Homework 1 - Coding Refresher
Due Friday September 13th
1 Matrix mortality, obtaining the zero matrix
Definition: The mortal matrix problem is the problem of determining, given a finite set of n x n matrices with integer entries, whether they can be multiplied in some order, possibly with repetition, to yield the zero matrix.
Given the above definition, develop a program that determines if a pair of given input matrices are a mortalpair. Your program should be capable of accepting any pair of n x n matrices and should return true if the pair of matrices are a mortal pair. DO NOT hard-code these two matrices for your solution. You can test your program using the following two matrices.
A = [2 -2; 2 2] and B = [0 0; 0 1]
2 Matrix mortality, coding complications
Consider the consequences of a user inputting a set of non-mortal matrices; such as two 3x3 filled with 1s. For this pair, it is obvious they are non-mortal; however, other sets are not as obvious. No need to look into formal proofs.
1. Build a safeguard into your program that does not allow the program to run longer than 5 minutes.
2. Explain why a safeguard like this is important for a problem such as this. Consider computabilityand potential programming issues.
3 Working with data sets Download the smart card data.csv from the bCourses website.
This file contains the metro smart card transaction data collected in a Chinese city for the duration of one day. The columns are Time In, Time Out, Card Id, Fare, StationId In and StationId Out. Every entry epresents 1 metro trip. Time In and Time Out is the time the person enter and exit the train. They are in local time. Card Id is the ID of the smart card. StationId In and StationId Out is the station ID of entry and exit station.
Assumptions to make:
1. No delays occurred along the track on the day this data was collected.
2. There is no need to transfer trains.
3. Employees of the metro have free travel.
Using the metro data, answer the following questions:
1. Determine how many employee trips were taken on this day. Attempt this question using a for loop and a built in search algorithm. Compare computation time and discuss why one may be faster than the other.
2. On average, is the commute from home to work, or work to home longer? You may assume a ”work day” of 6 hours or longer. You may ignore any card ID used more than 3 times in a day.
3. Determine the average travel time between train stations. Create a matrix with rows as station out and columns as station in. Which stations appear the farthest apart? Which stations appear the closest?
Submission Guidelines
These guidelines will continue throughout the semester
1. If there are theoretical portions of the question, unless otherwise stated, submit your answers as comments within your code.
2. Typically, one file shall be submitted per problem. In this assignment, problem 1 and 2 can be combined into one file named matrixMortality.
3. When multiple files are being submitted, submit as a zipped file with the naming format lastnameFirstname.
4. Submit the zipped file on bcourses by the due date at 11:59 pm PST.