From c549bca950fd740f6f9ec09d2d5f53276af09b16 Mon Sep 17 00:00:00 2001 From: Hykilpikonna Date: Fri, 21 Jan 2022 14:57:58 -0500 Subject: [PATCH] [+] Finish Prep3 --- practice/prep3.py | 160 +++++++++++++++++++++++++++++++++++ practice/prep3_functions.pdf | Bin 0 -> 102963 bytes 2 files changed, 160 insertions(+) create mode 100644 practice/prep3.py create mode 100644 practice/prep3_functions.pdf diff --git a/practice/prep3.py b/practice/prep3.py new file mode 100644 index 0000000..86729e1 --- /dev/null +++ b/practice/prep3.py @@ -0,0 +1,160 @@ +"""CSC111 Winter 2022 Prep 3: Programming Exercises + +Instructions (READ THIS FIRST!) +=============================== + +This Python module contains a few functions that you should implement. +Each function represents a recursively-defined mathematical function, +corresponding to one in the starter file prep3_functions.pdf. +(You do not need to modify or submit prep3_functions.pdf, but you'll +need to read it to complete this programming exercise.) + +We have marked each place you need to write code with the word "TODO". +As you complete your work in this file, delete each TODO comment. + +You do not need to add additional doctests. However, you should test your work carefully +before submitting it! + +Copyright and Usage Information +=============================== + +This file is provided solely for the personal and private use of students +taking CSC111 at the University of Toronto St. George campus. All forms of +distribution of this code, whether as given or with any changes, are +expressly prohibited. For more information on copyright for CSC111 materials, +please consult our Course Syllabus. + +This file is Copyright (c) 2022 Mario Badr and David Liu. +""" + + +def formula(n: int) -> float: + """Return the value given by Definition 1 in prep3_functions.py. + + Preconditions: + - n >= 0 + + >>> formula(0) + 4.0 + >>> formula(1) == 4 - 4/3 + True + >>> formula(2) == 4 - 4/3 + 4/5 + True + """ + if n == 0: + return 4.0 + elif n > 0: + return formula(n - 1) + ((4 * (-1) ** n) / (2 * n + 1)) + else: + raise ValueError(f'Precondition n >= 0 is violated. (n = {n})') + + +def formula_multiple_args(n: int, a: float, b: float) -> float: + """Return the value given by Definition 2 in prep3_functions.py. + + Preconditions: + - n >= 0 + + >>> formula_multiple_args(0, -1, -1) + 0.0 + >>> formula_multiple_args(1, 3, 2) + 2.0 + """ + if n == 0: + return 0.0 + elif n > 0: + return a * formula_multiple_args(n - 1, a, b) + b + else: + raise ValueError(f'Precondition n >= 0 is violated. (n = {n})') + + +def formula_double_recursion(n: int, m: int) -> int: + """Return the value given by Definition 3 in prep3_functions.py. + + Preconditions: + - n >= 0 + - m >= 0 + + >>> formula_double_recursion(0, 155) + 155 + >>> formula_double_recursion(1, 1) == 3 + (2 * 1) + True + """ + if n == 0: + return m + elif n > 0: + if m == 0: + return 2 * formula_double_recursion(n - 1, n) + elif m > 0: + return 3 + formula_double_recursion(n, m - 1) + else: + raise ValueError(f'Precondition m >= 0 is violated. (m = {m})') + else: + raise ValueError(f'Precondition n >= 0 is violated. (n = {n})') + + +# Note: the type annotation list[int] requires that you have Python 3.9 installed! +# If you haven't upgraded already, now is an excellent time to do so (check the +# "Software Installation/Upgrading Instructions" page on Quercus). +def create_list1(n: int) -> list[int]: + """Return the value given by Definition 4 in prep3_functions.py. + + Preconditions: + - n >= 0 + + >>> create_list1(0) + [0] + >>> create_list1(1) + [0, 0, 1] + >>> create_list1(2) + [0, 0, 1, 0, 0, 1, 2] + """ + if n == 0: + return [0] + elif n > 0: + return 2 * create_list1(n - 1) + [n] + else: + raise ValueError(f'Precondition n >= 0 is violated. (n = {n})') + + +def create_list2(n: int, m: int) -> list: + """Return the value given by Definition 5 in prep3_functions.py. + + Preconditions: + - n >= 0 + - m >= 0 + + TESTING NOTE: because this function makes two recursive calls instead of + just one, it will be a lot slower than your other functions! + We recommend testing your work with very small numbers, e.g. m, n <= 5. + + >>> create_list2(0, 155) + [155] + >>> create_list2(155, 0) + [155] + >>> create_list2(1, 1) + [[1], [1]] + >>> create_list2(2, 2) + [[[2], [[1], [1]]], [[[1], [1]], [2]]] + """ + if n == 0: + return [m] + elif m == 0: + return [n] + elif n > 0 and m > 0: + return [create_list2(n - 1, m), create_list2(n, m - 1)] + else: + raise ValueError(f'Precondition (n >= 0 and m >= 0) is violated. 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