lintcode:227.用栈模拟汉诺塔问题

Posted 2020-08-17

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。

 

具体思路在本笔记后面有记录！

以下为本人C++版详细过程！包括测试过程

 

 1 class Tower {
 2 public:
 3     // create three towers (i from 0 to 2)
 4     Tower(int i) {
 5     }
 6     // Add a disk into this tower
 7     void add(int d) {
 8         if (!disks.empty() && disks.top() <= d) {
 9             printf("Error placing disk %d\\n", d);
10             std::cout << "不符合Error disk.top："<< disks.top() << std::endl;
11         } else {
12             //cout << "成功加入:disks.push: " << d << endl;
13             disks.push(d);
14         }
15     }
16 
17     // @param t a tower
18     // Move the top disk of this tower to the top of t.
19     void moveTopTo(Tower &t) {
20         // Write your code here
21 
22         //std::cout <<"待加入的distks.top:"<< disks.top() << std::endl;
23         t.add(disks.top());
24         disks.pop();    // forget to drop the top member! // 核心丢失句！说明对stack构造器不够熟悉！
25     }
26 
27     // @param n an integer
28     // @param destination a tower
29     // @param buffer a tower
30     // Move n Disks from this tower to destination by buffer tower
31     void moveDisks(int n, Tower &destination, Tower &buffer) {
32         // Write your code here
33         if (n > 0) {
34             moveDisks(n-1,buffer,destination);
35             moveTopTo(destination);
36             buffer.moveDisks(n - 1, destination, *this);
37         }
38     }
39 
40     stack<int> getDisks() {
41         return disks;
42     }
43 
44 private:
45     stack<int> disks;
46 };
47 /**
48  * Your Tower object will be instantiated and called as such:
49  * vector<Tower> towers;
50  * for (int i = 0; i < 3; i++) towers.push_back(Tower(i));
51  * for (int i = n - 1; i >= 0; i--) towers[0].add(i);
52  * towers[0].moveDisks(n, towers[2], towers[1]);
53  * print towers[0], towers[1], towers[2]
54 */

 

　　

C++完整版参考：

 1  #include <iostream>
 2  #include <stack>
 3  
 4  using namespace std;
 5  
 6  struct Problem
 7  {
 8      int n;
 9      char src, mid, dst;
10      Problem(){}
11      Problem(int n, char s, char m, char d) : n(n), src(s), mid(m), dst(d) {}
12  };
13  
14  int main()
15  {
16      int n;
17      cin >> n;
18      stack<Problem> stk;
19      Problem curPrb;
20      stk.push(Problem(n, ‘A‘, ‘B‘, ‘C‘));
21      while (!stk.empty()) {
22          curPrb = stk.top();
23          stk.pop();
24          if (curPrb.n == 1)
25              cout << curPrb.src << "->" << curPrb.dst << endl;
26          else {
27              stk.push(Problem(curPrb.n-1, curPrb.mid, curPrb.src, curPrb.dst));
28              cout << curPrb.src << "->" << curPrb.dst << endl;
29              stk.push(Problem(curPrb.n-1, curPrb.src, curPrb.dst, curPrb.mid));
30          }
31      }
32  }