#HANOI TOWERS PUZZLE SERIES#

(1<=T<=50) Each test case contains a single integer N(1<=N<=50), indicating the number of pegs available.įor each test case in the input print a line containing an integer indicating the maximal number of balls that can be placed. The first line of the input contains a single integer T, indicating the number of test cases.

You may take a look at the picture above, since it shows us a best result for 4 pegs. Help the player to place as many balls as possible. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack. Three simple rules are followed: Only one disk can be moved at a time. He should first try ball 1, then ball 2, then ball 3. Well, this is a fun puzzle game where the objective is to move an entire stack of disks from the source position to another position. The player should place one ball on the top of a peg at a time. If the sum of the numbers on two balls is NOT a square number, they will push each other with a great force when they're too closed, so they can NEVER be put together touching each other. The balls look ordinary, but they are actually magic. The object of the Tower of Hanoi puzzle is to move all the disks from the left rod to the right rod. The game consists of N pegs and a LOT of balls. But on the other hand, they didn't not stopped thinking about similar puzzles with the Hanoi Tower. Hence, the Tower of Hanoi puzzle with n disks can be solved in minimum 2 n−1 steps.People stopped moving discs from peg to peg after they know the number of steps needed to complete the entire task.

#HANOI TOWERS PUZZLE SERIES#

+ 2 n-1 which is a GP series having common ratio r=2 and sum = 2 n - 1. Minimum steps required to move n disks from source to destįrom the above table, it is clear that for n disks, the minimum number of steps required are 1 + 2 1 + 2 2 + 2 3 +. The minimum number of steps required to move n disks from source to dest is quite intuitive from the time complexity analysis and also from the raw examples as shown in the table, Hence, the time complexity of the recursive solution of Tower of Hanoi is O(2n) which is exponential. $$TowerofHanoi(n, source, dest, aux) = ext-1$ Hence, the recursive solution for Tower of Hanoi having n disks can be written as follows, (again move all (n-1) disks from aux to dest. And finally, move disk 1 and disk 2 from aux to dest tower i.e.Then, move the 3 rd disk from source to dest tower i.e.First, move disk 1 and disk 2 from source to aux tower i.e.We can break down the above steps for n=3 into three major steps as follows, And at last, move disk 1 to dest tower on top of 2.Then move disk 2 to dest tower on top of disk 3.

Again Move disk 1 from aux to source tower.

Then, move disk 3 from source to dest tower.

Now move disk 1 from dest to aux tower on top of disk 2.

First, move disk 1 from source to dest tower.

To solve this problem, we need to just move that disk to dest tower in one step. Let’s start the problem with n=1 disk at source tower. if disk 1 is on a tower, then all the disks below it should be less than 3.

No large disk should be placed over a small disk.

You can move only one disk at a time from the top of any tower.

The task is to move all the disks from one tower, say source tower, to another tower, say dest tower, while following the below rules, Here’s what the tower of Hanoi looks for n=3, nth disk at the bottom and 1st disk at the top. These disks are stacked over one other on one of the towers in descending order of their size from bottom i.e. Tower of Hanoi is a mathematical puzzle which consists of three towers(or pegs) and n disks of different sizes, numbered from 1, the smallest disk, to n, the largest disk.

Hanoi towers puzzle