# What is the recursive formula for the Tower of Hanoi?

## What is the recursive formula for the Tower of Hanoi?

First they move the ( n -1)-disk tower to the spare peg; this takes M ( n -1) moves. Then the monks move the n th disk, taking 1 move. And finally they move the ( n -1)-disk tower again, this time on top of the n th disk, taking M ( n -1) moves. This gives us our recurrence relation, M ( n ) = 2 M ( n -1) + 1.

### What is the pattern for the Tower of Hanoi?

In Cyclic Hanoi, we are given three pegs (A, B, C), which are arranged as a circle with the clockwise and the counterclockwise directions being defined as A – B – C – A and A – C – B – A respectively. The moving direction of the disk must be clockwise. It suffices to represent the sequence of disks to be moved.

Why is the Tower of Hanoi considered recursive?

Using recursion often involves a key insight that makes everything simpler. In our Towers of Hanoi solution, we recurse on the largest disk to be moved. That is, we will write a recursive function that takes as a parameter the disk that is the largest disk in the tower we want to move.

Which of the following is the correct recurrence for recursive Tower of Hanoi puzzle?

Explanation: As there are 2 recursive calls to n-1 disks and one constant time operation so the recurrence relation will be given by T(n) = 2T(n-1)+c. Explanation: Minimum number of moves can be calculated by solving the recurrence relation – T(n)=2T(n-1)+c.

## What is the time complexity of Tower of Hanoi recursive algorithm?

Most of the recursive programs takes exponential time that is why it is very hard to write them iteratively . T(1) = 2k T(2) = 3k T(3) = 4k So the space complexity is O(n). Here time complexity is exponential but space complexity is linear .

### What is the efficiency of Tower of Hanoi algorithm?

The Tower of Hanoi problem with 3 pegs and n disks takes 2**n – 1 moves to solve, so if you want to enumerate the moves, you obviously can’t do better than O(2**n) since enumerating k things is O(k) .

Why is it called Towers of Hanoi?

The tower of Hanoi (also called the tower of Brahma or the Lucas tower) was invented by a French mathematician Édouard Lucas in the 19th century. It is associated with a legend of a Hindu temple where the puzzle was supposedly used to increase the mental discipline of young priests.

How is the recursion algorithm for Tower of Hanoi explained?

Looks simple, Right! Move Disk 1 from peg A to peg C. Then move disk 2 from peg A to peg B and, finally, move disk 1 from peg C to peg B. This solution takes 3 steps. You can easily move this stack from peg B to any other peg using these 3 steps.

## How do you move disks in Tower of Hanoi?

Move Disk 1 from peg A to peg C. Then move disk 2 from peg A to peg B and, finally, move disk 1 from peg C to peg B. This solution takes 3 steps. You can easily move this stack from peg B to any other peg using these 3 steps. But what if we have 3 disks – 1,2, and 3 stacked in peg A.

### When was the Tower of Hanoi game invented?

Tower of Hanoi game is a puzzle invented by French mathematician Édouard Lucas in 1883. There is a story about an ancient temple in India (Some say it’s in Vietnam – hence the name Hanoi) has a large room with three towers surrounded by 64 golden disks.

When do you use recursion to solve a problem?

Recursion is useful in solving problems which can be broken down into smaller problems of the same kind. But when it comes to solving problems using Recursion there are several things to be taken care of. Let’s take a simple example and try to understand those.