Explanation: The rule is to not put a disk over a smaller one. Putting a smaller disk over larger one is allowed. Explanation: Time complexity of the problem can be found out by solving the recurrence relation: T(n)=2T(n-1)+c.
What is the recurrence relation for 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 time complexity for Tower of Hanoi?
It depends what you mean by “solved”. 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) .
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 .
Can Tower of Hanoi be solved using Master Theorem?
Rules of puzzle: There are three pegs and a stack of n disks on one of the pegs. In the stack each disk has smaller radius than the one below it. … In this case a = 2,b = 1,d = 0, and the theorem tells us we have 2n disk moves necessary to solve the Towers of Hanoi puzzle.
How many moves does it take to solve the Tower of Hanoi for 5 disks?
Were you able to move the two-disk stack in three moves? Three is the minimal number of moves needed to move this tower. Maybe you also found in the games three-disks can be finished in seven moves, four-disks in 15 and five-disks in 31.
What is the time complexity of Tower of Hanoi problem Mcq?
Putting a smaller disk over larger one is allowed. Explanation: Time complexity of the problem can be found out by solving the recurrence relation: T(n)=2T(n-1)+c. Result of this relation is found to be equal to 2n.
Is Tower of Hanoi NP hard?
A complete verification of the solution would require examining each move (or each state) (to ensure no illegal moves are made). That would make verification at least as hard as the solution itself. So no, Tower of Hanoi is not in NP or in P (so far). It is NP-hard.
What is the time complexity for the selection sort algorithm?
In computer science, selection sort is an in-place comparison sorting algorithm. It has an O(n2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort.
What is the time complexity of binary search algorithm?
Time and Space complexity
The time complexity of the binary search algorithm is O(log n). The best-case time complexity would be O(1) when the central index would directly match the desired value.
What is the time complexity of merge sort algorithm?
The time complexity of MergeSort is O(n*Log n) in all the 3 cases (worst, average and best) as the mergesort always divides the array into two halves and takes linear time to merge two halves.
What is the problem of Tower of Hanoi?
Initially, all the disks are placed on one rod, one over the other in ascending order of size similar to a cone-shaped tower. The objective of this problem is to move the stack of disks from the initial rod to another rod, following these rules: A disk cannot be placed on top of a smaller disk.
What is the objective of Tower of Hanoi algorithm?
Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. 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.