Select the correct recurrence relation for Tower of Hanoi?
Question
Select the correct recurrence relation for Tower of Hanoi?
Solution 1
The correct recurrence relation for the Tower of Hanoi problem is T(n) = 2T(n-1) + 1.
Here's a step-by-step explanation:
-
The problem of Tower of Hanoi is a classic example of recursion. The problem can be solved by breaking it down into smaller sub-problems.
-
If we have n disks, we first move the top n-1 disks to an auxiliary peg, which takes T(n-1) moves.
-
Then, we move the largest disk to the destination peg, which takes 1 move.
-
Finally, we move the n-1 disks from the auxiliary peg to the destination peg, which again takes T(n-1) moves.
-
Therefore, the total number of moves required is T(n) = 2T(n-1) + 1.
Solution 2
The correct recurrence relation for the Tower of Hanoi problem is T(n) = 2T(n-1) + 1.
Here's a step-by-step explanation:
-
The problem of Tower of Hanoi is a classic example of recursion. The problem can be solved by breaking it down into smaller sub-problems, which are essentially the same problem but with fewer disks.
-
The recurrence relation for the Tower of Hanoi problem can be derived from the steps needed to solve the problem.
-
To move n disks from one peg to another using a third peg, we first move n-1 disks to the third peg, then move the nth disk to the second peg, and finally move the n-1 disks from the third peg to the second peg.
-
Each of these steps is a recursive call, and moving the nth disk takes one step, hence the recurrence relation: T(n) = 2T(n-1) + 1.
-
This recurrence relation correctly represents the number of moves required to solve the Tower of Hanoi problem.
Similar Questions
Select the correct recurrence relation for Tower of Hanoi?ans.T(n)= 2T(n-1)+1T(n)= 2T(n)+1T(n)= 2T(n-1)+2T(n)= 2T(n-2)+2 Previous Marked for Review Next
HOW many numbers of moves required to solve the tower of hanoi problem with 4 disks a)12b)11c)16d)15
The tower of Hanoi is a famous puzzle where we have three rods and N disks. The objective of the puzzle is to move the entire stack to another rod. You are given the number of discs N. Initially, these discs are in the rod 1. You need to write a java program to print all the steps of discs movement so that all the discs reach the 3rd rod. Also, you need to find the total moves and present the output as follows. Let the solution for the problem be a recursive solution.Note: The discs are arranged such that the top disc is numbered 1 and the bottom-most disc is numbered N. Also, all the discs have different sizes and a bigger disc cannot be put on the top of a smaller disc. Input format :The line of input indicates the number of disks.Output format :Refer to the sample output for the output format.Sample test cases :Input 1 :3Output 1 :Move disk 1 from rod A to rod CMove disk 2 from rod A to rod BMove disk 1 from rod C to rod BMove disk 3 from rod A to rod CMove disk 1 from rod B to rod AMove disk 2 from rod B to rod CMove disk 1 from rod A to rod CTotal steps: 7
Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. The objective of the puzzle is to move all disks from source rod to destination rod using third rod (say auxiliary). The rules are :1) Only one disk can be moved at a time.2) A disk can be moved only if it is on the top of a rod.3) No disk can be placed on the top of a smaller disk.Print the steps required to move n disks from source rod to destination rod.Source Rod is named as 'a', auxiliary rod as 'b' and destination rod as 'c'.
The Tower of Hanoi (also called the Tower of Brahma or Lucas') is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:1. Only one disk can be moved at a time.2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e. a disk can only be moved if it is the uppermost disk on a stack.3. No disk may be placed on top of a smaller disk.Your task is that given N disks, print the minimum number of moves required in order to solve the problem, followed by the actual moves.Input FormatThe first line of input contains T - number of test cases. Its followed by T lines, each line containing a single number denoting the number of disks.Output FormatFor each test case, print the minimum number of moves required in order to solve the problem, followed by the actual moves, separated by newline. Refer sample output for more details.Assumptions1. The rods are named A, B and C.2. All the disks are initially placed on rod A.3. You have to move all the disks from rod A to rod C.Constraints1 <= T <= 101 <= N <= 15ExampleInput213Output1Move 1 from A to C7Move 1 from A to CMove 2 from A to BMove 1 from C to BMove 3 from A to CMove 1 from B to AMove 2 from B to CMove 1 from A to C
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.