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。
思路：
我们假设函数hanoi(n, a, b, c)用于将n个圆盘由a移动到c，b作为辅助柱子。

if n!=0 then            ;预定值
  hanoi(n-1, a, c, b)    ;将n-1个盘子由a移动到b，以c为辅助柱子（注意参数顺序）
  move(n,a,c)      ;将a上的最后一个盘子移动到c
  hanoi(n-1, b, a, c)    ;将n-1个盘子由b移动到c，以a为辅助柱子
endif                   ;完成

.hpp

#ifndef C227_H
#define C227_H
#include<iostream>
#include<stack>
using namespace std;
class Tower {
private:
    stack<int> disks;
public:
    /* * @param i: An integer from 0 to 2 */
    Tower(int i) {
        // create three towers
    }

    /* * @param d: An integer * @return: nothing */
    void add(int d) {
        // Add a disk into this tower
        if (!disks.empty() && disks.top() <= d) {
            printf("Error placing disk %d", d);
        }
        else {
            disks.push(d);
        }
    }

    /* * @param t: a tower * @return: nothing */
    void moveTopTo(Tower &t) {
        // Move the top disk of this tower to the top of t.
        t.add(disks.top());
        disks.pop();
    }

    /* * @param n: An integer * @param destination: a tower * @param buffer: a tower * @return: nothing */
    void moveDisks(int n, Tower &destination, Tower &buffer) {
        // Move n Disks from this tower to destination by buffer tower
        if (n <= 0)
            return;
        else if (n == 1)
            moveTopTo(destination);
        else{
            moveDisks(n - 1, buffer, destination);
            moveTopTo(destination);
            buffer.moveDisks(n - 1, destination,*this);
        }
    }

    /* * @return: Disks */
    stack<int> getDisks() {
        // write your code here
        return disks;
    }
};

#endif
/** * Your Tower object will be instantiated and called as such : *vector<Tower> towers; *for (int i = 0; i < 3; i++) towers.push_back(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] */

.cpp

#include"c227.h"
#include<vector>
void print(Tower t)
{
    stack<int> sk = t.getDisks();
    while (!sk.empty())
    {
        cout << sk.top() << " ";
        sk.pop();
    }
    cout << endl;
}
int main()
{
    int n = 5;
    vector<Tower> towers;
    for (int i = 0; i < 3; ++i)
        towers.push_back(Tower(i));
    for (int i = n-1; i >= 0; --i)
        towers[0].add(i);
    towers[0].moveDisks(n, towers[2], towers[1]);
    cout << "towers[0]: " << endl;
    print(towers[0]);
    cout << "towers[1]: " << endl;
    print(towers[1]);
    cout << "towers[2]: " << endl;
    print(towers[2]);
    return 0;
}