I want you to complete this assignment
Assignment 4 – Due December 4th , 202 2 at 11:55 pm Each program must start with a multi -line comment as shown below. Replace each occurrence of DentStew and Stew Dent with your name. Replace yyyy/mm/dd with the date you completed the program. # DentStewAxQy.py # # Course: COMP 1012 # Instructor: Abolfazl # Assignement: x Question y # Author: Stew Dent # Version: yyyy/mm/dd # # Purpose: The purpose of the program. Begin each program with the following statement. from time import ctime The name of each program should be of the form: LastnameFirstnameAnQm.py If your name is Stew Dent and the program is for assignment 4 question 1 then the name of the program would be: DentStewA 4Q1.py No email submission will be accepted, zero will be granted otherwise as the mark for the assignment. Attach the .py file for each program. There should be only one submission in which all of the programs are written and separated with appropriate comments . Do NOT use zip, rar or any other packaging of your files! Question 1 You must use dictionary in this question. Do not use arrays in this question! The purpose of this question is to write a Python program that can work with lists and dictionaries. Assume that you want to use dictionary to find different solutions of the equation below: 2x -3y+z=5 Pass a list of the coefficients to a function. For example for the above equation the list of equations would be : Coeff= [2, -3,1] Also, w e know that x,y, and z are integer and generally in the range of -9 to 9. T he range of each x,y and z is entered by user. Write a function that generates all the possible described situation with the header: def build Pos sibleAnswers (Coeff, Xmin , Xmax , Ymin , Ymax , Zmin , Zmax ): Call this function to build all possible answer for this equation. The function displays the prompt to tell the user what to enter. If the user does not enter valid input display the appropriate error message as described below and display the prompt again asking for more input from the user. Repeat this until the user enters valid input. When the user enters valid input return possible combination s of the answers in a list . Error situations: • If the user presses enter/return without entering anything display the message 'Missing input!' • If the input s are not integers display the value of the input and t he message 'is not valid!' • If the input s are not in the desired range, print ‘Out of range!’ Write a function that begins with the following header: def computeError (a, k): Given the value of a, the list that is the output of the “buildPossibleAnswers” function and “k” is the desired right -hand side of the equation; for the example above, k=5 . The output of “computeErrors” should be a dictionary in which the possible answers are the key element and the di fference between the output of the equation because of those values and the expected output is the value for that key element. Note: Keep in mind that a key in a dictionary is in “ string”; therefore, you have to convert possible answer to string before a dding it to your dictionary. For example if we call two functions buildPossibleAnswers and computeError respectively , the answer should like below for the mentioned equation: a=buildPossibleAnswers([2, -3,1], -9, 9, -9, 9, -9, 9 ) computeError(a, 5) Your possible answers and errors for the equation 2x -3y+z=5 are: {'[1, -1, -1]': 1, '[1, -1, -2]': 2, '[1, -1, -3]': 3, '[1, -1, -4]': 4, '[1, -1, -5]': 5, '[1, -1, 0]': 0, '[1, -1, 1]': -1, '[1, -1, 2]': -2, '[1, -1, 3]': -3, '[1, -1, 4]': -4, '[1, -1, 5]': -5, '[1, -1, 6]': -6, '[1, -2, -1]': -2, '[1, -2, -2]': -1, '[1, -2, -3]': 0, '[1, -2, -4]': 1, '[1, -2, -5]': 2, '[1, -2, 0]': -3, '[1, -2, 1]': -4, '[1, -2, 2]': -5, '[1, -2, 3]': -6, '[1, -2, 4]': -7, '[1, -2, 5]': -8, '[1, -2, 6]': -9, '[1, -3, -1]': -5, '[1, -3, -2]': -4, '[1, -3, -3]': -3, … } (‘…’ means that the list might be longer and may continue) In the next step, you have to choose the options that makes the error between the value of the inserted numbers and the actual value zero. In the other word, you have to find the answers of this equation. Write a function that begins with the following he ader: def findSolutions (R): where R is the output of the previous function “computeErrors” In the final step, write a main script and call all these function s in it and print the possible answers like below: Note: Make sure that your program returns back the answers in list. --------------------------------------------------------------------------------- -------------- There are total 12 possible answers for this equations in the desired range: X Y Z 1:[1, -2, -3] 2:[1, -1, 0] 3:[1, 0, 3] 4:[1, 1, 6] 5:[2, -2, -5] 6:[2, -1, -2] 7:[2, 0, 1] 8:[2, 1, 4] 9:[3, -1, -4] 10:[3, 0, -1] 11:[3, 1, 2] 12:[3, 2, 5] Programmed by Stew Dent . Date: Tue Nov 15 3 20 :22 :14 202 2 End of processing. The main program does the following: • Using string replication display a line of dashes. • Calls all the function that you wrote in the previous steps • Display a message that indicates number of possible solution in the desired range of user • Showing the time and date at the end o f the process Note: There is NO function named main in this program! Question 2 The purpose of this question is to write a complete Python program that finds the area under a parabola between 2 values on the X axis using Monte Carlo technique. An example of a parabola is shown below. The area under the parabola between the two points where the curve crosses the X axis is to be approximated. The parabola shown above is created using equation (1). y(x) = a(x - h) 2 + k, where a = -k/h 2 (1) k is the largest Y coordinate of the parabola and h is the corresponding X coordinate. The X coordinates range from 0 to 2×h. In this example h is 10 and k is 10. COMP 1012 – Computer Programming for Scientists and Engineers Page 6 of 8 Write a function that begins with the following header: def getPositive(prompt): Call this function to get all input from the user. Valid input is either an int greater than zero or a float greater than zero. The function displays the prompt to tell the user what to enter. If the user does not enter valid input display the appropriate error message as described below and display the prompt again asking for more input from the user. Repeat this until the user enters valid in- put. When the user enters valid input greater than zero return that input. Error situations: • If the user presses enter/return without entering anything display the message 'Missing input!' • If the input causes an exception when passed to eval display the value of the input and the message 'is not valid input!' • If the input is not an int nor a float display the value of the input and the message 'is not a number!' • If the input is less than or equal to zero display the value of the input and the message 'is not greater than zero!' Write a function that begins with the following header: def parabola(h, k, xCoordinates): Given the values of h, k and an array of X coordinates this function creates an ar- ray of Y coordinates using equation (1). There will be one Y coordinate for each X coordinate. Return the array of Y coordinates. You must compute the array of Y coordinates from the X coordinates using vec- tor arithmetic. You must not use any loops in this function. Write a function that begins with the following header: def monteCarlo(fx, h, k, points): This function is given the name of a function fx to call, the values of h and k that define the parabola and the number of random points to create. The X coordi- nates of the random points go from 0 to 2×h. The Y coordinates of the random points go from 0 to k. Call fx to compute the Y coordinates of the points on the pa- rabola for the random X coordinates. A point is under the parabola if its Y coordi- nate is less then or equal to the corresponding Y coordinate on the parabola. Com- pute the approximate area under the parabola. Return the area. Write a function that begins with the following header: COMP 1012 – Computer Programming for Scientists and Engineers Page 7 of 8 def main(): This function calls getPosNumber three times, once to get t he number of intervals / points, once to get the value of h and once to get value of k. It computes the ac- tual area of the parabola using the formula: area = 4. × h × k / 3., where h and k define the parabola. Call monteCarlo to compute the approximate area under the parabola from x = 0 to x = 2×h. The output from the program should be as shown below. The main program, not to be confused with the function named main , must con- tain the import statements, the functions and a call to main . A sample run of the program is shown below on the next page. Enter the number of intervals / points: 10000000 Enter the value of h in cm: 15 Enter the value of k in cm: 25 Area computed using the Monte Carlo technique. Area is from x=0.00 to x=30.00 Approximate area of the parabola is 4.99777050000000e+02 cm^2 Actual area of the parabola is 5.00000000000000e+02 cm^2 The error in the approximation is 2.229500e -01 cm^2 Programmed by Stew Dent. Date: Tue Nov 15 21:32 :18 20 22 . End of processing. Hand in your complete Python program. COMP 1012 – Computer Programming for Scientists and Engineers Page 8 of 8 Question 2 Note: Use sets and dictionary to solve this question ! In this question, you will learn how to read a file and recognize prime number in it.For this purpose, you have to first write a function that read the provided text file (A4_Q3.txt). Then, converts all the strings to the integer numbers and return the nu mbers in an array . The header of this function would be: def txt2Int(filename ) filename is the name of the text file that you want to read its contents. To recognize if any of the numbers in the file is prime, use the output of txt2Int function as the input for PrimeRec function. def PrimeRec(Num) where Num is the output of the txt2Int function. The PrimeRec function should be able to recognize the numbers that are not prime and return back one of their divisors in a dictionary. For this question, in the output: 1) The set of primes should be sorted. 2) No need to sort the dictionary of non -prime numbers 3) For the dictionary of non -primes, each non -prime number is a key and the divisor that is displayed as the value of each key, is the largest divisor not equal to the main number (key) itself. Therefore, the output of the code would be like below: --------------------------------------- -------------------------------------------------- Prime set is: {2, 3, 5, 7, 11, and 13 } Dictionary of none prime numbers and a divisor: {12: [6], 14: [7], 10: [5], 50:
[25], 123: [41], 18: [9], 124: [62], 9: [3], 145: [29], 632: [316], 32: [16], 253: [23], 819: [273]} Programmed by Stew Dent. Date: Tue Nov 15 22 :01 :48 202 2 End of processing .
