# Display a pole segment without a disk: 104. emptySpace = ' ' * ( TOTAL_DISKS - width ) 101. The end of the list is the top of the tower. disks cannot rest on top of a smaller disk. Move the tower of disks, one disk at a time, to another tower. print ( """The Tower of Hanoi, by Al Sweigart 17. COMPLETE_TOWER = list ( range ( TOTAL_DISKS, 0, - 1 )) 13. TOTAL_DISKS = 5 # More disks means a more difficult puzzle. This is useful for finding the disk currently at the top of the tower.ġ. Just as someList and someList allow us to access the first and second values in a list, Python lets us use negative indexes to access values from the end of the list using expressions like someList and someList, which access the last and second-to-last values in a list, respectively.
For example, would represent the following tower: append() and pop() list methods can add and remove values from the end of the list, respectively. The first integer in the list represents the bottom disk, and the last integer represents the top disk. The data structure that represents a tower is a list of integers. AB to moves a disk from tower A to tower B.) || || || || || || || ||Įnter the letters of "from" and "to" towers, or QUIT. Largerĭisks cannot rest on top of a smaller disk. When you run towerofhanoi.py, the output will look like this: The Tower of Hanoi, by Al Sweigart Can you discover it? (Hint: Try setting the TOTAL_DISKS variable to 3 or 4 to solve an easier version first.) The Program in Action Figuring out a certain pattern will help you solve this puzzle. However, only one disk can be moved at a time, and larger disks cannot be placed on top of smaller ones. The object of the game is to move one tower of disks to another pole. Depth First Search vs.The Tower of Hanoi is a stack-moving puzzle game that features three poles on which you can stack various-sized disks.Dynamic Programming Vs Greedy Algorithm.Divide and Conquer Vs Dynamic Programming.Thus, T(n) = O(2 n) Simulation of Tower of Hanoiįollowing image shows simulation of the tower of hanoi with tree disks. To shift 1 disk from source to destination peg takes only one move, so T(1) = 1. Similarly, replace n by n – 2 in Equation (1), Let us solve this recurrence using forward and backward substitution:īy putting this value back in Equation (1), And each call corresponds to one primitive operation, so recurrence for this problem can be set up as follows: Step 3: Every call makes two recursive calls with a problem size of n – 1. Step 2: Primitive operation is to move the disk from one peg to another peg Step 1:Move disk C from the src peg to dst peg There can be n number of disks on source peg. If priests transfers the disks at a rate of one disk per second, with optimum number of moves, then also it would take them 2 64 – 1 seconds, which is around 585 billion years, which is 42 times the age of the universe as of now. According to legend, the world will end when the final move of the puzzle is completed. As a result, the puzzle is also known as the Tower of Brahma. Since that time, Brahmin priests have been rotating these disks in line with the unchanging laws of Brahma, fulfilling the order of an ancient prophesy.
Almost soon, stories about the ancient and magical nature of the puzzle surfaced, including one about an Indian temple in Kashi Vishwanath having a huge chamber with three time-worn pillars in it, encircled by 64 golden disks. Édouard Lucas, a French mathematician, developed the puzzle in 1883. Final position Story, Fun, Myth, Truth – What not?