Assignment 1
COMP9021, Trimester 1, 2025
1 General matters
1.1 Aim
The purpose of the assignment is to:
• develop your problem solving skills;
• let you carefully read specifications and follow them;
• let you design and implement the solutions to problems in the form of small sized Python programs;
• let you practice the use of arithmetic computations, tests, repetitions, fundamental Python data
types, Unicode characters;
• have control over print statements.
1.2 Submission
Your programs will be stored in files named solitaire_1.py and solitaire_2.py. After you have devel oped and tested your programs, upload them using Ed (unless you worked directly in Ed). Assignments
can be submitted more than once; the last version is marked. Your assignment is due by March 31,
10:00am.
1.3 Assessment
The assignment is worth 13 marks. It is going to be tested against a number of inputs. For each test, the
automarking script will let your program run for 30 seconds.
Assignments can be submitted up to 5 days after the deadline. The maximum mark obtainable reduces
by 5% per full late day, for up to 5 days. Thus if students A and B hand in assignments worth 12 and 11,
both two days late (that is, more than 24 hours late and no more than 48 hours late), then the maximum
mark obtainable is 11.7, so A gets min(11.7, 12) = 11.7 and B gets min(11.7, 11) = 11.
The outputs of your programs should be exactly as indicated.
1.4 Reminder on plagiarism policy
You are permitted, indeed encouraged, to discuss ways to solve the assignment with other people. Such
discussions must be in terms of algorithms, not code. But you must implement the solution on your
own. Submissions are routinely scanned for similarities that occur when students copy and modify other
people’s work, or work very closely together on a single implementation. Severe penalties apply.
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2 Decks, shuffling
2.1 Decks
The first exercise simulates a solitaire game that is played with 32 cards, namely, the Ace, Seven, Eight,
Nine, Ten, Jack, Queen and King of each of the 4 suits, with the following convention.
• Numbers from 0 to 7 denote the Hearts, from the Ace of Hearts up to the King of Hearts.
• Numbers from 8 to 15 denote the Diamonds, from the Ace of Diamonds up to the King of Diamonds.
• Numbers from 16 to 23 denote the Clubs, from the Ace of Clubs up to the King of Clubs.
• Numbers from 24 to 31 denote the Spades, from the Ace of Spades up to the King of Spades.
So for instance, 6 denotes the Queen of Hearts, and 26 denotes the Eight of Spades.
The second exercise simulates a solitaire game that is played with 52 cards, with the following convention.
• Numbers from 0 to 12 denote the Hearts, from the Ace of Hearts up to the King of Hearts.
• Numbers from 13 to 25 denote the Diamonds, from the Ace of Diamonds up to the King of Diamonds.
• Numbers from 26 to 38 denote the Clubs, from the Ace of Clubs up to the King of Clubs.
• Numbers from 39 to 51 denote the Spades, from the Ace of Spades up to the King of Spades.
So for instance, 16 denotes the Four of Diamonds, and 36 denotes the Jack of Clubs.
2.2 Shuffling
Both exercises require to shuffle a deck of cards, either the full deck (of 32 or 52 cards) or a subset of the
full deck. For that purpose, the following convention is followed.
By shuffling a deck of cards, we mean randomising the corresponding set of numbers by providing the
list of those numbers, in increasing order, as an argument to the shuffle() function of the random
module. For instance,
• to shuffle the whole deck of 52 cards, we could do
>>> cards = list(range(52))
>>> shuffle(cards)
• and to shuffle the deck of all 52 cards except for the Four of Diamonds and the Jack of Clubs, we
could do
>>> cards = sorted(set(range(52)) - {16, 36})
>>> shuffle(cards)
To make sure that results are predictable, just before calling the shuffle() function, the seed() function
of the random module should be called with a given argument. By shuffling the deck of all (52) cards
with 678 given to seed(), we mean doing something equivalent to:
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>>> cards = list(range(52))
>>> seed(678)
>>> shuffle(cards)
which by the way, lets cards denote
[11, 12, 22, 38, 15, 16, 14, 28, 4, 34, 46, 48, 33,
18, 5, 17, 27, 37, 50, 51, 31, 41, 9, 1, 39, 3,
29, 40, 43, 23, 25, 13, 19, 35, 26, 42, 24, 32, 44,
45, 6, 36, 8, 47, 2, 30, 10, 49, 21, 0, 20, 7]
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3 First solitaire game
3.1 Game description
It is played with 32 cards. The aim is to get rid of enough cards and be left with the 4 Aces in sequence,
possibly together with other cards before or after the 4 Aces. Elimination of cards proceeds over 3 stages,
with all cards still in play being distributed over 4 stacks for the first stage, 3 stacks for the second stage,
and 2 stacks for the third and last stage. The cards are shuffled only once, just before the game begins.
At the start of the first stage, the cards in the deck are facing down, so with the first card in the deck
at the bottom and with the last card in the deck at the top, and distributed from the top to the bottom
of the deck over 4 stacks, so the first, second, third and fourth cards at the top of the deck become the
cards at the bottom of the first (leftmost), second, third and fourth (rightmost) stacks, respectively, the
fifth, sixth, seventh and eight cards at the top of the deck become the cards directly above the cards
at the bottom of the first, second, third and fourth stacks, respectively, etc. The first stack is turned
upside down so its cards are now facing up. All cards at the top of the stack are discarded until an Ace is
uncovered, unless there is no Ace in the first stack in which case the whole stack is discarded. If an Ace
has been uncovered then what is left of the stack is turned upside down and then put aside, so with the
Ace now facing down on the table. The same is done with the second, third and fourth stacks, each time
turning what is left of the stack, if anything, upside down and putting it aside above the cards that have
been previously kept, if any.
For the second stage, the same procedure is followed, except that the cards that have been put aside are
distributed over 3 stacks instead of 4. There will be one more card in the first stack than in the third
stack if the number of cards that is left is not a multiple of 3, and there will be one more card in the
second stack than in the third stack if the number of cards that is left is equal to 2 modulo 3. Note that
the last card that is distributed (facing down) is the first Ace that has been uncovered during the first
stage.
The same is done for the third stage, except that the cards that have been put aside are distributed over
2 stacks.
At the end of the third stage, the cards that have been last put aside are taken from top to bottom and
displayed from left to right facing up. The 4 Aces are necessarily all there but the game is won only if
they occur in sequence, without any other card between two of them. Of course if there are only 4 cards
left then the game is known to be won before they are revealed.
3.2 Playing a single game (3.5 marks)
Your program will be stored in a file named solitaire_1.py. Executing
$ python3 solitaire_1.py
at the Unix prompt should produce the following output (ending in a single space):
Please enter an integer to feed the seed() function:
with the program now waiting for your input, which should be an integer, and which you can assume will
be an integer. Your program will feed that integer to seed() before calling shuffle(), as described in
Section 2, to shuffle the deck of 32 cards.
Here is a possible interaction for a game that is lost.
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Here is a possible interaction for a game that is won.
The output starts with an empty line followed by a line that reads:
Deck shuffled, ready to start!
The next line of output represents the 32 card deck, with all cards facing down (32 ]s). It is followed
with an empty line.
The beginning of the first round is announced by a line that reads:
Distributing the cards in the deck into 4 stacks.
The next two rounds are announced by a line that reads:
Distributing the cards that have been kept into _ stacks.
with _ being 3 for the second round and 2 for the third round. That line is a followed by 5 lines:
• a representation of the stacks that remain, the starts of two adjacent stacks being 12 characters
away;
• an empty line (whose purpose will be explained further down);
• a representation of all cards that have been discarded, facing up, using [ for all of them except for
the last (top) one, that is properly displayed—that line being empty in the first stage;
• an empty line (whose purpose will be explained further down);
• an empty line.
Then, for each stage, the output consists of groups of 12 or 13 lines, each group being structured as
follows.
• The first line in the group reads as one of the following:
– No ace in _ stack, after it has been turned over.
with _ one of first, second, third and fourth, or
– _ [(and last)] card in _ stack, after it has been turned over, is an ace.
with
∗ the first _ one of First, Second, Third, Fourth, Fifth, Sixth, Seventh and Eighth,
∗ the second _ one of First, Second, Third and Fourth,
∗ (and last) added when the card is indeed the last one in the stack.
• The second line in the group depicts the stacks that remain with for the one being processed, what
is left of it after it has been turned upside down and all cards that do not have an Ace above them
have been discarded one after the other; so either there is nothing left of the stack or what is left
has an Ace at the top.
• The third line in the group depicts all cards that have been discarded one after the other from the
stack being processed, with at the top the last card in the stack if no Ace has been found, and the
card just above the Ace that has been found otherwise.
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• The fourth line in the group depicts the cards that have been discarded up to then, facing up.
• The fifth line in the group depicts the cards that have been put aside up to then, facing down.
• The sixth line in the group is empty.
• The seventh line in the group reads as one of the following:
– Discarding|Adding to the cards that have been discarded all cards in the stack.
or
– Discarding|Adding to the cards that have been discarded the card before the ace.
or
– Discarding|Adding to the cards that have been discarded the _ cards before the ace.
with _ an integer at least equal to 2.
If nothing had been discarded yet, Discarding is used; otherwise, Adding to the cards that have
been discarded is used.
• In case an Ace has been found, the next line reads as one of the following:
– Keeping|Also keeping the ace, turning it over.
or
– Keeping|Also keeping the ace and the card after, turning them over.
or
– Keeping|Also keeping the ace and the _ cards after, turning them over.
with _ an integer at least equal to 2.
If nothing had been put aside yet, Keeping is used; otherwise, Also keeping is used.
• The line that follows depicts the stacks that remain to be processed, if any.
• The line that follows is empty.
• The line that follows depicts the cards that have now been discarded (possibly unchanged).
• The line that follows depicts the cards that have now been put aside (possibly unchanged).
• The last line in the group is empty.
The output ends with a group of 6 lines:
• The first line in the group reads:
Displaying the _ cards that have been kept.
with _ an integer (necessarily at least equal to 4).
• The second line in the group reads: You lost! or You won!
• The next two lines in the group are empty.
• The penultimate line in the group depicts the cards that have been discarded over the game.
• The last line in the group depicts all cards that have been put aside at the end of the game, displayed
facing up next to each other.
Note that there is no tab anywhere in the output and no line has any trailing space.
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3.3 Playing many games and estimating probabilities (3 marks)
Executing
$ python3
at the Unix prompt and then
>>> from solitaire_1 import simulate
at the Python prompt should allow you to call the simulate() function, that takes two arguments.
• The first argument, say n, is meant to be a strictly positive integer, and you can assume that it is
a strictly positive integer, that represents the number of games to play.
• The second argument, say i, is meant to be an integer, and you can assume that it is an integer.
The function simulates the playing of the game n times,
• the first time shuffling the deck of all cards with i given to seed(),
• if n ≥ 2, the second time shuffling the deck of all cards with i + 1 given to seed(),
• …
• the n
th and last time, shuffling the deck of all cards with i + n − 1 given to seed().
Here is a possible interaction.
Probabilities are computed as floating point numbers and formatted with 2 digits after the decimal point.
Only strictly positive probabilities and the corresponding number of cards left when winning are output
(including the cases, if any, when they are smaller than 0.005%, and so output as 0.00%). The output is
sorted in increasing number of cards left when winning.
There is a single space to the left and to the right of the separating vertical bar, with all lines consisting
of precisely 45 characters.
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4 Second solitaire game
4.1 Game description
It is played with 52 cards. The Sevens are removed from the deck and placed on the table, facing up,
with from left to right, the Seven of Diamonds, the Seven of Clubs, the Seven of Spades, and the Seven
of Hearts, making sure there is enough space on the table to place above the Sevens all cards from the
Eights up to the Kings, and below the Sevens all cards from the Sixes down to the Aces, with all cards
belonging to the same suit ending up in the same column. Up to 3 stages are allowed to eventually place
all cards. For each stage, all cards that remain are stacked facing down, and the card at the top is taken
off the stack, again and again until there is no card left. A card taken off the top of the stack is placed
at the location where it has to be if the card just above or the card just below in its suit has been placed
already, and in case that is not possible, it is put aside, facing up, above all cards already put aside, if
any. If the card could be placed, we then check whether the card at the top of the cards that have been
put aside, if any, can itself extend the column for its suit, and it if can, place it at the location where it
has to be and again, check the card at the top of the cards that have been put aside, if any, stopping when
there is no card left amongst those that have been put aside or when there are some cards left but the
one at the top cannot extend the column for its suit, at which point we take off the card at the top of the
stack of cards left to process, if any. At the time the stack has become empty, either all cards have been
appropriately placed on the table and the game is won, or there is at least one stage left, in which case
the stack of cards put aside is turned upside down and becomes the stack of cards to process, proceeding
exactly as during the previous stage. So the game is lost if the game is played over 3 stages and not all
cards have been appropriately placed on the table at the end of the third stage. The 48 cards (the whole
deck with all Sevens removed) are shuffled only once, just before the game begins.
4.2 Playing a single game (3.5 marks)
Your program will be stored in a file named solitaire_2.py. Executing
$ python3 solitaire_2.py
at the Unix prompt should produce the following output (ending in a single space)
Please enter an integer to feed the seed() function:
with the program now waiting for your input, which should be an integer, and which you can assume will
be an integer. Your program will feed that integer to seed() before calling shuffle(), as described in
Section 2, to shuffle the 52 cards minus the four Sevens.
The output starts with an empty line followed by
There are _ lines of output; what do you want me to do?
Enter: q to quit
a last line number (between 1 and _)
a first line number (between -1 and -_)
a range of line numbers (of the form m--n with 1 <= m <= n <= _)
with all occurrences of _ denoting the same number. The program should wait for the input on the next
line, aligned under q and the three leftmost as above. Until q is input, the program should output an
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empty line, do what it is requested to do if the input is correct, output an empty line and prompt the
user again. The program exits when q is input. The input is correct if it is exactly as required, including
integers being within the required ranges (noting that positive numbers should not be preceded with +),
except that there can be any amount of space at the beginning of the input, at the end of the input,
before the first - if entering a range, and after the second - if entering a range (no space between the
minus sign and the digits of a negative number...).
• The first kind of input will let the program output the first n lines of the collected output, with n
being the number provided as input,
• the second kind of input will let the program output the last n lines of the collected output, with
−n being the number provided as input, and
• the third kind of input will let the program output that part of the collected output that ranges
between the mth and n
th lines, mth and n
th lines included, with m and n being the numbers provided
as input.
Here is a possible interaction.
Here is a possible interaction that displays the complete collected output for a game that is lost.
Here is a possible interaction that displays the complete collected output for a game that is won.
When the input is correct, the first line of collected output reads
All 7s removed and placed, rest of deck shuffled, ready to start!
and the second line of collected output represents the 48 cards, with all cards facing down (48 ]s). It
is followed by en empty line (whose purpose will be explained further down), followed by 6 empty lines
to accommodate the Kings, Queens, Jacks, Tens, Nines and Eights. Then comes a line that depicts
the Sevens, followed by 6 empty lines to accommodate the Sixes, Fives, Fours, Threes, Twos and Aces,
followed by an empty line.
The rest of the collected output consists of lines that read
Starting _ round...
with _ being first, or second if there is a second stage, or third if there is a third stage, followed by an
empty line. That is followed by a sequence of lines that are structured as follows.
• First is a line that reads
Cannot place card from top of stack of cards left☹️
or
Cannot place card from top of stack of cards put aside ☹️
or
Placing card from top of stack of cards left ***2;
or
Placing card from top of stack of cards put aside ***2;
• In all cases except for Cannot place card from top of stack of cards put aside ☹️, then comes a line
that depicts the stack of cards that remain to be processed, facing down, followed by a line that
depicts all cards that have been taken off the stack and could not be placed, facing up.
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• In case a card could be placed, either from the stack of cards left or from the stack of cards put
aside, come the 13 lines for the Kings down to the Aces to display the cards that have been placed
up to now.
• Last comes an empty line.
When Placing card from top of stack of cards left ***2; is used, the stack of cards to process decreases by
one. When Placing card from top of stack of cards put aside ***2; is used, the stack of cards that could
not be placed decreases by one. In both cases, the card that can be placed is displayed at the intended
location. In the first case, the card is ”discovered” as the card just added to those already placed, whereas
in the second case, the card is known since it was facing up and so we know where to look to find it as
the card just added to those already placed.
Cannot place card from top of stack of cards left ☹️ is used when a card is taken off the stack to process
and cannot be placed. Cannot place card from top of stack of cards put aside☹️ is used when a card has
just been placed and the stack of cards that could not be placed is not empty while the card at its top
still cannot be placed. In the first case, that card is “discovered” and becomes the new card at the top of
the stack of cards that could not be placed.
As soon as all cards have been placed, a last line is added to the collected output that reads:
You placed all cards, you won 👍
If there is a third stage and it ends with some cards still waiting to be placed, a last line is added to the
collected output that reads:
You could not place _ cards, you lost 👎
with _ the number of cards that could not be placed.
Each placed card is displayed with the appropriate Unicode character after one, two, three or four
tab characters depending on whether the position of the card on the row is the first, the second, the
third or the fourth, respectively, as determined by its suit, and of course after the Unicode characters for
any preceding card on the row. No line has any trailing space.
4.3 Playing many games and estimating probabilities (3 marks)
Executing
$ python3
at the Unix prompt and then
>>> from solitaire_2 import simulate
at the Python prompt should allow you to call the simulate() function, that takes two arguments.
• The first argument, say n, is meant to be a strictly positive integer, and you can assume that it is
a strictly positive integer, that represents the number of games to play.
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• The second argument, say i, is meant to be an integer, and you can assume that it is an integer.
The function simulates the playing of the game n times,
• the first time shuffling the deck of all cards with i given to seed(),
• if n ≥ 2, the second time shuffling the deck of all cards with i + 1 given to seed(),
• …
• the n
th and last time, shuffling the deck of all cards with i + n − 1 given to seed().
Here is a possible interaction.
Probabilities are computed as floating point numbers and formatted with 2 digits after the decimal point.
Only strictly positive probabilities and the corresponding number of cards left are output (including the
cases, if any, when they are smaller than 0.005%, and so output as 0.00%). The output is sorted in
decreasing number of cards left.
There is a single space to the left and to the right of the separating vertical bar, with all lines consisting
of precisely 32 characters.
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