24 Card Game

24 Card Game

1 24 Card Game
In this exercise, you will write code to find all possible solutions for a given 4-card combination
and print each solution in postfix notation. A combination can be a solution only if it evaluates to
24.
In this game, 4 cards are randomly picked from a standard deck of 52 cards. We will use
the values of these 4 cards and a combination of addition, subtraction, multiplication, division,
modulus and concatenation to produce the value 24. Note that each of the 4 cards can only be
used once.
For the purposes of this assignment, we will consider the following to be the face values of
each card in a suit:
′A
′
: 1
′2
′
: 2
′3
′
: 3
′4
′
: 4
′5
′
: 5
′6
′
: 6
′7
′
: 7
′8
′
: 8
′9
′
: 9
′10′
: 10
′
J
′
: 11
′Q′
: 12
′K
′
: 13
For example, if the 4 cards chosen are “8 8 3 3” we can produce the value 24 by doing the
following operation: # 8
3− 8
3
Note that there are many possible solutions for a given 4-card combination. For instance the
cards “8 8 3 3” can produce 34 different solutions which produce 24. Read the following link for
more information about the game: https://en.wikipedia.org/wiki/24_Game.
2 Postfix Notation
Postfix notation is an unambiguous way of writing an arithmetic expression without parentheses.
It is defined so that if “(exp1) op (exp2)” is a normal, fully parenthesized expression whose operation is op, the postfix version of this is “pexp1 pexp2 op” where pexp1 is the postfix version of
1
exp1 and pexp2 is the postfix version of exp2. The postfix version of a single number or variable
is just that number or variable.
For example, the postfix version of “((6 − 1) ∗ (7 + 2)) / 4” will be equal to “6 1 − 7 2 +
∗ 4 /”.
3 Fractions in Python
The very first line in the skeleton code imports the smaller module ‘Fraction’ from module ‘fractions’. A module is simply a file containing Python definitions and statements. We can use the
following methods to perform the required arithmetic operation.
In [7]: Fraction.__add__
Fraction.__sub__
Fraction.__mul__
Fraction.__truediv__
Fraction.__mod__
4 Evaluating a postfix expression
The evaluate() method will take in a string containing a postfix expression. In this function, as
long as the size of the stack is not 0, you will pop the next element from the stack. If the element
is an operation (i.e. is either ‘+’, ‘-’, ‘*’, ‘/’, ‘%’ or ‘c’) you will pop the next two elements from the
stack, which will always be card values. Try playing around with different postfix notations to see
why this is true. Evaluate the two numbers using the operation. If the operation is division and
the denominator is 0, you can simply return None to the function and terminate the evaluation,
because this means that it will not evaluate to 24 anyway. You must also return None if the expression isn’t a valid postfix expression. If the element is a card value, then just push the value
back onto the stack. Once the function finishes running, the final remaining element on the stack
will be the result of evaluating the postfix expression.
5 Checking if a postfix expression is valid or not
In the isvalid() method, you must call evaluate method for the postfix expression to check if it
returns None or if it returns a value. This method returns a boolean value.
6 To do:
1. Complete the evaluate() method and make sure to account for division by zero and invalid
postfix expressions.
2. Complete the isvalid() method to check if a postfix expession is valid or not.
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