![]() ![]() A trivial solution to Double Decker is to simply treat it as a standard instance of the Tower of Hanoi with 2n disks and, thus, will need the usual 2 2n − 1 = 4n − 1 move. Public class Solution VariationsĭOUBLE DECKER In this variation, called Double Decker, we duplicate every disk to create a stack of 2n disks with two of each size as shown in Figure.įor the convenience of notation, we will consider (only for this variant) that a stack of height n has 2n disks. move D disk to A or vice versa depending upon bigger of the two (i%3=0) Repeat above steps till loop is completeīase Case: if(n=1) move S disk to D and exit 1. move S disk to A or vice versa depending upon bigger of the two (i%3=2) 3. ![]() move S disk to D or vice versa depending upon bigger of the two (i%3=1) 2. ![]() If disk are odd or even (n%2 = 0) temp = D D = A A = temp //Basically interchanging Destination and Auxilaryįor (2 PW n)-1 times follow below these three steps 1. The Wikipedia page on Tower of Hanoi has a section on a binary solution where the steps for an N-disk Tower of Hanoi are encoded in the binary representation of the numbers 0 to 2 N. move D disk to A or vice versa depending upon bigger of the two (i%3=0) Repeat above steps till loop is completeĭry Run when disks are odd or even in number It can be programmed without recursion and without stacks (or simulated stacks). move A disk to D or vice versa depending upon bigger of the two (i%3=0) Repeat above steps till loop is complete if odd for (2 PW n)-1 times follow below these three steps 1. We discussed problem of Tower of Hanoi earlier and written a recursive function to solve the problem, Recursive functions take lot of extra memory (New. move S disk to D or vice versa depending upon bigger of the two (i%3=2) 3. move S disk to A or vice versa depending upon bigger of the two (i%3=1) 2. The Tower of Hanoi (also called The problem of Benares Temple 1 or Tower of Brahma or Lucas' Tower 2 and sometimes pluralized as Towers, or simply pyramid puzzle 3) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. If disks are odd or even if even for (2 PW n)-1 times follow below these three steps 1. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2 n − 1, where n is the number of disks. With 3 disks, the puzzle can be solved in 7 moves. No larger disk may be placed on top of a smaller disk.Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: 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. ![]()
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