1 R Back to fully parenthesised expressions

Modify the program fully_parenthesised.py from Lab 9, that deals with arithmetic expressions written in infix, fully parenthesised, and built from natural numbers using the binary +, -, * and / operators, still using a stack but to build an expression tree rather than to evaluate the expression

(that is, representing an expression of the form (first_argument operator second_argument) as a tree whose value is operator, and whose left and right nodes are the subtrees that represent first_argument and second_argument, respectively. The function evaluate() is then reimplemented so as to recursively evaluate the expression from the tree.

Next is a possible interaction.

$ python3

>>> from fully_parenthesised import *

>>> parse_tree(100).print_binary_tree()

100

>>> parse_tree([(1 20) + 300]).print_binary_tree() 1

20

300

>>> parse_tree(( 1 [ 20 + 300] )).print_binary_tree()

1

20

300

>>> parse_tree({{20*4}/5}).print_binary_tree()

20

*

4

/

5

>>> parse_tree([ 20 * (4 / 5) ]).print_binary_tree()

20

*

4

/

5

>>> parse_tree((1 + {20 * (30 400)})).print_binary_tree()

1

20

*

30

400

>>> parse_tree({(1 + 20)*(30 400)}).print_binary_tree()

1

20

*

30

400

2 R Possible subtractions yielding a given sum

Write a program subtractions.py that takes as input an iterable L of nonnegative integers and an integer N, and displays all ways of inserting minus signs and parentheses in L, resulting in an expression that evaluates to N. For this question we make use of eval().

Next is a possible interaction.

$ python3

>>> from subtractions import *

>>> subtractions((1, 2, 3, 4, 5), 1)

1 ((2 3) (4 5))

(1 ((2 3) 4)) 5

>>> subtractions((1, 2, 3, 4, 5), 2)

>>> subtractions((1, 2, 3, 4, 5), 3)

1 (2 (3 (4 5)))

1 ((2 (3 4)) 5)

(1 (2 3)) (4 5)

>>> subtractions((1, 2, 3, 4, 5), 4)

>>> subtractions((1, 2, 3, 4, 5), 5)

(1 2) ((3 4) 5)

>>> subtractions((1, 3, 2, 5, 11, 9, 10, 8, 4, 7, 6), 40)

1 ((((3 2) 5) 11) (9 ((((10 8) 4) 7) 6)))

1 ((((((3 2) 5) 11) 9) 10) (8 (4 (7 6))))

1 ((((((3 2) 5) 11) 9) 10) ((8 (4 7)) 6))

1 (((((((3 2) 5) 11) 9) 10) (8 4)) (7 6))

1 (((((3 2) 5) 11) (9 (((10 8) 4) 7))) 6)

1 ((((((3 2) 5) 11) (9 ((10 8) 4))) 7) 6)

1 (((((((3 2) 5) 11) (9 (10 8))) 4) 7) 6)

1 ((((((((3 2) 5) 11) (9 10)) 8) 4) 7) 6)

(1 3) ((((2 5) 11) 9) (10 (((8 4) 7) 6)))

(1 3) (((((2 5) 11) 9) (10 ((8 4) 7))) 6)

(1 3) ((((((2 5) 11) 9) (10 (8 4))) 7) 6)

(1 3) (((((((2 5) 11) 9) (10 8)) 4) 7) 6)

(1 ((((3 2) 5) 11) 9)) ((((10 8) 4) 7) 6)

((1 3) ((((2 5) 11) 9) 10)) (((8 4) 7) 6)

(1 ((((((3 2) 5) 11) 9) 10) 8)) (4 (7 6))

(1 ((((((3 2) 5) 11) 9) 10) (8 (4 7)))) 6

(1 (((((((3 2) 5) 11) 9) 10) (8 4)) 7)) 6

((1 ((((((3 2) 5) 11) 9) 10) 8)) (4 7)) 6

3 Building a general tree (optional)

Consider a file named tree.txt containing numbers organised as a tree, a number at a depth of N in the tree being preceded with N tabs in the file. The file can also contain any number of lines with nothing but blank lines. Using the module general_tree.py, write a program read_and_build_tree.py that reads the contents of the file. If the file does not contain a proper representation of a tree then the program outputs an error message; otherwise, it builds the tree (an instance of GeneralTree()) and prints it out using the same representation as in the file (except for the possible blank lines of course).

$ python3

$ cat tree.txt

2

3

1

4

5

7

8

9

10

11

12

6

1

$ python3 read_and_build_tree.py tree.txt does not contain the correct representation of a tree.

$ cat tree.txt

2

3

1

4

5

7

8

9

6

$ python3 read_and_build_tree.py tree.txt does not contain the correct representation of a tree. $ cat tree.txt

2

3

1

4

5

7

8

9

10

11

12

6

$ python3 read_and_build_tree.py 2

3

1

4

5

7

8

9

10

11

12

6

$

4 Back to context free grammars (optional)

Modify the program context_free_grammar.py from Lab 9, that deals with a context free grammar for a set of arithmetic expressions, so that rather than implementing the function evaluate(), a function parse_tree() is implemented to build an object of type BinaryTree to represent the parse tree of the expression.

Next is a possible interaction.

$ python3

>>> from context_free_grammar import *

>>> parse_tree(100).print_binary_tree()

100

>>> parse_tree(1 20 + 300).print_binary_tree()

1

20

300

>>> parse_tree(1 (20 + 300)).print_binary_tree()

1

20

300

>>> parse_tree(20 * 4 / 5).print_binary_tree()

20

*

4

/

5

>>> parse_tree(20 * (4 / 5)).print_binary_tree()

20

*

4

/

5

>>> parse_tree(1 + 20 * (30 400)).print_binary_tree()

1

20

*

30

400

>>> parse_tree((1 + 20) * (30 400)).print_binary_tree()

1

20

*

30

400