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Write a program to solve the Towers of Hanoi problem. This is accomplished by trivially moving the disk without the need for a temporary holding area. The process ends when the last task involves moving n = 1 disk, i.e., the base case. c) Move the n-1 disks from peg 2 to peg 3, using peg 1 as a temporary holding area. b) Move the last disk (the largest) from peg 1 to peg 3. 5.23 | Towers of Hanoi for the case with four disks. Moving n disks can be viewed in terms of moving only n - 1 disks (and hence the recursion) as follows: a) Move n - 1 disks from peg 1 to peg 2, using peg 3 as a temporary holding area.įig. Instead, if we attack the problem with recursion in mind, it immediately becomes tractable. If we were to approach this problem with conventional methods, we'd rapidly find ourselves hopelessly knotted up in managing the disks. We wish to develop an algorithm that will print the precise sequence of disk-to-disk peg transfers. Let's assume that the priests are attempting to move the disks from peg 1 to peg 3. Supposedly the world will end when the priests complete their task, so there's little incentive for us to facilitate their ef- forts. A third peg is available for temporarily holding the disks. 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 at no time may a larger disk be placed above a smaller disk. The initial stack had 64 disks threaded onto one peg and arranged from bottom to top by decreasing size.
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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. 5.23) is one of the most famous of these. Problem Scan 5.36 (Towers of Hanoi) Every budding computer scientist must grapple with certain classic problems, and the Towers of Hanoi (see Fig. For 5% bonus, can you see a relationship between the number of disks that need to be moved and the number of moves it takes to move them? What formula would you use to calculate the number of moves necessary for “n” disks? If the priests move 1 disk per second, how many years will it take for the priests to move all 64 disks? The base case occurs when the number of disks moved = 1 and is described in the book.
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Move Count = 15 Programming Notes: 1) Make sure your recursive algorithm has a way to stop. Include a report at the end that reveals this number.įor some sample runs: Now moving 3 disks from Peg 1 to Peg 3: 1, 1 2, w Move #: Move #: Move #: Move #: Move #: # Move #: Move #: Move: Move: Move: Move: Move: Move: Move: ^ ^ ^ ^ ^ ^ ^ WWWNNW 2 5, 5, 6, 7, Move Count = 7 Now moving 4 disks from Peg 2 to Peg 1: 1, Move #: Move #: Move #: Move #: Move #: Move #: Move #: Move #: Move #: Move #: Move #: Move #: Move #: Move #: Move #: Move: Move: Move: Move: Move: Move: Move: Move: Move: Move: Move: Move: Move: Move: Move: WNNWWWNNEENWNN ~~~~~~~~~~~~~~~ WENNPPWWNWPW 10, 12, 13, 14, 15, In addition to the above, include a counter that counts the number of moves printed. As described in the book, your program should print out the exact set of instructions necessary to move the selected number of disks from the current peg to the target peg. (Your program needs to calculate this.) Test your program on several values for the number of disks to be moved, for example: 3,5,8, and 10. Your program will thereafter assume that the third peg, i.e., the one not mentioned in steps (2) and (3) above, will be used as the temporary storage peg. The peg to which we wish to move the disks, i.e., the "target" peg. The peg the disks are currently on, i.e., the "current" peg. Have your program get the following information from the user: 1) The number of disks to be moved. As the book suggests, you should use a recursive function with four input parameters. CS1325 - Introduction to Programming page: 5 Your task: Implement the Towers of Hanoi solution using the recursive method described in the book. A scan of that problem will be provided below for those who don't have the book.
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208 of the Deitel text book (8th edition). Transcribed image text: Program 2 – Towers of Hanoi A complete description of the Towers of Hanoi problem is found in problem 5.36, p.