Lab 07: Finding the Defect

Lab 07: Finding the Defect
In this lab, you will be presented with a list of collection of n coins. All of these
coins have identical weights except for one. The goal of the lab is to identify the
defective coin by using a scale that can compare weights of two groups of coins.
Representing the Collection of Coins and Scale
A Scale class that represents both the collection of coins and the scale will be
provided. The class will have the following ADT:
• __init__(self, L) - initialize a Scale object with L, which is the list of
weights of coins
• weigh(self, range1, range2) - range1 and range2 are both tuples of
two elements which represent a range of coins. Returns 1 if the sum of
the weights of elements in range2 are more than weights of elements in
range1. Returns 0 if the weights are equal, and -1 otherwise.
• __len__(self) - returns the length of the collection of coins
L= [1,1,1,1,1,2,1,1,1]
s = Scale(L)
print(s.weigh((0,3), (3,9)))
1
As the sum of weights from [3,9) is larger than the sum of the weigths from
[0,3), the function will output 1. You will use this class to implement a function
to determine the index of the defective weight. It is important to note that
your function should not depend on the implementation of Scale, it should only
depend on the defined ADT above.
Goal
Implement a function, defects, which takes in a Scale object and returns an
integer which is the index of the defective coin. It should use the weigh method
of the Scale class to divide the problem into smaller pieces, atleast halve the
problem. The final product should have a runtime of O(log n).
For example, the following is an example output:
L= [1,1,1,1,1,2,1,1,1]
s = Scale(L)
print(defects(s))
5
1
A case you may run into when trying to halve the list is how to tackle odd
length lists. An easy solution is to check the middle element manually. Then,
the remaining even number of elements can be handled by dividing as before.
Summary
For this lab, you should implement the defects method that takes in a Scale
object and returns the index of the defective coin. This method should use the
weigh method of the Scale object to divide the problem and find a solution in
logarithmic time. An example Scale class will be provided for testing. However,
your solution should not depend on the implementation of Scale. All it should
rely on is the ADT provided for Scale in this lab.
2