Kindly help me with the following tasks. You may want to start with explanations for me and then pseudo-codes, I should be able to take it from there. They are exercises from deitel how to program for Python. I have done a lot of thinking and its almost discouraging me. Please help. Thanks.
4.4 An integer greater than 1 is said to be prime if it is divisible by only 1 and itself. For example, 2, 3, 5 and 7 are prime numbers, but 4, 6, 8 and 9 are not. a) Write a function that determines whether a number is prime. b) Use this function in a program that determines and prints all the prime numbers between 2 and 1,000. c) Initially, you might think that n/2 is the upper limit for which you must test to see whether a number is prime, but you need go only as high as the square root of n. Rewrite the program and run it both ways to show that you get the same result. 4.5 An integer number is said to be a perfect number if the sum of its factors, including 1 (but not the number itself), is equal to the number. For example, 6 is a perfect number, because 6 = 1 + 2 + 3. Write a function perfect that determines whether parameter number is a perfect number. Use this function in a program that determines and prints all the perfect numbers between 1 and 1000. Print the factors of each perfect number to confirm that the number is indeed perfect. Challenge the power of your computer by testing numbers much larger than 1000. 4.7 Write a program that plays the game of “guess the number” as follows: Your program chooses the number to be guessed by selecting an integer at random in the range 1 to 1000. The program then displays I have a number between 1 and 1000. Can you guess my number? Please type your first guess. The player then types a first guess. The program responds with one of the following: 1. Excellent! You guessed the number! Would you like to play again (y or n)? 2. Too low. Try again. 3. Too high. Try again. If the player's guess is incorrect, your program should loop until the player finally gets the number right. Your program should keep telling the player Too high or Too low to help the player “zero in” on the correct answer. After a game ends, the program should prompt the user to enter "y" to play again or "n" to exit the game. 4.8 (Towers of Hanoi) Every budding computer scientist must grapple with certain classic problems. The Towers of Hanoi (see Fig. 4.23) is one of the most famous of these. Legend has it that, in a temple in the Far East, priests are attempting to move a stack of disks from one peg to another. The initial stack had 64 disks threaded onto one peg and arranged from bottom to top by decreasing size. The priests are attempting to move the stack from this peg to a second peg, under the constraints that exactly one disk is moved at a time and that at no time may a larger disk be placed above a smaller disk. A third peg is available for holding disks temporarily. Supposedly, the world will end when the priests complete their task, so there is little incentive for us to facilitate their efforts. Let us assume that the priests are attempting to move the disks from peg 1 to peg 3. We wish to develop an algorithm that will print the precise sequence of peg-to-peg disk transfers. If we were to approach this problem with conventional methods, we would rapidly find ourselves hopelessly knotted up in managing the disks. Instead, if we attack the problem with recursion in mind, it immediately becomes tractable. Moving n disks can be viewed in terms of moving only n - 1 disks (hence, the recursion), as follows: a) Move n - 1 disks from peg 1 to peg 2, using peg 3 as a temporary holding area. b) Move the last disk (the largest) from peg 1 to peg 3. c) Move the n - 1 disks from peg 2 to peg 3, using peg 1 as a temporary holding area. The process ends when the last task involves moving n = 1 disk, i.e., the base case. This is accomplished trivially by moving the disk without the need for a temporary holding area. Write a program to solve the Towers of Hanoi problem. Use a recursive function with four parameters: a) The number of disks to be moved b) The peg on which these disks are initially threaded c) The peg to which this stack of disks is to be moved d) The peg to be used as a temporary holding area Your program should print the precise instructions it will take to move the disks from the starting peg to the destination peg. For example, to move a stack of three disks from peg 1 to peg 3, your program should print the following series of moves: 1 → 3 (This means move one disk from peg 1 to peg 3.) 1 → 2 3 → 2 1 → 3 2 → 1 2→ 3 1→ 3 -- Sent from my mobile device Elegbede Muhammed Oladipupo OCA +2348077682428 +2347042171716 www.dudupay.com Mobile Banking Solutions | Transaction Processing | Enterprise Application Development _______________________________________________ Tutor maillist - Tutor@python.org To unsubscribe or change subscription options: http://mail.python.org/mailman/listinfo/tutor
