题目链接. Description 三塔汉诺塔问题,给一个 \(3 \times 3\) 的矩阵 \(t\),\(t_{i, j}\) 表示从 \(i\) 塔移动一个盘子到 \(j\) 塔的花费. 初始状态 \(n\) 个盘子都在第一个盘子,要求将所有的移到第三个盘子,求最小花费. Solution 显然可以间接移动,花费有可能更优,先用 Floyd 算法算出从 \(i\) 间接 / 直接移动到 \(j\) 的最小花费,设 \(d_{i,j}\) 表示从 \(i\) 到 \(j\) 的最小花费.…

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…

非递归算法: 根据圆盘的数量确定柱子的排放顺序: 若n为偶数,按顺时针方向依次摆放 A B C: 若n为奇数,按顺时针方向依次摆放 A C B. 然后进行如下操作: (1)按顺时针方向把圆盘1从现在的柱子移动到下一根柱子,即当n为偶数时,若圆盘1在柱子A,则把它移动到B:若圆盘1在柱子B,则把它移动到C:若圆盘1在柱子C,则把它移动到A. (2)接着,把另外两根柱子上可以移动的圆盘移动到新的柱子上.即把非空柱子上的圆盘移动到空柱子上,当两根柱子都非空时,移动较小的圆盘. (3)反复进行(1)(2…

[问题描述] 有A, B, C三个塔座,A上套有n个直径不同的圆 盘,按直径从小到大叠放,形如宝塔,编号1, 2, 3 … n. 要求将n个圆盘从A移到C,叠放顺序不变,移动过程中遵循 下列原则: w每次只能移一个圆盘 w圆盘可在三个塔座上任意移动 w任何时刻,每个塔座上不能将大盘压到小盘上   [解决方法] n=1时,直接把圆盘从A移到C n>1时,先把上面n-1个圆盘从A移到B,然后将n号盘从A移到C,再将n-1个盘从B移到C.即把求解n个圆盘的Hanoi问题转化为求解n-1个圆盘的Hano…

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 \…

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…

假设柱子标为A,B.C.要由A搬至C,在仅仅有一个盘子时,就将它直接搬至C:当有两个盘子,就将B作为辅助柱.假设盘数超过2个.将第二个下面的盘子遮起来,就非常easy了.每次处理两个盘子,也就是:A->B.A->C.B->C这三个步骤,而被遮起来的部分,事实上就由方程的递归处理. 代码例如以下: #include <stdio.h> void hanoi(int n,char A,char B,char C){ if(n == 1){ printf("Move sh…

把前n个碟子从第一个塔移动到第三个塔有两种方法: 1.把前n-1个移动到第二个塔,把第n个移动到第三个塔,然后把前n-1个从第二个移动到第三个: 2.把前n-1个移动到第三个塔,把第n个移动到第二个塔,然后把前n-1个继续移动到第一个的塔,把第N个移动到第三个塔,最后把前n个移动到第三个塔就行了: 状态转移方程: a=dp[i][3-i-j][k-1]+matrix[i][j]+dp[3-i-j][j][k-1];b=dp[i][j][k-1]+matrix[i][3-i-j]+dp[j][i]…

CF392B Tower of Hanoi 题意翻译 河内塔是一个众所周知的数学难题.它由三根杆和一些可以滑动到任何杆上的不同尺寸的圆盘组成.难题从一个整齐的杆中开始,按照尺寸从小到大的顺序排列,最小的位于顶部,从而形成一个圆锥形状.难题的目标是将整个杆移动到另一个杆,遵循以下简单规则: 一次只能移动一个圆盘. 每一步都是从其中一个杆取出上面的圆盘并将它放在另一个杆的顶部,即只有当圆盘是杆中最上面的圆盘时才能移动圆盘. 没有圆盘可能放置在较小的圆盘顶部. 有了三个圆盘,这个难题可以通过七个步骤解…

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…

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…

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…

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…

Tower of Hanoi Time Limit: 1000MS   Memory Limit: 131072K Total Submissions: 1895   Accepted: 646 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…

javascript实现汉诺塔动画效果 当初以为不用html5也很简单,踩了javascript单线程的大坑后终于做出来了,没事可以研究下,对理解javascript的执行过程还是很有帮助的,代码很烂大家凑合着看. <html> <head> <meta charset="UTF-8"> <title>Tower of Hanoi 2.0.0</title> <script src="http://apps.b…

  A Different Task  The (Three peg) Tower of Hanoi problem is a popular one in computer science. Briefly the problem is to transfer all the disks from peg-A to peg-C using peg-B as intermediate one in such a way that at no stage a larger disk is abov…

A Different Task The (Three peg) Tower of Hanoi problem is a popular one in computer science. Briefly the problem is to transfer all the disks from peg-A to peg-C using peg-B as intermediate one in such a way that at no stage a larger disk is above a…

是任意形式的递归,是化解的一般式. 主题所谓的“递归调用化解为栈处理”,意思是,将递归函数调用化解为“一个由stack_push stack_pop stack_top等函数调用组成的循环式子”.这里的 stack_push, stack_pop, stack_top是指,程序员自己实现的一个ADT(Abstract Data Type)中的函数操作接口,这个ADT叫做栈.要知道,在C语言中,函数调用链本身就是栈处理的,处理C语言中函数调用链的是进程栈/线程栈,进程栈/线程栈是一个C语言程序运行…

Perhaps you all have heard the mythical story about Tower of Hanoi (The details of this story is not required to solve this problem): “There is a tower of Hanoi with 64 disks and three pegs and the preists make one move everyday and the earth will be…

 A Different Task  The (Three peg) Tower of Hanoi problem is a popular one in computer science. Briefly the problem is to transfer all the disks from peg-A to peg-C using peg-B as intermediate one in such a way that at no stage a larger disk is above…

程序背景: 汉诺塔(Tower of Hanoi)又称河内塔,问题是源于印度一个古老传说的益智玩具.大梵天创造世界的时候做了三根金刚石柱子,在一根柱子上从下往上按照大小顺序摞着64片黄金圆盘.大梵天命令婆罗门把圆盘从下面开始按大小顺序重新摆放在另一根柱子上.并且规定,在小圆盘上不能放大圆盘,在三根柱子之间一次只能移动一个圆盘. #include<iostream> using namespace std; void hanoi(int n, char A, char B, char C,int…

# -*- coding: utf-8 -*- #汉诺塔移动问题 # 定义move(n,a,b,c)函数,接受参数n,表示3个柱子A.B.C中第1个柱子A的盘子数量 # 然后打印出把所有盘子从A借助B移动到C的方法 def move(n,a,b,c): if n==1: print('move', a, '-->', c) else: move(n-1,a,c,b) move(1,a,b,c) move(n-1,b,a,c) move(5,'A','B','C') #计算移动步数 def f(n…

国际 C 语言混乱代码大赛(IOCCC, The International Obfuscated C Code Contest)是一项国际编程赛事,从 1984 年开始,每年举办一次(1997年.1999年.2002年.2003年和2006年例外).目的是写出最有创意的最让人难以理解的C语言代码. 获奖者列表 1984 anonymous    prints hello world, where read is write 1984 decot    prints garbage, weird…

20162314 2017-2018-1 <Program Design & Data Structures>Learning Summary Of The First Week Summary of teaching materials Algorithm analysis is the basic project of the computer science. Increasing function prove that the utilization of the time a…

Description Perhaps you all have heard the mythical story about Tower of Hanoi (The details of this story is not required to solve this problem): “There is a tower of Hanoi with 64 disks and three pegs and the preists make one move everyday and the e…

困扰已久,难以攻克的汉诺塔总结来啦 Part One 汉诺塔到底是什么呢? 汉诺塔(Tower of Hanoi)源于印度传说中,大梵天创造世界时造了三根金钢石柱子,其中一根柱子自底向上叠着64片黄金圆盘.大梵天命令婆罗门把圆盘从下面开始按大小顺序重新摆放在另一根柱子上.并且规定,在小圆盘上不能放大圆盘,在三根柱子之间一次只能移动一个圆盘.                        --引用维基百科 也就是说把圆盘从一个柱子,移动到另一个柱子,中途需要一个柱子来辅助完成,并且在这个过程中必须…

1.下载 https://github.com/kdlucas/byte-unixbench/archive/v5.1.3.tar.gz 2.修改Makefile 交叉编译 #CC=gccCC = arm-linux-gnueabihf-gcc 3.make 4.修改Run 将main函数中的 preChecks();注释掉,因为其中有 system("make all"); 5.将编译过的整个byte-unixbench-5.1.3拷贝到开发板上.已经手动编译过了,此时Run是在小板…

What is a search problem: A solution to a search problem is a sequence of actions (a path) from s0 to a goal state. It is optimal if it has minimum sum of step costs. Traditional Problem: Tower of Hanoi. 解释:搜索问题可以解释为从original state to target state构建的…