在经典的汉诺塔问题中,有 3 个塔和 N 个可用来堆砌成塔的不同大小的盘子。要求盘子必须按照从小到大的顺序从上往下堆 (如,任意一个盘子,其必须堆在比它大的盘子上面)。同时,你必须满足以下限制条件:
(1) 每次只能移动一个盘子。
(2) 每个盘子从堆的顶部被移动后,只能置放于下一个堆中。
(3) 每个盘子只能放在比它大的盘子上面。
请写一段程序,实现将第一个堆的盘子移动到最后一个堆中。
递归方式实现:
public static void move(int n,char from,char help,char to){
if(n==0){
return;
}
move(n-1, from, to, help);
System.out.println("move from "+from+" to "+to);
move(n-1, help, from, to);
}
用栈方式实现:
public class Tower {
private Stack<Integer> disks;
// create three towers (i from 0 to 2)
public Tower(int i) {
disks = new Stack<Integer>();
}
// Add a disk into this tower
public void add(int d) {
if (!disks.isEmpty() && disks.peek() <= d) {
System.out.println("Error placing disk " + d);
} else {
disks.push(d);
}
}
// @param t a tower
// Move the top disk of this tower to the top of t.
public void moveTopTo(Tower t) {
// Write your code here
t.add(disks.pop());
}
// @param n an integer
// @param destination a tower
// @param buffer a tower
// Move n Disks from this tower to destination by buffer tower
public void moveDisks(int n, Tower destination, Tower buffer) {
// Write your code here
if(n==0)return;
moveDisks(n-1,buffer,destination);
moveTopTo(destination);
buffer.moveDisks(n-1, destination, this);
}
public Stack<Integer> getDisks() {
return disks;
}
}
/**
* Your Tower object will be instantiated and called as such:
* Tower[] towers = new Tower[3];
* for (int i = 0; i < 3; i++) towers[i] = new Tower(i);
* for (int i = n - 1; i >= 0; i--) towers[0].add(i);
* towers[0].moveDisks(n, towers[2], towers[1]);
* print towers[0], towers[1], towers[2]
*/