Algorithmic程序语言讲解、c/c++，Python，Java编程设计辅导
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Name
Student Id
Assessed Coursework
Course Name Algorithmic Foundations 2
% Contribution to final
course mark
10%
Solo or Group 9 Solo 9 Group
Anticipated Hours 10
Submission Instructions
Use the latex template and submit the generated pdf
through moodle (do not submit the source latex file).
Failure to follow the submission instructions will lead to a
penalty of 2 bands.
Please Note: This Coursework cannot be Re-Assessed
Code of Assessment Rules for Coursework Submission
Deadlines for the submission of coursework which is to be formally assessed will be published in course
documentation, and work which is submitted later than the deadline will be subject to penalty as set out below.
The primary grade and secondary band awarded for coursework which is submitted after the published deadline will
be calculated as follows:
(i) in respect of work submitted not more than five working days after the deadline
a. the work will be assessed in the usual way;
b. the primary grade and secondary band so determined will then be reduced by two secondary bands
for each working day (or part of a working day) the work was submitted late.
(ii) work submitted more than five working days after the deadline will be awarded Grade H.
Penalties for late submission of coursework will not be imposed if good cause is established for the late submission.
You should submit documents supporting good cause via MyCampus.
Penalty for non-adherence to Submission Instructions is 2 bands
Algorithmic Foundations 2
Assessed Exercise 2
Notes for guidance
1. There are two assessed exercises. Each is worth 10% of your final grade for this
module. Your answers must be the result of your own individual e↵orts.
2. Please use the latex template and submit your the generated pdf via moodle (do not
submit the latex source file).
3. Please ensure you have filled out your tutorial group, name and student id.
4. Failure to follow the submission instructions will lead to a penalty for
non-adherence to submission instructions of 2 bands.
5. As stated on the cover sheet deadline for completing this assessed exercise is 16:30
Monday, November 23, 2020.
6. The exercise is marked out of 30 using the included marking scheme. Credit will be
given for partial answers.
AF2 - Assessed Exercise 2 2
1. (a) Show that if n divides m where n and m are positive integers greater than 1, then [4]
a ⌘ b (mod m) implies a ⌘ b (mod n) for any positive integers a and b.
(b) Show that a·c ⌘ b·c (mod m) with a, b, c and m integers with m2
does not [3]
imply a ⌘ b (mod m).
(c) Using the Euclidean Algorithm, find gcd(3084, 1424). Show your working. [3]
2. A company has a contract to cover the four walls, ceiling, and floor of a factory building [5]
with fire-retardant material. The building is rectangular where of width 280m, length
336m and height 168m. Square panels can be manufactured in any size of whole metres.
For safety reasons, the building must be covered in complete panels (i.e. panels cannot
be cut). What is the minimum number of equally sized square panels that are required
to line the interior of the building? Explain your answer.
3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6. [5]
Hint: considering splitting into cases where integers are of the form a·k+b or (a·k+b)
for k 2 N where a and b are fixed for a given case, b varies over the cases and the least
significant digit of the integer depends on only b.
Note: the least significant digit of an integer is the digit farthest to the right in a
integer. For example, the least significant digits of 1007 and 26 are 7 and 6 respectively.
4. Use mathematical induction to show that for any n 2 N, if n2,
5. Use mathematical induction to show that 2 divides n [5] 2
n for all n 2 N.
Name
Student Id
Assessed Coursework
Course Name Algorithmic Foundations 2
% Contribution to final
course mark
10%
Solo or Group 9 Solo 9 Group
Anticipated Hours 10
Submission Instructions
Use the latex template and submit the generated pdf
through moodle (do not submit the source latex file).
Failure to follow the submission instructions will lead to a
penalty of 2 bands.
Please Note: This Coursework cannot be Re-Assessed
Code of Assessment Rules for Coursework Submission
Deadlines for the submission of coursework which is to be formally assessed will be published in course
documentation, and work which is submitted later than the deadline will be subject to penalty as set out below.
The primary grade and secondary band awarded for coursework which is submitted after the published deadline will
be calculated as follows:
(i) in respect of work submitted not more than five working days after the deadline
a. the work will be assessed in the usual way;
b. the primary grade and secondary band so determined will then be reduced by two secondary bands
for each working day (or part of a working day) the work was submitted late.
(ii) work submitted more than five working days after the deadline will be awarded Grade H.
Penalties for late submission of coursework will not be imposed if good cause is established for the late submission.
You should submit documents supporting good cause via MyCampus.
Penalty for non-adherence to Submission Instructions is 2 bands
Algorithmic Foundations 2
Assessed Exercise 2
Notes for guidance
1. There are two assessed exercises. Each is worth 10% of your final grade for this
module. Your answers must be the result of your own individual e↵orts.
2. Please use the latex template and submit your the generated pdf via moodle (do not
submit the latex source file).
3. Please ensure you have filled out your tutorial group, name and student id.
4. Failure to follow the submission instructions will lead to a penalty for
non-adherence to submission instructions of 2 bands.
5. As stated on the cover sheet deadline for completing this assessed exercise is 16:30
Monday, November 23, 2020.
6. The exercise is marked out of 30 using the included marking scheme. Credit will be
given for partial answers.
AF2 - Assessed Exercise 2 2
1. (a) Show that if n divides m where n and m are positive integers greater than 1, then [4]
a ⌘ b (mod m) implies a ⌘ b (mod n) for any positive integers a and b.
(b) Show that a·c ⌘ b·c (mod m) with a, b, c and m integers with m2
does not [3]
imply a ⌘ b (mod m).
(c) Using the Euclidean Algorithm, find gcd(3084, 1424). Show your working. [3]
2. A company has a contract to cover the four walls, ceiling, and floor of a factory building [5]
with fire-retardant material. The building is rectangular where of width 280m, length
336m and height 168m. Square panels can be manufactured in any size of whole metres.
For safety reasons, the building must be covered in complete panels (i.e. panels cannot
be cut). What is the minimum number of equally sized square panels that are required
to line the interior of the building? Explain your answer.
3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6. [5]
Hint: considering splitting into cases where integers are of the form a·k+b or (a·k+b)
for k 2 N where a and b are fixed for a given case, b varies over the cases and the least
significant digit of the integer depends on only b.
Note: the least significant digit of an integer is the digit farthest to the right in a
integer. For example, the least significant digits of 1007 and 26 are 7 and 6 respectively.
4. Use mathematical induction to show that for any n 2 N, if n2,
5. Use mathematical induction to show that 2 divides n [5] 2
n for all n 2 N.