67 lines
1.5 KiB
C++
67 lines
1.5 KiB
C++
|
/**
|
||
|
|
* File: hanota.cpp
|
||
|
|
* Created Time: 2023-07-17
|
||
|
|
* Author: krahets (krahets@163.com)
|
||
|
|
*/
|
||
|
|
|
||
|
|
#include "../utils/common.hpp"
|
||
|
|
|
||
|
|
/* 移动一个圆盘 */
|
||
|
|
void move(vector<int> &src, vector<int> &tar) {
|
||
|
|
// 从 src 顶部拿出一个圆盘
|
||
|
|
int pan = src.back();
|
||
|
|
src.pop_back();
|
||
|
|
// 将圆盘放入 tar 顶部
|
||
|
|
tar.push_back(pan);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* 求解汉诺塔问题 f(i) */
|
||
|
|
void dfs(int i, vector<int> &src, vector<int> &buf, vector<int> &tar) {
|
||
|
|
// 若 src 只剩下一个圆盘，则直接将其移到 tar
|
||
|
|
if (i == 1) {
|
||
|
|
move(src, tar);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
// 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf
|
||
|
|
dfs(i - 1, src, tar, buf);
|
||
|
|
// 子问题 f(1) ：将 src 剩余一个圆盘移到 tar
|
||
|
|
move(src, tar);
|
||
|
|
// 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar
|
||
|
|
dfs(i - 1, buf, src, tar);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* 求解汉诺塔问题 */
|
||
|
|
void solveHanota(vector<int> &A, vector<int> &B, vector<int> &C) {
|
||
|
|
int n = A.size();
|
||
|
|
// 将 A 顶部 n 个圆盘借助 B 移到 C
|
||
|
|
dfs(n, A, B, C);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Driver Code */
|
||
|
|
int main() {
|
||
|
|
// 列表尾部是柱子顶部
|
||
|
|
vector<int> A = {5, 4, 3, 2, 1};
|
||
|
|
vector<int> B = {};
|
||
|
|
vector<int> C = {};
|
||
|
|
|
||
|
|
cout << "初始状态下：\n";
|
||
|
|
cout << "A =";
|
||
|
|
printVector(A);
|
||
|
|
cout << "B =";
|
||
|
|
printVector(B);
|
||
|
|
cout << "C =";
|
||
|
|
printVector(C);
|
||
|
|
|
||
|
|
solveHanota(A, B, C);
|
||
|
|
|
||
|
|
cout << "圆盘移动完成后：\n";
|
||
|
|
cout << "A =";
|
||
|
|
printVector(A);
|
||
|
|
cout << "B =";
|
||
|
|
printVector(B);
|
||
|
|
cout << "C =";
|
||
|
|
printVector(C);
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|