Cracking the Coding Interview - Fooo

Solutions to Chapter 3 | Stacks and Queues
3 4 In the classic problem of the Towers of Hanoi, you have 3 rods and N disks of different
sizes which can slide onto any tower The puzzle starts with disks sorted in ascending
order of size from top to bottom (e g , each disk sits on top of an even larger one) You
have the following constraints:
SOLUTION
(A) Only one disk can be moved at a time
(B) A disk is slid off the top of one rod onto the next rod
(C) A disk can only be placed on top of a larger disk
Write a program to move the disks from the first rod to the last using Stacks
CareerCup com
pg 52
We need to move N disks from Rod 1 to Rod 3, but let’s start from the beginning Moving the
top disk is easy - we just move it to Disk 3
Can we move the top two disks? Yes:
1 Move Disk 1 from Rod 1 to Rod 2
2 Move Disk 2 from Rod 1 to Rod 3
3 Move Disk 1 from Rod 2 to Rod 3
Can we move the top three disks?
1 We know we can move the top two disks around from one Rod to another (as shown
earlier), so let’s assume we have moved Disk 1 and 2 to Rod 2
2 Move Disk 3 to Rod 3
3 Again we know we can move the top two disks around, so let’s move them from Rod 2
to Rod 3
This approach leads to a natural recursive algorithm:
1 public static void main(String[] args)
2 int n = 5;
3 Tower[] towers = new Tower[n];
4 for (int i = 0; i < 3; i++) towers[i] = new Tower(i);
5 for (int i = n - 1; i >= 0; i--) towers[0].add(i);
6 towers[0].moveDisks(n, towers[2], towers[1]);
7 }
8
9 public class Tower {
10 private Stack disks;
11 private int index;
12 public Tower(int i) {
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