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0-basics November 28, 2023 1 Python review: Values, variables, types, lists, and strings These first few notebooks are a set of exercises designed to reinforce various aspects of Python programming. Study hint: Read the test code! You’ll notice that most of the exercises below have a place for you to code up your answer followed by a "test cell." That’s a code cell that checks the output of your code to see whether it appears to produce correct results. You can often learn a lot by reading the test code. In fact, sometimes it gives you a hint about how to approach the problem. As such, we encourage you to try to read the test cells even if they seem cryptic, which is deliberate! Debugging tip: Read assertions. The test cells often run an assert statement to see whether some condition that it thinks should be true is true. If an assertion fails, look at the condition being checked and use that as a guide to help you debug. For example, if an assertion reads, assert a + b == 3 , and that fails, inspect the values and types of a and b to help determine why their sum does not equal 3. Exercise 0 (1 point). Run the code cell below. It should display the output string, Hello, world! . In [1]: print ( "Hello, world!" ) Hello, world! Exercise 1 ( x_float_test : 1 point). Create a variable named x_float whose numerical value is one (1) and whose type is floating-point (i.e., float ). In [4]: ### ### YOUR CODE HERE ### x_float = 1.0 In [5]: # ` x_float_test ` : Test cell assert x_float == 1 , f " ` x_float ` has the wrong value ( {x_float} rather than 1.0)" assert type (x_float) is float , f " ` type(x_float) ` == {type(x_float)} rather than ` float ` print ( " \n (Passed!)" ) (Passed!) 1

Exercise 2 ( strcat_ba_test : 1 point). Complete the following function, strcat_ba(a, b) , so that given two strings, a and b , it returns the concatenation of b followed by a (pay attention to the order in these instructions!). In [7]: def strcat_ba (a, b): assert type (a) is str , f "Input argument ` a ` has ` type(a) ` is {type(a)} rather than assert type (b) is str , f "Input argument ` b ` has ` type(b) ` is {type(b)} rather than ### ### YOUR CODE HERE ### return b + a In [8]: # ` strcat_ba_test ` : Test cell # Workaround: # Python 3.5.2 does not have ` random.choices() ` (available in 3.6+) def random_letter (): from random import choice return choice( ' abcdefghijklmnopqrstuvwxyz ' ) def random_string (n, fun = random_letter): return '' . join([ str (fun()) for _ in range (n)]) a = random_string( 5 ) b = random_string( 3 ) c = strcat_ba(a, b) print ( ' strcat_ba(" {} ", " {} ") == " {} " ' . format(a, b, c)) assert len (c) == len (a) + len (b), " ` c ` has the wrong length: {len(c)} rather than {len( assert c[: len (b)] == b assert c[ - len (a):] == a print ( " \n (Passed!)" ) strcat_ba("eahxx", "zbn") == "zbneahxx" (Passed!) Exercise 3 ( strcat_list_test : 2 points). Complete the following function, strcat_list(L) , which generalizes the previous function: given a list of strings, L[:] , returns the concatenation of the strings in reverse order. For example: strcat_list([ ' abc ' , ' def ' , ' ghi ' ]) == ' ghidefabc ' In [9]: def strcat_list (L): assert type (L) is list ### ### YOUR CODE HERE ### return '' . join( map ( str , L[:: -1 ])) 2

In [10]: # ` strcat_list_test ` : Test cell n = 3 nL = 6 L = [random_string(n) for _ in range (nL)] Lc = strcat_list(L) print ( ' L == {} ' . format(L)) print ( ' strcat_list(L) == \ ' {} \ ' ' . format(Lc)) assert all ([Lc[i * n:(i +1 ) * n] == L[nL - i -1 ] for i, x in zip ( range (nL), L)]) print ( " \n (Passed!)" ) L == [ ' llr ' , ' ddw ' , ' dxn ' , ' oep ' , ' ogd ' , ' szs ' ] strcat_list(L) == ' szsogdoepdxnddwllr ' (Passed!) Exercise 4 ( floor_fraction_test : 1 point). Suppose you are given two variables, a and b , whose values are the real numbers, a ≥ 0 (non-negative) and b > 0 (positive). Complete the function, floor_fraction(a, b) so that it returns ⌊ a b ⌋ , that is, the floor of a b . The type of the returned value must be int (an integer). In [11]: def is_number (x): """Returns ` True ` if ` x ` is a number-like type, e.g., ` int ` , ` float ` , ` Decimal() ` , from numbers import Number return isinstance (x, Number) def floor_fraction (a, b): assert is_number(a) and a >= 0 assert is_number(b) and b > 0 ### ### YOUR CODE HERE ### return int (a // b) In [12]: # ` floor_fraction_test ` : Test cell from random import random a = random() b = random() c = floor_fraction(a, b) print ( ' floor_fraction( {} , {} ) == floor( {} ) == {} ' . format(a, b, a / b, c)) assert b * c <= a <= b * (c +1 ) assert type (c) is int , f "type(c) == {type(c)} rather than ` int ` " print ( ' \n (Passed!) ' ) floor_fraction(0.044995573154997914, 0.49256039375921157) == floor(0.09135036784340811) == 0 (Passed!) 3

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Exercise 5 ( ceiling_fraction_test : 1 point). Complete the function, ceiling_fraction(a, b) , which for any numeric inputs, a and b , corresponding to real numbers, a ≥ 0 and b > 0, returns ⌈ a b ⌉ , that is, the ceiling of a b . The type of the returned value must be int . In [13]: def ceiling_fraction (a, b): assert is_number(a) and a >= 0 assert is_number(b) and b > 0 ### ### YOUR CODE HERE ### return int ( - ( - a // b)) In [14]: # ` ceiling_fraction_test ` : Test cell from random import random a = random() b = random() c = ceiling_fraction(a, b) print ( ' ceiling_fraction( {} , {} ) == ceiling( {} ) == {} ' . format(a, b, a / b, c)) assert b * (c -1 ) <= a <= b * c assert type (c) is int print ( " \n (Passed!)" ) ceiling_fraction(0.8115577738044994, 0.42646156251440515) == ceiling(1.9030033305219305) == 2 (Passed!) In [15]: a = 0.3 b = 0.1 c = ceiling_fraction(a, b) print (f "{a/b}" ) print ( ' ceiling_fraction( {} , {} ) == ceiling( {} ) == {} ' . format(a, b, a / b, c)) assert b * (c -1 ) <= a <= b * c assert type (c) is int 2.9999999999999996 ceiling_fraction(0.3, 0.1) == ceiling(2.9999999999999996) == 3 Exercise 6 ( report_exam_avg_test : 1 point). Let a , b , and c represent three exam scores as numerical values. Complete the function, report_exam_avg(a, b, c) so that it computes the average score (equally weighted) and returns the string, ' Your average score: XX ' , where XX is the average rounded to one decimal place. For example: report_exam_avg( 100 , 95 , 80 ) == ' Your average score: 91.7 ' In [18]: def report_exam_avg (a, b, c): #assert is_number(a) and is_number(b) and is_number(c) ### 4

### YOUR CODE HERE ### avg = (a + b + c) /3 return ( ' Your average score: ' + str ( round (avg, 1 ))) In [19]: # ` report_exam_avg_test ` : Test cell msg = report_exam_avg( 100 , 95 , 80 ) print (msg) assert msg == ' Your average score: 91.7 ' print ( "Checking some additional randomly generated cases:" ) for _ in range ( 10 ): ex1 = random() * 100 ex2 = random() * 100 ex3 = random() * 100 msg = report_exam_avg(ex1, ex2, ex3) ex_rounded_avg = float (msg . split()[ -1 ]) abs_err = abs (ex_rounded_avg *3 - (ex1 + ex2 + ex3)) / 3 print ( " {} , {} , {} -> ' {} ' [ {} ]" . format(ex1, ex2, ex3, msg, abs_err)) assert abs_err <= 0.05 print ( " \n (Passed!)" ) Your average score: 91.7 Checking some additional randomly generated cases: 27.78367308710379, 71.95711132447614, 62.570801779943906 -> ' Your average score: 54.1 ' [0.00386 84.61229196821417, 98.60141504976954, 90.37598366467579 -> ' Your average score: 91.2 ' [0.003436 66.6912520012273, 11.16148814795378, 52.946898240090626 -> ' Your average score: 43.6 ' [0.000120 57.92021515738315, 12.758732959503316, 95.05341805209702 -> ' Your average score: 55.2 ' [0.04412 18.02949697406353, 77.86811211857753, 92.87403576891272 -> ' Your average score: 62.9 ' [0.023881 46.812355262994565, 83.10333302915377, 83.13169171864023 -> ' Your average score: 71.0 ' [0.01579 9.359584627876227, 94.18934555861566, 71.36081782616559 -> ' Your average score: 58.3 ' [0.003249 67.71615377917351, 4.4914207773978365, 30.09822017799786 -> ' Your average score: 34.1 ' [0.00193 27.54397922204118, 4.481514045319745, 77.674958219558 -> ' Your average score: 36.6 ' [0.03318283 43.463419365352316, 42.76050000505237, 66.2174869754471 -> ' Your average score: 50.8 ' [0.013802 (Passed!) Exercise 7 ( count_word_lengths_test : 2 points). Write a function count_word_lengths(s) that, given a string consisting of words separated by spaces, returns a list containing the length of each word. Words will consist of lowercase alphabetic characters, and they may be separated by multiple consecutive spaces. If a string is empty or has no spaces, the function should return an empty list. For instance, in this code sample, count_word_lengths( ' the quick brown fox jumped over the lazy dog ' ) == [ 3 , 5 , 5 , 3 , 6 the input string consists of nine (9) words whose respective lengths are shown in the list. 5

In [20]: def count_word_lengths (s): assert all ([x . isalpha() or x == ' ' for x in s]) assert type (s) is str ### ### YOUR CODE HERE ### return [ len (x) for x in s . split()] In [21]: # ` count_word_lengths_test ` : Test cell # Test 1: Example qbf_str = ' the quick brown fox jumped over the lazy dog ' qbf_lens = count_word_lengths(qbf_str) print ( "Test 1: count_word_lengths( ' {} ' ) == {} " . format(qbf_str, qbf_lens)) assert qbf_lens == [ 3 , 5 , 5 , 3 , 6 , 4 , 3 , 4 , 3 ] # Test 2: Random strings from random import choice # 3.5.2 does not have ` choices() ` (available in 3.6+) #return '' .join([choice( ' abcdefghijklmnopqrstuvwxyz ' ) for _ in range(n)]) def random_letter_or_space (pr_space =0.15 ): from random import choice, random is_space = (random() <= pr_space) if is_space: return ' ' return random_letter() S_LEN = 40 W_SPACE = 1 / 6 rand_str = random_string(S_LEN, fun = random_letter_or_space) rand_lens = count_word_lengths(rand_str) print ( "Test 2: count_word_lengths( ' {} ' ) == ' {} ' " . format(rand_str, rand_lens)) c = 0 while c < len (rand_str) and rand_str[c] == ' ' : c += 1 for k in rand_lens: print ( " => ' {} ' " . format (rand_str[c:c + k])) assert (c + k) == len (rand_str) or rand_str[c + k] == ' ' c += k while c < len (rand_str) and rand_str[c] == ' ' : c += 1 # Test 3: Empty string print ( "Test 3: Empty strings..." ) assert count_word_lengths( '' ) == [] assert count_word_lengths( ' ' ) == [] print (count_word_lengths( ' the ' )) 6

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print ( " \n (Passed!)" ) Test 1: count_word_lengths( ' the quick brown fox jumped over the lazy dog ' ) == [3, 5, 5, 3, 6, 4 Test 2: count_word_lengths( ' pe yxjuw gxewect x xcztri gd b f shyz ' ) == ' [2, 5, 7, 1, 6, 2, 1 => ' pe ' => ' yxjuw ' => ' gxewect ' => ' x ' => ' xcztri ' => ' gd ' => ' b ' => ' f ' => ' shyz ' Test 3: Empty strings... [3] (Passed!) Fin! You’ve reached the end of this part. Don’t forget to restart and run all cells again to make sure it’s all working when run in sequence; and make sure your work passes the submission process. Good luck! 7

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