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Lab 09 – Generators – Linked Lists – Trees
Q1: Scale
Implement the generator function scale(s, k), which yields elements of the given iterable s, scaled by k. As an extra challenge, try writing this function using a yield from statement!
def scale(s, k):
“””Yield elements of the iterable s scaled by a number k.
>>> s = scale([1, 5, 2], 5)
>>> type(s)
<class ‘generator’>
>>> list(s)
[5, 25, 10]
>>> m = scale(naturals(), 2)
>>> [next(m) for _ in range(5)]
[2, 4, 6, 8, 10]
“””
“*** YOUR CODE HERE ***”
Q2: Link to List
Write a function link_to_list that takes in a linked list and returns the sequence as a Python list. You may assume that the input list is shallow; none of the elements is another linked list.
Try to find both an iterative and recursive solution for this problem!
def link_to_list(link):
“””Takes a linked list and returns a Python list with the same elements.
>>> link = Link(1, Link(2, Link(3, Link(4))))
>>> link_to_list(link)
[1, 2, 3, 4]
>>> link_to_list(Link.empty)
[]
“””
“*** YOUR CODE HERE ***”
Q3: Cumulative Sum
Write a function cumulative_sum that mutates the Tree t so that each node’s label becomes the sum of all labels in the subtree rooted at the node.
def cumulative_sum(t):
“””Mutates t so that each node’s label becomes the sum of
all labels in the corresponding subtree rooted at t.
>>> t = Tree(1, [Tree(3, [Tree(5)]), Tree(7)])
>>> cumulative_sum(t)
>>> t
Tree(16, [Tree(8, [Tree(5)]), Tree(7)])
“””
“*** YOUR CODE HERE ***”
Q4: Is BST
Write a function is_bst, which takes a Tree t and returns True if, and only if t is a valid binary search tree, which means that:
Each node has at most two children
The children are valid binary search trees
For every node, the entries in that node’s left child are less than or equal to the label of the node
For every node, the entries in that node’s right child are greater than the label of the node
Note that, if a node has only one child, that child could be considered either the left or right child. You should take this into consideration.
Hint: It may be helpful to write helper functions bst_min and bst_max that return the minimum and maximum, respectively, of a Tree if it is a valid binary search tree.
def is_bst(t):
“””Returns True if the Tree t has the structure of a valid BST.
>>> t1 = Tree(6, [Tree(2, [Tree(1), Tree(4)]), Tree(7, [Tree(7), Tree(8)])])
>>> is_bst(t1)
True
>>> t2 = Tree(8, [Tree(2, [Tree(9), Tree(1)]), Tree(3, [Tree(6)]), Tree(5)])
>>> is_bst(t2)
False
>>> t3 = Tree(6, [Tree(2, [Tree(4), Tree(1)]), Tree(7, [Tree(7), Tree(8)])])
>>> is_bst(t3)
False
>>> t4 = Tree(1, [Tree(2, [Tree(3, [Tree(4)])])])
>>> is_bst(t4)
True
>>> t5 = Tree(1, [Tree(0, [Tree(-1, [Tree(-2)])])])
>>> is_bst(t5)
True
>>> t6 = Tree(1, [Tree(4, [Tree(2, [Tree(3)])])])
>>> is_bst(t6)
True
>>> t7 = Tree(2, [Tree(1, [Tree(5)]), Tree(4)])
>>> is_bst(t7)
False
