关于汉诺塔的递归,记住一个结论是,转移n个盘子至少需要2^n-1步 #include<iostream> #include<cstdio> #include<cmath> #include<cstring> #include<algorithm> #include<string> using namespace std; int two[100005],pos[100005]; int main() { int n,nn[5],i,j…

Description You all must know the puzzle named "The Towers of Hanoi". The puzzle has three pegs and N discs of different radii, initially all disks are located on the first peg, ordered by their radii - the largest at the bottom, the smallest at…

3.4 In the classic problem of the Towers of Hanoi, you have 3 towers and N disks of different sizes which can slide onto any tower. The puzzle starts with disks sorted in ascending order of size from top to bottom (i.e., each disk sits on top of an e…

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…

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…

ural 2029 Towers of Hanoi Strike Back 链接:http://acm.timus.ru/problem.aspx?space=1&num=2029 题意:汉诺塔问题,给定一串只有(A, B, C)的字符串(A代表在第一根柱子,B代表在第二根柱子,C代表在第三根柱子),从前往后代表盘子的大小,第 i 个字母代表di i 个盘子在某个柱子上.问移动给定字母状态的盘子最少需要多少步. 思路:首先,从后往前看(最大的盘子),如果不在当前柱子上,那么移动到目标柱子需要 2…

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…

Towers of Hanoi Time Limit: 3000MS   Memory Limit: 16000K Total Submissions: 2213   Accepted: 986 Case Time Limit: 1000MS Description Surely you have already come across the Towers of Hanoi problem: Wooden disks of different sizes are stacked on thre…

The Towers of Hanoi Revisited Time Limit: 5 Seconds Memory Limit: 32768 KB Special Judge You all must know the puzzle named ��The Towers of Hanoi��. The puzzle has three pegs and N discs of different radii, initially all disks are located on the firs…

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…

Problem The Tower of Hanoi puzzle was invented by French mathematician Édouard Lucas in the second half of the 19th century. Here is its formulation. There are three rods, denoted by the letters A, B, and C, and n disks of different integer sizes fro…

在这里我们将构造一个基于HT for Web的HTML5+JavaScript来实现汉诺塔游戏. 汉诺塔的游戏规则及递归算法分析请参考http://en.wikipedia.org/wiki/Tower_of_Hanoi. 知道了汉诺塔的规则和算法,现在就开始创建元素.用HT for Web(http://www.hightopo.com)现有的3D模板创建底盘和3根柱子不是问题,问题是要创建若干个中空的圆盘.一开始的想法是:创建一个圆柱体,将圆柱体的上下两端隐藏,设置柱面的宽度来实现圆盘的效果…

Your mission is to move the stack from the left peg to the right peg. The rules are well known: Only one disk may be moved at a time. Each move consists of taking the upper disk from one of the pegs and sliding it onto another rod, on top of the othe…

题意:给定N(1<= N <=64)个盘子和M(4<= M <= 65)根柱子,问把N个盘子从1号柱子移动到M号柱子所需要的最少步数,并且输出移动过程. 分析:设f[i][j]表示将i个盘通过j个柱子从第一根柱子移动到最后一根柱子所需要的最少次数,f[i][j]的得到的最优移动方案是先将最小的path[i][j]个盘移动到某一根柱子上,然后通过一个dfs输出移动次序. #include <cstdlib> #include <cstring> #includ…

题目链接:http://sfxb.openjudge.cn/dongtaiguihua/E/ 题目描述:4个柱子的汉诺塔,求盘子个数n从1到12时,从A移到D所需的最大次数.限制条件和三个柱子的汉诺塔问题相同. 解题思路:采用动态规划算法的思路为先从将k个盘子使用4个柱子的方法从A移到B,然后将A上剩下的n-k个盘子使用3个柱子的方法移到D上,然后再使用4个柱子的方法将B上的k个盘子移到D上.可以明白这道题会产生很多重复子问题.所以先计算出使用3个柱子的方法从A移到B的次数用数组f3保存.然后计…

转载请注明出处,谢谢http://blog.csdn.net/ACM_cxlove?viewmode=contents    by---cxlove 题意 :n个圆盘,m个柱子的汉诺塔输出步骤. http://acm.sgu.ru/problem.php?contest=0&problem=202 经典的递归问题,见具体数学第一章 先DP求出最短步骤,并记录路径. 然后 递归输出. import java.util.*; import java.io.*; import java.math.*;…

题目链接 题目大意:把汉诺双塔按指定顺序排好的最少步数 我写这题写了很久...终于发现不dp不行 把一个双重塔从一根桩柱移动到另一根桩柱需要移动多少次? 最佳策略是移动一个双重 (n-1) 塔,接着移动两个最大的圆盘,然后再次移动双重 (n-1) 塔,从而 $A_n = 2 * A_{n-1} + 2,A_n = 2^{n+1} - 2 $. 这会交换两个最大的圆盘,其余的 \(2n-2\) 个圆盘次序不变. 如果在最后的排列中要把所有同样尺寸的圆盘恢复成原来的从上到下的次序,需要移动多少次?…

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&…

题意:就是让你求出4个塔的汉诺塔的最小移动步数,(1 <= n <= 12) 那么我们知道3个塔的汉诺塔问题的解为:d[n] = 2*d[n-1] + 1 ,可以解释为把n-1个圆盘移动到一个临时柱子上,然后将1个最大圆盘移动到目标的主子,最后再将n-1个圆盘移动到目标柱子. 为什么是n-1和1的组合呢,因为当你将n-i个圆盘移动到一个临时柱子上的时候,你会发现只靠两个柱子最多能移动1个圆盘.所以这个i=1 如果推到到4个柱子的汉诺塔,f[n] = min(f[n],2*f[n-i]+d[i]…

多柱汉诺塔问题. 引用自wiki百科 多塔汉诺塔问题 在有3个柱子时,所需步数的公式较简单,但对于4个以上柱子的汉诺塔尚未得到通用公式,但有一递归公式(未得到证明,但目前为止没有找到反例): 令为在有k个柱子时,移动n个圆盘到另一柱子上需要的步数,则: 对于任何移动方法,必定会先将个圆盘移动到一个中间柱子上,再将第n到第n-m个圆盘通过剩下的k-1个柱子移到目标柱子上,最后将m个在中间柱子上的圆盘移动到目标柱子上.这样所需的操作步数为. 进行最优化,易得: . #include <bits/st…

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…

[题目链接] http://poj.org/problem?id=1958 [算法] 先考虑三个塔的情况,g[i]表示在三塔情况下的移动步数,则g[i] = g[i-1] * 2 + 1 再考虑四个塔的情况,f[i]表示在四塔情况下的移动步数,则f[i] = min{2*f[j]+g[i-j]} [代码] #include <algorithm> #include <bitset> #include <cctype> #include <cerrno> #i…

说明:河内之塔(Towers of Hanoi)是法国人M.Claus(Lucas)于1883年从泰国带至法国的,河内为越战时北越的首都,即现在的胡志明市:1883年法国数学家 Edouard Lucas曾提及这个故事,据说创世纪时Benares有一座波罗教塔,是由三支钻石棒(Pag)所支撑,开始时神在第一根棒上放置64个由上至下依由小至大排列的金盘(Disc),并命令僧侣将所有的金盘从第一根石棒移至第三根石棒,且搬运过程中遵守大盘子在小盘子之下的原则,若每日仅搬一个盘子,则当盘子全数搬运完毕之…

前言 回家休息第3天了,状态一直不是太好,主要是要补牙,检查身体,见同学见亲戚,心里又着急校招,难得能腾出时间来好好思考,这里也是看<cracking the coding interview>,看到了汉诺塔问题,这里记录一下 思路分析 汉诺塔是递归的经典题目,这里先介绍使用递归的关键: 使用递归的一个关键就是:我们先定义一个函数,不要着急去实现它,但是要明确它的功能 对于汉诺塔问题,我们定义如下函数原型: void hanoi(char src, char mid, char dst, in…

[题目描述] In the classic problem of Towers of Hanoi, you have 3 towers and N disks of different sizes which can slide onto any tower. The puzzle starts with disks sorted in ascending order of size from top to bottom (i.e., each disk sits on top of an ev…

Description In the classic problem of Towers of Hanoi, you have 3 towers and N disks of different sizes which can slide onto any tower. The puzzle starts with disks sorted in ascending order of size from top to bottom (i.e., each disk sits on top of…

In the classic problem of Towers of Hanoi, you have 3 towers and N disks of different sizes which can slide onto any tower. The puzzle starts with disks sorted in ascending order of size from top to bottom (i.e., each disk sits on top of an even larg…

Statements: This blog was written by me, but most of content  is quoted from book[Data Structure with Java Hubbard] [Description] we have seen important examples of functions that are more naturally defined and more easily understood by using recursi…

Hanoi Tower Time Limit: 2 Seconds Memory Limit: 65536 KB You all must know the puzzle named "The Towers of Hanoi". The puzzle has three pegs (peg 1, peg 2 and peg 3) and N disks of different radii. Initially all disks are located on the first pe…