COMP**21 Principles of Programming
Term 1, 2024
Coding Quiz 1
Worth 4 marks and due Week 3 Thursday @ 9pm
Description
You are provided with a stub in which you need to insert your code where indicated without doing any
changes to the existing code to complete the task. The current code will generate a mapping (that is, a
dictionary) based on a seed and an upper bound values provided by the user. Your task is to process the
list of cycles based on the generated mapping and the reversed dictionary as described below.
Marking
List of Cycles 2 marks
Reversed Dictionary 2 marks
--------------------------------------------
Total 4 marks
Due Date and Submission
Quiz 1 is due Week 3 Thursday 29 February 2024 @ 9.00pm (Sydney time).
Note that late submission with 5% penalty per day is allowed up to 3 days from the due date, that is, any
late submission after Week 3 Sunday 3 March 2024 @ 9pm will be discarded.
Make sure not to change the filename quiz_1.py while submitting by clicking on [Mark] button in Ed.
It is your responsibility to check that your submission did go through properly using Submissions link in Ed
otherwise your mark will be zero for Quiz 1.
Test Cases
$ python quiz_1.py
Enter two integers: 0 4
The generated mapping is:
 {2: 3, 4: 1}
The keys are, from smallest to largest:
 [2, 4]
Properly ordered, the cycles given by the mapping are:
 []
The (triply ordered) reversed dictionary per lengths is:
{1: {1: [4], 3: [2]}}
$ python quiz_1.py
Enter two integers: **
The generated mapping is:
 {1: 1, 3: 3, 5: 6, 6: 6}
The keys are, from smallest to largest:
 [1, 3, 5, 6]
Properly ordered, the cycles given by the mapping are:
 [[1], [3], [6]]
The (triply ordered) reversed dictionary per lengths is:
{1: {1: [1], 3: [3]}, 2: {6: [5, 6]}}
$ python quiz_1.py
Enter two integers: 0 11
The generated mapping is:
 {2: 7, 3: 11, 4: 10, 5: 10, 7: 2, 9: 5, 10: 10, 11: 5}
The keys are, from smallest to largest:
 [2, 3, 4, 5, 7, 9, 10, 11]
Properly ordered, the cycles given by the mapping are:
 [[2, 7], [10]]
The (triply ordered) reversed dictionary per lengths is:
{1: {2: [7], 7: [2], 11: [3]}, 2: {5: [9, 11]}, 3: {10: [4, 5, 10]}}

$ python quiz_1.py
Enter two integers: 10 9
The generated mapping is:
 {1: 5, 2: 6, 3: 5, 4: 5, 5: 6, 6: 7, 7: 1, 9: 6}
The keys are, from smallest to largest:
 [1, 2, 3, 4, 5, 6, 7, 9]
Properly ordered, the cycles given by the mapping are:
 [[1, 5, 6, 7]]
The (triply ordered) reversed dictionary per lengths is:
{1: {1: [7], 7: [6]}, 3: {5: [1, 3, 4], 6: [2, 5, 9]}}
$ python quiz_1.py
Enter two integers: 20 11
The generated mapping is:
 {2: 4, 3: 9, 4: 4, 5: 8, 6: 2, 7: 5, 8: 11, 9: 1, 10: 10, 11: 5}
The keys are, from smallest to largest:
 [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
Properly ordered, the cycles given by the mapping are:
 [[4], [5, 8, 11], [10]]
The (triply ordered) reversed dictionary per lengths is:
{1: {1: [9], 2: [6], 8: [5], 9: [3], 10: [10], 11: [8]},
2: {4: [2, 4], 5: [7, 11]}}
$ python quiz_1.py
Enter two integers: 50 15
The generated mapping is:
 {1: 5, 2: 14, 3: 15, 4: 3, 5: 5, 6: 5, 7: 15, 8: 6, 9: 10, 10: 15, 11: 12,
12: 15, 13: 14, 14: 8, 15: 9}
The keys are, from smallest to largest:
 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
Properly ordered, the cycles given by the mapping are:
 [[5], [9, 10, 15]]
The (triply ordered) reversed dictionary per lengths is:
{1: {3: [4], 6: [8], 8: [14], 9: [15], 10: [9], 12: [11]},
2: {14: [2, 13]},
3: {5: [1, 5, 6]},
4: {15: [3, 7, 10, 12]}}

$ python quiz_1.py
Enter two integers: 12 38
The generated mapping is:
 {1: 11, 2: 13, 3: 38, 4: 38, 5: 6, 6: 36, 7: 9, 8: 37, 9: 4, 10: 9, 11: 36,
12: 6, 13: 3, 15: 29, 16: 8, 17: 13, 19: 22, 20: 3, 21: 38, 22: 33, 24: 12, 25:
4, 27: 11, 28: 23, 29: 22, 30: 3, 31: 11, **: 17, 33: 9, 34: 26, 35: 30, 36:
31, 37: 22, 38: 37}
The keys are, from smallest to largest:
 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 19, 20, 21, 22, 24,
25, 27, 28, 29, 30, 31, **, 33, 34, 35, 36, 37, 38]
Properly ordered, the cycles given by the mapping are:
 [[4, 38, 37, 22, 33, 9], [11, 36, 31]]
The (triply ordered) reversed dictionary per lengths is:
{1: {8: [16],
 12: [24],
 17: [**],
 23: [28],
 26: [34],
 29: [15],
 30: [35],
 31: [36],
 33: [22]},
2: {4: [9, 25], 6: [5, 12], 13: [2, 17], 36: [6, 11], 37: [8, 38]},
3: {3: [13, 20, 30],
 9: [7, 10, 33],
 11: [1, 27, 31],
 22: [19, 29, 37],
 38: [3, 4, 21]}}

$ python quiz_1.py
Enter two integers: 34 56
The generated mapping is:
 {1: 34, 2: 8, 3: 35, 4: 11, 5: 28, 6: **, 7: 24, 9: 27, 10: 38, 11: 4, 12:
38, 15: 4, 16: 55, 17: 39, 19: 35, 20: 55, 23: 22, 24: 33, 25: 2, 26: 12, 27:
35, 28: 13, 29: 1, 30: 53, 31: 38, **: 2, 33: 29, 34: 12, 35: 1, 36: 8, 37: 48,
38: 55, 39: 33, 40: 42, 41: 41, 43: 25, 44: 50, 45: 56, **: 6, 48: 35, 49: 5
2, 50: 4, 51: 1, 52: 40, 53: 43, 54: 17, 55: 48, 56: 41}
The keys are, from smallest to largest:
 [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 15, 16, 17, 19, 20, 23, 24, 25, 26, 27,
28, 29, 30, 31, **, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, **, 48,
49, 50, 51, 52, 53, 54, 55, 56]
Properly ordered, the cycles given by the mapping are:
 [[1, 34, 12, 38, 55, 48, 35], [4, 11], [6, **], [41]]
The (triply ordered) reversed dictionary per lengths is:
{1: {6: [**],
 11: [4],
 13: [28],
 17: [54],
 22: [23],
 24: [7],
 25: [43],
 27: [9],
 28: [5],
 29: [33],
 34: [1],
 39: [17],
 40: [52],
 42: [40],
 43: [53],
 **: [6],
 50: [44],
 52: [49],
 53: [30],
 56: [45]},
2: {2: [25, **],
 8: [2, 36],
 12: [26, 34],
 33: [24, 39],
 41: [41, 56],
 48: [37, 55]},
3: {1: [29, 35, 51], 4: [11, 15, 50], 38: [10, 12, 31], 55: [16, 20, 38]},
4: {35: [3, 19, 27, 48]}}

Hints
(1) The cycles
A cycle is a path that starts and ends with the same key.
Similarly, a path of length at least 1 in which no key appears more than once, except the first key is the same as the
last key, is called a cycle.
A cycle is a list of keys [k1, k2, k3, …, kn] where the first key k1 of the list is the value of the last
key kn, that is, the following key:value elements must exist in the mapping (or dictionary):
k1: k2, k2: k3, …, kn-1: kn, and kn: k1
For instance, in the example with 10 9 as input, there is one cycle:
[1, 5, 6, 7]
since the following key: value elements are in the mapping (or dictionary):
{1: 5}, {5: 6}, {6: 7}, and {7: 1}
Make sure when recording the cycle do not repeat the first key at the end, that is, for the following cycle:
1 5 6 7 1
{1:5} {5:6} {6:7} {7:1}
It should be recorded as [1, 5, 6, 7] not [1, 5, 6, 7, 1]
Please also note that the keys in the cycle are not necessarily ordered. The only requirement is that the first
elements of the cycles are in order (and not the elements within the cycle) as shown in the example with 12 38 as
input:
[[4, 38, 37, 22, 33, 9], [11, 36, 31]]
The two cycles above are not ordered. However, looking at the first elements of the cycles only, the two cycles are
ordered since 4 is smaller than 11.
(2) The (triply ordered) reversed dictionary per lengths
For instance, in the example with 0 4 as input:
The generated mapping is:
{2: 3, 4: 1}
The (triply ordered) reversed dictionary per lengths is:
{1:[4], 3:[2]}  first generate the reversed dictionary
{1: {1: [4], 3: [2]}}  final result
In the example with ** as input:
The generated mapping is:
{1: 1, 3: 3, 5: 6, 6: 6}
The (triply ordered) reversed dictionary per lengths is:
{1:[1], 3:[3], 6:[5,6]}  first generate the reversed dictionary
{1: {1: [1], 3: [3]}, 2: {6: [5, 6]}}  final result
Triply ordered because there are three levels of sorting:
• level 1: per length which is the key of the outer dictionary
• level 2: per original value which is the key of the inner dictionary
• level 3: the values of the inner dictionary which are lists are sorted
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