If the legend were true, and if the priests were able to move disks at a rate of one per second, using the smallest number of moves, it would take them 2 64 − 1 seconds or roughly 585 billion years to finish, which is about 42 times the current age of the universe. According to the legend, when the last move of the puzzle is completed, the world will end. The puzzle is therefore also known as the Tower of Brahma.

Acting out the command of an ancient prophecy, Brahmin priests have been moving these disks in accordance with the immutable rules of Brahma since that time. Numerous myths regarding the ancient and mystical nature of the puzzle popped up almost immediately, including one about an Indian temple in Kashi Vishwanath containing a large room with three time-worn posts in it, surrounded by 64 golden disks. The puzzle was introduced to the West by the French mathematician Édouard Lucas in 1883. 4.4 General shortest paths and the number 466/885.2.2.1 Logical analysis of the recursive solution.2.1.1 Simpler statement of iterative solution.The minimal number of moves required to solve a Tower of Hanoi puzzle is 2 n − 1, where n is the number of disks. With 3 disks, the puzzle can be solved in 7 moves. No disk may be placed on top of a disk that is smaller than it.

Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.The objective of the puzzle is to move the entire stack to the last rod, obeying the following rules: The puzzle begins with the disks stacked on one rod in order of decreasing size, the smallest at the top, thus approximating a conical shape. The Tower of Hanoi (also called The problem of Benares Temple or Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers, or simply pyramid puzzle ) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. If you notice, the Step-1 & Step-3 are recursive calls to the same function.Tower of Hanoi interactive display at Mexico City's Universum Museum Step-3: Move n-1 discs from E to D using S The solution to this problem can be easily thought in a recursive approach. The Problem: Move n Discs from S to D using EĬan be solved in 3 steps: Step-1: Move n-1 discs from S to E using D Void towerOfHanoi(char s, char d, char e, int n) * and n is the number of discs (initially in s)

The signature of the function will be /* The three char represents the characters representing three rods Write a function that accept the names of three rods (S, D & E) and the number of discs, and print the movement of discs between the rods such that all the rods are moved from S to D. You cannot place a larger disc on the top of a smaller disc ever.įor example: If the Pegs are named as S, D & E (Source, Destination & Extra) and there are 4 discs, the initial state will be.You have to move all the discs from source rod to Destination rod, with below 2 restrictions: All discs are initially inserted into one rod in increasing order (smallest at the top and largest disc at the bottom). There are 3 pegs (Rods) and number of discs, each of different size, which can be inserted into the rods.

Programming hanoi towers