Can Tower of Hanoi be solved by Master Theorem?
if n = 0, return HanoiPuzzle(n − 1) [Move n-1 disks to another peg following rules of the game.] Move one disk [Move the largest disk to the open peg (a legal move).] … 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.
Where we Cannot apply master theorem?
Recall that we cannot use the Master Theorem if f(n) (the non-recursive cost) is not polynomial. There is a limited 4-th condition of the Master Theorem that allows us to consider polylogarithmic functions. This final condition is fairly limited and we present it merely for completeness.
Can the master method be applied to the recurrence?
The master method is a formula for solving recurrence relations of the form: T(n) = aT(n/b) + f(n), where, n = size of input a = number of subproblems in the recursion n/b = size of each subproblem.
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 FN in master theorem?
In the Master Theorem, f(n) is the function which gives the non-recursive part of the recursive definition of the runtime.
What is Big O notation in algorithm?
Big-O notation is the language we use for talking about how long an algorithm takes to run (time complexity) or how much memory is used by an algorithm (space complexity). Big-O notation can express the best, worst, and average-case running time of an algorithm.
What is regularity condition in master theorem?
Imagine the recurrence aT(n/b) + f(n) in the form of a tree. Case 1 covers the case when the children nodes does more work than the parent node.
What is non polynomial difference in Master Theorem?
It is said that we can not apply Master Theorem to T(n)=aT(n/b)+f(n) if there is a non-polynomial difference between f(n) and nlogba. Polynomial difference means: f(n)/nlogb(a)=nc for any real number c. … That means there’s non-polynomial difference, right?
On which of the following recurrences The Master Theorem fails?
Master Theorem fails in the following cases: When f ( n ) is smaller than n log b a but not polynomially smaller. This is a gap between cases 1 and 2 . When f ( n ) is larger than n log b a but not polynomially larger. This is a gap between cases 2 and 3 .
What is the result of the recurrence which fall under second case of Masters theorem?
Under what case of Master’s theorem will the recurrence relation of merge sort fall? Explanation: The recurrence relation of merge sort is given by T(n) = 2T(n/2) + O(n). So we can observe that c = Logba so it will fall under case 2 of master’s theorem.