题目描述 求解 \(n\) 个盘子 \(4\) 座塔的 Hanoi 问题最少需要多少步 问题分析 考虑 \(3\) 座塔的 Hanoi 问题,记 \(f[i]\) 表示最少需要多少步, 则 \(f[i] = 2 * f[i - 1] + 1\) , 即把前 \(n - 1\) 个盘子从 \(A\) 移动到 \(B\), 然后把最下面的盘子移动到 \(C\), 最终把前面的 \(n - 1\) 个盘子移到 \(C\) 考虑把4个盘子的情况转移到三个的情况,则有 \[f[i] = \min_{1 \…

Strange Towers of Hanoi Time Limit: 1000MS Memory Limit: 30000K Total Submissions: 2677 Accepted: 1741 Description Background Charlie Darkbrown sits in another one of those boring Computer Science lessons: At the moment the teacher just explains the…

题目传送门 Strange Towers of Hanoi Time Limit: 1000MS   Memory Limit: 30000K Total Submissions: 3117   Accepted: 2004 Description Background Charlie Darkbrown sits in another one of those boring Computer Science lessons: At the moment the teacher just exp…

The teacher points to the blackboard (Fig. 4) and says: "So here is the problem: There are three towers: A, B and C. There are n disks. The number n is constant while working the puzzle. All disks are different in size. The disks are initially stacke…

说是递推,其实也算是个DP吧. 就是4塔的汉诺塔问题. 考虑三塔:先从a挪n-1个到b,把最大的挪到c,然后再把n-1个从b挪到c,所以是 f[i] = 2 * f[i-1] + 1; 那么4塔类似: 先在4塔模式下挪j个到b,然后在三塔模式下挪n-j个到d,然后再在4塔模式下挪j个到d. 故状态转移方程: d[i] = min(2 * d[j] + f[n-j]) ,其中1 <= j < n 初始条件:f[n]与d[1] = 1; 然后就没有然后了. #include <cstdio&…

Strange Towers of Hanoi 大体意思是要求\(n\)盘4的的hanoi tower问题. 总所周知,\(n\)盘3塔有递推公式\(d[i]=dp[i-1]*2+1\) 令\(f[i]\)为4塔转移步骤. \(f[i]=min(f[i],f[k]*2+d[i-k])\) 即先以4塔以上面的\(k\),再以3塔移\(i-k\),最后以4塔移动回去. 可以推广到\(n\)盘\(m\)塔 2018.5.26…

Strange Towers of Hanoi Time Limit: 1000MS Memory Limit: 30000K Total Submissions: 3784 Accepted: 2376 Description Background  Charlie Darkbrown sits in another one of those boring Computer Science lessons: At the moment the teacher just explains the…

Tower of Hanoi Time Limit: 1000MS   Memory Limit: 131072K Total Submissions: 1853   Accepted: 635 Description The Tower of Hanoi is a puzzle consisting of three pegs and a number of disks of different sizes which can slide onto any peg. The puzzle st…

本文已做成视频教程投稿b站(视频版相对文本版有一些改进),点击观看视频教程 本文主要通过三个实例来帮助大家理解递归(其展示动画已上传B站): 谢尔宾斯基三角形(Sierpinski Triangle),点击观看动画 汉诺塔(Tower of Hanoi),点击观看动画 迷宫探索(Maze Exploring),点击观看动画 本文代码已上传到github:https://github.com/BigShuang/recursion-with-turtle 本文参考文献:Problem Solvin…

我对状态空间的理解:https://www.cnblogs.com/AKMer/p/9622590.html 题目传送门:http://poj.org/problem?id=1958 题目要我们求四柱汉诺塔的步数最小值,将盘子数在\(1\)到\(12\)之间的全部求出来. 状态空间即为移动盘子对应的步数. 对于三柱汉诺塔,相信大家都非常熟悉了.我们假设三柱汉诺塔上有\(n\)个盘子,\(f[n]\)表示将\(n\)个盘子移动到另一根柱子上的最小步数,那么显然: \(f[n]=f[n-1]*2+1…