NC67. 汉诺塔问题
描述
我们有由底至上为从大到小放置的 n 个圆盘,和三个柱子(分别为左/中/右即left/mid/right),开始时所有圆盘都放在左边的柱子上,按照汉诺塔游戏的要求我们要把所有的圆盘都移到右边的柱子上,要求一次只能移动一个圆盘,而且大的圆盘不可以放到小的上面。示例1
输入:
2
输出:
["move from left to mid","move from left to right","move from mid to right"]
C++ 解法, 执行用时: 2ms, 内存消耗: 464KB, 提交时间: 2021-05-22
class Solution { public: vector<string> getSolution(int n) { // write code here helper(n, "left", "mid", "right"); return ans; } int helper(int n,string left, string mid, string right){ if(n==0) return 0; if(n==1){ ans.push_back("move from "+left+" to "+right); return 0; } helper(n-1, left, right, mid); ans.push_back("move from "+left+" to "+right); helper(n-1, mid, left, right); return 0; } private: vector<string> ans; };
C++ 解法, 执行用时: 2ms, 内存消耗: 476KB, 提交时间: 2021-03-15
class Solution { public: vector<string> getSolution(int n) { // write code here vector<int> A; vector<int> B; vector<int> C; for(int i = 0; i < n; i++) { A.push_back(i); } string left = "left"; string mid = "mid"; string right = "right"; hanoi(n,A,B,C,left,mid,right); return res; } private: vector<string> res; void hanoi(int n,vector<int>& A,vector<int>& B,vector<int>& C,string& left,string& mid,string& right) { if(n == 1) { C.push_back(A.back()); A.pop_back(); string temp = "move from " + left + " to " + right; res.push_back(temp); return ; } hanoi(n-1,A,C,B,left,right,mid); C.push_back(A.back()); A.pop_back(); string temp = "move from " + left + " to " + right; res.push_back(temp); hanoi(n-1,B,A,C,mid,left,right); } };
C++ 解法, 执行用时: 2ms, 内存消耗: 476KB, 提交时间: 2021-02-23
class Solution { public: vector<string> getSolution(int n) { // write code here //三个柱子 A B C vector<string> ans; hanota(ans, n, "left", "mid", "right"); return ans; } void hanota(vector<string> &ans, int n, string from, string mid, string to) { if (n == 1) { ans.push_back("move from " + from + " to " + to); //最后剩一个时,直接放到目的地 return; } hanota(ans, n - 1, from, to, mid); //将A上面的n - 1个通过C移动到 B hanota(ans, 1, from, mid, to); //将A上最后一个移动到C hanota(ans, n - 1, mid, from, to); //将B上面的n - 1个通过A移动到C } };
C++ 解法, 执行用时: 2ms, 内存消耗: 476KB, 提交时间: 2021-02-20
class Solution { public: vector<string> getSolution(int n) { // write code here vector<string> res; move(n,"left","mid","right", res); return res; } void move(int n, string left, string mid, string right, vector<string>& res){ string s; if(n==1){ s = "move from "+left+" to "+right; res.push_back(s); return; } move(n-1,left, right, mid, res); move(1,left,mid, right, res); move(n-1,mid,left,right, res); } };
C++ 解法, 执行用时: 2ms, 内存消耗: 480KB, 提交时间: 2021-05-29
class Solution { public: vector<string> result; vector<string> getSolution(int n) { // 第一步:把n-1个盘子从left 借助 right,移动到mid柱子上 // 第二步:把剩下最大的那一个盘子从left移动到 right柱子上 // 第三步:把n-1个盘子从mid 借助 left,移动到right柱子上 Hanoi(n, "left", "mid", "right"); return result; } //把n个盘子从left 借助 mid,移动到right柱子上 void Hanoi(int n,string left,string mid,string right){ if(n==0) return ; //把n-1个盘子从left 借助 right,移动到mid柱子上 Hanoi(n-1, left, right, mid); //把剩下最大的那一个盘子从left移动到 right柱子上 string t = "move from " + left + " to " + right; result.push_back(t); //把n-1个盘子从mid 借助 left,移动到right柱子上 Hanoi(n-1, mid, left, right); } };