >>> balance_tree(t1)
    >>> t1
    Tree(1, [Tree(2, [Tree(3), Tree(3), Tree(3)]), Tree(3, [Tree(4), Tree(4)])])
    """
    "*** YOUR CODE HERE ***"

solution

def balance_tree(t):
    """Balance a tree.

    >>> t1 = Tree(1, [Tree(2, [Tree(2), Tree(3), Tree(3)]), Tree(2, [Tree(4), Tree(4)])])
    >>> balance_tree(t1)
    >>> t1
    Tree(1, [Tree(2, [Tree(3), Tree(3), Tree(3)]), Tree(3, [Tree(4), Tree(4)])])
    """
    "*** YOUR CODE HERE ***"
    def helper(t):
        if t.is_leaf():
          return t.label
        else:
          weight=[helper(b) for b in t.branches]
          max_weight=max(weight)
          for b,weight in zip(t.branches,weight):
              b.label+=max_weight-weight
          return sum(b.label for b in t.branches)+t.label
    helper(t)