Exercise 2 Write a function called cumsum that takes a list of numbers and returns the cumulative sum; that is, a new list where the ith element is the sum of the first i+1 elements from the original list. For example: >>> t = [1, 2, 3] >>> cumsum(t) [1, 3, 6]
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![Exercise 2
Write a function called cumsum that takes a list of numbers and returns the cumulative sum;
that is, a new list where the ith element is the sum of the first i+1 elements from the original
list. For example:
>>> t = [1, 2, 3]
>>> cumsum(t)
[1, 3, 6]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6389447-1237-4af0-b5c6-eb1260425b55%2F8a2f7a84-c5dd-4b52-9e34-afc6b4e7a900%2Fagg2hlr_processed.png&w=3840&q=75)
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Solved in 3 steps with 1 images
- Exercise, maxCylinderVolume F# system function such as min or methods in the list module such as List.map are not allowed Write a function maxCylinderVolume that takes a list of floating-point tuples that represent dimensions of a cylinder and returns the volume of the cylinder that has the largest volume. Each tuple has two floating point values that are both greater than zero. The first value is the radius r and the second value is the height h. The volume of the cylinder is computed using ??2h. The value π is represented in F# with System.Math.PI. If the list is empty, return 0.0. Examples: > maxCylinderVolume [(2.1, 3.4); (4.7, 2.8); (0.9, 6.1); (3.2, 5.4)];;val it : float = 194.3137888> maxCylinderVolume [(0.33, 0.66)];;val it : float = 0.2257988304def cartesianproduct(lst): """Takes a list of sets/frozensets and computes their Cartesian product""" cartesianproduct: This function should accept a list of one or more sets or frozensets (you can convert between them using set(fro_st) and frozenset(st)). Its output is a set or frozenset encoding the cartesian product; thus a list of two sets [{0,1}, {1,2}] could give back {(0,1),(0,2),(1,1),(1,2)}. In general, an input list of length N will yield a set of tuples of length N each.two_sum is a Python function that takes in a list of integers (elements) and an integer number (num) and returns True if there exist two values in elements that add up to num, otherwise, function returns False. def two_sum(elements: List[int], num: int): for i in range(len(elements)): for j in range(i + 1): if elements[i] + elements[j] == num: return True return False Study above function and answer below questions: A. What is time complexity of two_sum? B. Is it possible to improve on above algorithm performance (in terms of its asymptotic cost)? If yes, describe your algorithm, be detailed as much as possible.
- Write a function that returns the greatest common divisor (GCD) of integers in a list. Use the following function header:def gcd(numbers):Write a test program that prompts the user to enter five numbers, invokes the function to find the GCD of these numbers, and displays the GCD.Matrix Multiplication by a Scalar Please write a function calculate (matrix, scalar) that takes two arguments: a nested list that represents a matrix and an integer that represents a scalar. The function returns a nested list that corresponds to the result of matrix multiplication by a scalar. Your function should work with the following code: if __name__ == '__main__': scalar 3 A = [[1,0,0], [0,1,0], [0,0,1]] D calculate (A, scalar) assert D == [[3,0,0], [0,3,0], [0,0,3]] Save your function and the main code in a file called matrix.py and upload it here.Exercise 1 Write a function called nested_sum that takes a list of lists of integers and adds up the elements from all of the nested lists. For example: >>> t = [[1, 2], [3], [4, 5, 6]] >>> nested_sum(t) 21
- struct Node { int data; Node * next; }; Node • head; a. Write a function named addNode that takes in a variable of type int and inserts it at the head of the list. b. Write a function named removeNode that removes a node at the head of the list.The mapped list pattern Our second pattern is the mapped list pattern, described in video 4 3 mapped list pattern. Often we need to write a function that takes a list as a parameter and returns a new list in which each item in the original list is "mapped" to a new item in the result list. For example, the following function takes a list of numbers as a parameter and returns a list of all the numbers squared, e.g. squares ( [1, 3, 7]) returns [1, 9, 49]. def squares (nums): "Returns the squares of the given numbers""" result = [] for num in nums: result.append (num * num) return result Although this is just a special case of the accumulator pattern, it is so common that we give it its own name: the mapped list pattern. Consider the following function: def squares(nums): ""Returns the squares of the given numbers""" result = [] for num in nums: result.append (num * num) return result If the main program calls print(squares ( [5, -3, 2, 7]) what is the state table for the function…16-Write a function called find_integer_with_most_divisors that receives a list of integers and returns the integer from the list with the most divisors .In the event of a tie, the first case with the most divisors returns .For example: If the list looks like this: [8, 12, 18, 6] In this list, the number 8 has four divisors, which are ;[1,2,4,8] :The number 12 has six divisors, which are ;[1,2,3,4,6,12] :The number 18 has six divisors, which are ;[1,2,3,6,9,18] :And the number 6 has four divisors, which are : [1,2,3,6]Note that both items 12 and 18 have the maximum number of divisors and are equal in number of divisors (both have 6 divisors) .Your function must return the first item with the maximum number of divisors ;Therefore it must return the following value: 12
- Write the code of the following functions: def fillX(pointsX,lowerLimit, upperLimit): This function receives a list pointsX and returns the same list with values between loverLimit and upperLimit. There are number of them.Code in python Given a list, L, the function front_two creates a new list of length 2 out of the first two items in L as follows: In the new list, the second item becomes the first item, and the first item becomes the second. If L contains only one item, the first item in the new list should be the value None. If L is empty, both items in the new list should be value None. The function returns the new list. For example: Test Result L = ['a', 'b', 'c', 'd'] print(front_two(L)) ['b', 'a'] L = [] print(front_two(L)) [None, None] L = [5, 2] print(front_two(L)) [2, 5] L = [7] print(front_two(L)) [None, 7]Algorithm Efficiency 1- Programming Problem Part 1 Write a function that will have a list as an input, the task of the function is to check if all the elements in the list are unique,( i.e. no repetition of any value has occurred in the list), then the function returns true otherwise it returns false. Your program should include a main method that call the method to test it. (If you would use built-in functions in Python, use lists’ or dictionaries’ methods as we studied their time efficiency in class) 2- Algorithm AnalysisFor the function you implemented in part 1, please calculate T(n), which represents the running time of your algorithm in terms of n. Where n is the length of the list. Then find the order of magnitude of your algorithm (Big O). 3- Algorithms Comparison Please find another algorithm that solves part 1, write the code, calculate T(n) and find Big O. Then compare the efficiency with the algorithm from part1 to determine the more efficient one.