artesianproduct: 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.
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- ] ] get_nhbr In the cell below, you are to write a function called "get_nhbr(Ist, graph)" that takes in two inputs: a list of vertices and a graph. The function is to return a list that contains the neighborhood of the vertices in 'Ist' (remember that this means you are finding the union of the individual vertices' neighborhoods). + Code + Markdown After compiling the above cell, you should be able to compile the following cell and obtain the desired outputs. print (get_nhbr(["A", "D"], {"A" : ["B"], "B" : ["A", "D", "E"], "C" : ["E"], "D":["B"], "E":["B","C","F"], "F":["E"]}), get_nhbr(["B", "C", "F"], {"A" : ["B"], "B" : ["A", "D", "E"], "C" : ["E"], "D":["B"], "E":["B","C","F"], "F":["E"]})) This should return ["B"] ["A", "D", "E"] Python Pythononsider an input string TAM of letters ‘A’, ‘M’, and ‘T’. This string, which is given by the user, ends with ‘#’. It should be stored in a table (or array), called TAMUK. The number of each of these letters is unknown. We have a function, called SWAP(TAM,i,j), which places the ith letter in the jth entry of string TAM and the jth letter in the ith entry of TAM. Note that SWAP(TAM,i,j) is defined for all integers i and j between 0 and length(TAM)–1, where length(TAM) is the number of letters of TAM. 1. Using our algorithmic language, write an algorithm, called Sort_TAM, which sorts the letters in the array TAMUK in a way that all T’s appear first, followed by all A’s, and followed by all M’s. The algorithm Sort_TAM should have one parameter: The array TAMUK. Also, your solution is correct only if the following four constraints are satisfied: - Constraint 1: Each letter (‘A’, ‘M’, or ‘T’) is evaluated only once. - Constraint 2: The function SWAP(TAM,i,j) is used only when it is…Problem 1: Lo Shu Magic Square The Lo Shu Magic Square is a grid with 3 rows and 3 columns. The Lo Shu Magic Square has the following properties: • The grid contains the numbers 1 through 9 exactly.• The sum of each row, each column, and each diagonal all add up to the same number. This is shown in Figure ➔➔➔ "Attached Image" In a python program, you can simulate a magic square using a two-dimensionallist. Write a function that accepts a two-dimensional list as an argumentand determines whether the list is a Lo Shu Magic Square. Test thefunction in a program. Below is the main() function and some globalconstants. You may need to define multiple functions to organize yourcode. # Global constants ROWS = 3 # The number of rowsCOLS = 3 # The number of columnsMIN = 1 # The value of the smallest numberMAX = 9 # The value of the largest numberdef main():# Create a two-dimensional list.test_list = [ [4, 9, 2],[3, 5, 7],[8, 1, 6] ] # Display the list in row and column…
- [] [] partite_sets In the cell below, you are to write a function "partite_sets (graph)" that takes in a BIPARTITE graph as its input, and then returns a single list whose two entries are the partite sets of the graph as lists (the order of the sets outputed does not matter). After compiling the above cell, you should be able to compile the following cell and obtain the desired outputs. print (partite_sets({"A" : ["B", "C"], "B" : partite_sets({"A" : ["B", "C"], "B" : ["A"], "C" : ["A"]}), ["A", "D"], "C" : ["A", "D"], "D" : ["B", "C"]})) This should return [["B","C"], ["A"]] [["A","D"], ["B","C"]] (the order in which the entries appear does not matter) Python Python***python only*** Write a function votes_by_race() which takes a list of dicts as a parameter and returns a dict. For example, given the following list: votes = [{'for': 'A, 'age': 35, 'race': 'w'}, {'for': 'B', 'age': 40, 'race': 'b'}, {'for': 'B', 'age': 20, 'race': 'b'}, {'for': 'A', 'age': 30, 'race': 'a'}, {'for': 'A', 'age': 41, 'race': 'w'}, ] The call votes_by_race(votes) should return the following dict:{"White": 2, 'Black': 2, 'Asian': 1, "Hispanic': 0}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…
- Write the function splitList that takes the first argument list and splits it into two: a list of all the elements that are less than the head (the second argument), and a list of all the elements that are greater than or equal to the head (the third argument): listElementT splitList(listADT list, listADT* ItList, listADT* geList); Note that the head is returned by the function. a) Write this function as a recursive function. b) Write this function as a nonrecursive function.Python please! Generalized image blender function Create a function blend images() which takes multiple RGB images as an input, and outputs a blended image. The function should accept following parameters 1. image list- A Python list of 3D arrays where each 3D array corresponds to an RGB image 2. weight list-A Python list of float values between (0, 1) corresponding to the pixel weight to be given to each image-e.g. [0.2, 0.3, 0.1, 0.4] for 4 images. The sum of the weights should be equal to 1. Test your function against a provided list of 5 images with following weight lists (i.e. 2 blended images) [0.2, 0.2, 0.2, 0.2, 0.2]- blend all 5 images [0.2, 0.3, 0.5]- blend first 3 images NOTE: DO NOT USE pre-existing image blending functions.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
- 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 = 0.2257988304Count dominators def count_dominators(items): An element of items is said to be a dominator if every element to its right (not just the one element that is immediately to its right) is strictly smaller than it. By this definition, the last item of the list is automatically a dominator. This function should count how many elements in items are dominators, and return that count. For example, dominators of [42, 7, 12, 9, 13, 5] would be the elements 42, 13 and 5. Before starting to write code for this function, you should consult the parable of "Shlemiel the painter" and think how this seemingly silly tale from a simpler time relates to today's computational problems performed on lists, strings and other sequences. This problem will be the first of many that you will encounter during and after this course to illustrate the important principle of using only one loop to achieve in a tiny fraction of time the same end result that Shlemiel achieves with two nested loops. Your workload…Please use python for this problem: Please use Python when answering the question: Question 2: numPairs Write a function numPairs that accepts two arguments, a target number and a list of numbers. The function then returns the count of pairs of numbers from the list that sum to the target number. In the first example the answer is 2 because the pairs (0,3) and (1,2) both sum to 3. The pair can be two of the same number, e.g. (2,2) but only if the two 2’s are separate twos in the list. In the last example below, there are three 2’s, so there are three different pairs (2,2) so there are 5 pairs total that sum to 4. Output is shown in the picture attached. Also, make sure all of the code works for the output: