find the files attached
Assignment problem 1 Part 2a: Prime Number Finder (Note part 2a, 2b and 2c are the same parts of the whole problem 2 but they should be done in separate files) Write a program that prompts the user to enter in a positive number. Only accept positive numbers - if the user supplies a negative number or zero you should re-prompt them. You can assume an integer will be entered here. Next, determine if the given number is a prime number. A prime number is a number that has no positive divisors other than 1 and itself. For example, 5 is prime because the only numbers that evenly divide into 5 are 1 and 5. 6, however, is not prime because 1, 2, 3 and 6 are all divisors of 6. Here's a sample running of the program: Enter a positive number to test: 5 2 is NOT a divisor of 5 ... continuing 3 is NOT a divisor of 5 ... continuing 4 is NOT a divisor of 5 ... continuing 5 is a prime number! And here's another running: Enter a positive number to test: 9 2 is NOT a divisor of 9 ... continuing 3 is a divisor of 9 ... stopping 9 is not a prime number. Some notes on your program: • 1 is technically not a prime number. • Once you find a number that evenly divides into your test number you do not need to continue testing additional numbers - the number cannot be prime. Part 2b: Find all Prime Numbers between 1 and 1000 Next, make a copy of Part A and update it so that the program now finds all prime numbers between 1 and 1000. Here's a sample running of your program: 1 is technically not a prime number. 2 is a prime number! 3 is a prime number! 5 is a prime number! 7 is a prime number! 11 is a prime number! ... cut ... 977 is a prime number! 983 is a prime number! 991 is a prime number! 997 is a prime number! Part 2c: Custom Number Range Make a copy of Part B and update it so that the user can choose to examine a specific range of numbers for prime numbers. Here's a sample running of your program: Start number: 5 End number: -5 Start and end must be positive Start number: 5 End number: 3 End number must be greater than start number Start number: 5 End number: 23 5 7 11 13 17 19 23 Some notes on your program: • You need to ensure that the start and end numbers are both positive. You can assume an integer will be entered for both inputs. • You also need to ensure that the start number is less than the end number. Assignment problem 2 Part 3: Modern Art Monte Carlo Simulation You've decided to visit the Metropolitan Museum of Art with some friends and notice an interesting painting on the wall: One of your friends wonders out loud how probable it would to hit a colored section of the painting if they were to close their eyes and throw a dart at random at the canvas. You tell your friend that this is a very bad idea, but because you are in an Introduction to Computer Programming class you know that you can use your newly acquired Python skills to solve this problem! For this program you will be writing some code that will simulate the throwing of a random dart at this modern art painting. To do this you can repeatedly generate a random coordinate within the painting area and test to see which shape (if any) the dart falls into. Note that the playing field is 800 units wide and 500 units high, so you will be generating random coordinates within this range as part of your simulation. When you are finished you should calculate the % chance of a dart hitting a particular shape. Refer to the schematic below for the exact measurements of the painting. Hint: Start off by simulating just one dart toss and use the coordinate plane to determine if the dart has fallen into one of the colored regions. Start off with the red rectangle since it will be the simplest shape to work with -- how can you write a statement to determine if a point falls within a rectangle? From there, expand this logic and apply it to the other shapes. Hint: you may need the distance formula again to determine if a point falls within a circular region! Once you are confident that you have designed an effective algorithm you can scale up and place your code inside a loop. Here’s a a few sample runnings of the program with user input underlined: Number of throws: 10000 Total time elapsed: 0.02 seconds Red 1,292 (12.92%) Green 665 (6.65%) Blue 675 (6.75%) Grey 132 (1.32%) Yellow 970 (9.70%) Misses 6,266 (62.66%) Number of throws: -50 Invalid, try again. Number of throws: 100000 Total time elapsed: 0.21 seconds Red 13,293 (13.29%) Green 6,746 (6.75%) Blue 6,677 (6.68%) Grey 1,095 (1.09%) Yellow 9,207 (9.21%) Misses 62,982 (62.98%)) Number of throws: 5000000 Total time elapsed: 9.92 seconds Red 656,087 (13.12%) Green 336,296 (6.73%) Blue 335,014 (6.70%) Grey 56,941 (1.14%) Yellow 469,395 (9.39%) Misses 3,146,267 (62.93%) Some hints: • You can always assume the user will enter an integer when prompted, but you will need to validate it so that it falls within the desired range (1 or larger) • Start off by generating a single random point within the bounds of the painting (an x value between 0 and 800 and a y value between 0 and 500). The coordinate system shown here is one that is standard in the world of computer graphics -- notice that the origin point is at the top left side of the screen, and that the y axis only contains positive values. • You can generate a random floating point number within a given range by using the random.uniform() function. This function takes two arguments - a low boundary and a high boundary - and generates a floating point number within this range (edges inclusive) • Next, write a series of tests to see if the number you just picked falls within one of the shapes shown. If so, you should update an accumulator to go count this as a "hit" to that particular region. • The distance formula may be helpful in determining if a point falls within a circle (hint: if the distance from a point to the center of a circle is less than the radius of that circle then the point can be considered inside of that circle. • The green circle intersects with the blue circle. Their intersection forms a grey region. • Once this works for a single point you will need to design a loop to iterate a large number of times and repeat this process. We sometimes call this a 'Monte Carlo' simulation, which is designed to approximate a solution to a problem through the use of random numbers. • Because of this you will see different numbers when you run your program. The percentages that get generates should roughly match the percentages shown here. • The more "throws" you compute the closer you will get to the actual solution. • You can ask Python to generate the current time by calling the time.time() function. You will need to import the time module in order to call this function. This function returns the current time based on your computer's internal clock as a single floating point number. Every time you call this number it will get bigger, indicating the current time as measured in 'seconds' since the Unix Epoch. Hint: to compute the total execution time of your program you may need to capture the time before you begin your simulation and after your simulation finishes. • Your "execution time" value will likely be different than the ones given here in the sample output. This is due to the fact that every computer will run at a slightly different rate based on processor speed, available memory, etc. • You will need to format your output to match the sample output above (i.e. all of your values should line up) https://en.wikipedia.org/wiki/Unix_time Extra Credit: Modern Art Visualization with Turtle Graphics For this program you will be using Turtle Graphics to display a graphical representation of your modern art painting "throws". Here's a visual of what this could look like: Turtle Graphics rendering of 10,000 throws Turtle Graphics rendering of 100,000 throws Here are some hints on how to get started: • Begin by asking the user if they want to draw the result of the program. This input should be validated and should be case insensitive (i.e. "YES", "yes" and any other case variation of the word "yes" should both turn on Turtle Graphics mode. • First, set up a canvas that will be big enough to represent your throws. For example, the size of the painting board is 800px by 500px - perhaps you could set up a canvas that mirrored those proportions • Next,