Instructions - Submit your solutions on Canvas by the deadline displayed online. - Your submission must include a single Python module (file with extension ".py") that includes all of the code necessary to answer the problems. All of your code should run without error. - Problem numbers must be clearly marked with code comments. Problems must appear in order, but later problems may use functions defined in earlier problems. - Functions must be documented with a docstring describing at least (1) the function's purpose, (2) any and all parameters, (3) the return value. Code should be commented such that its function is clear. - You may use standard library modules only (e.g., no numpy or pandas), but you will not receive credit for using a function that exactly duplicates the requested behavior. - All solutions to the given problems must be your own work. If you use third-party code for ancillary tasks, you must cite them. Problem 1 Define a function called cummax (x) that satisfies the following criteria: - Calculates and returns a list giving the cumulative maxima of elements of x - The cumulative max for an element means the max of all previous elements and the current element - The return value should be a list with the same length as x - You may assume x is a list of numbers Examples: In : cummax([1,7,2,11,90,8,100]) Out: [1,7,7,11,90,90,100] In : cummax ([99,99,100,100,22]) Out: [99,99,99,100,100] Problem 2 Define a function called cumsum (x) that satisfies the following criteria: - Calculates and returns a list giving the cumulative sums of elements of x - The cumulative sum for an element means the sum of all previous elements plus the current element - The return value should be a list with the same length as x - You may assume x is a list of numbers Examples: In : cumsum([1,2,3,4,5,6]) Out: [1,3,6,10,15,21] In : cumsum ([1.11,2.22,3.33]) Out: [1.11,3.33,6.66] In : cumsum ([0,1,1,0,0,1,0,1]) Out: [0,1,2,2,2,3,3,4] Problem 3 Define a function called tokenize(s) that satisfies the following criteria: - Tokenizes a string s into a list of words (based on seperation by any white space) - The returned tokens should contain only alphanumeric characters - The returned tokens should be suitable for caseless comparisons Hint: You may find it helpful to write a separate helper function for sanitizing the individual tokens. Examples: In : tokenize("Hello, world!") Out: ['hello', world'] In : tokenize("Hi! Hi! Who are you?") Out: ['hi', 'hi', 'who', 'are', 'you'] Problem 4 Define a function called count_words(s) that satisfies the following criteria: - Counts the occurences of unique words in a string s and returns the result as a dictionary - Word uniqueness should not consider case or any non-alphanumeric characters Hint: You may find it helpful to write a separate helper function that builds a dictionary of unique values and their counts. Examples: In : count_words("I am that I am.") Out: {i:2, : 2, 'that': 1\} In : count_words("We are not who we are.") Out: \{'we': 2, 'are': 2, 'not': 1, 'who': 1\} Problem 5 Define a function called ifelse(test, yes, no) that satisfies the following criteria: - Chooses elements from yes or no based on the values of test - If test [i] is True, then choose yes [i] - If test [i] is Frue, then choose no [i] - The return value should be a list with the same length as x - You may assume all inputs are the same length and test is a list of booleans Examples: In : ifelse([True, True, False ],[1,2,3],[1.1,2.2,3.3] ) Dut: [1,2,3.3] In : ifelse([False, True, True], ["a", "b", "c"], [1, 2, 3]) Out: [1,b ', ' c ' ]