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Problem 1. Successor Function [30] Tower of Hanoi is a famous game. In this game, there are some disks and rods and disk can be placed on other rods based on some rules. The rule of this game can be found at (https://en.wikipedia.org/wiki/Tower of Hanoi). In this problem, we consider a modi ed version of…

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Problem 1. Successor Function [30]

Tower of Hanoi is a famous game. In this game, there are some disks and rods and disk can be placed on other rods based on some rules. The rule of this game can be found at (https://en.wikipedia.org/wiki/Tower of Hanoi).

In this problem, we consider a modi ed version of Tower of Hanoi game. It has the following rules:

In each step, only one disk can be moved.

In each step, a disk can only be moved to the adjacent rod(s). A disk can only be placed in an empty rod or on a larger rod.

There can be more than three rods in this game. In the beginning, all disk can be randomly placed on di erent rods.

Write a program Hanoi.java to print the successor states of an input state.

Input: n String str1; str2; ::: which represents n rods. Each string str represents the status of disks on this rod. We assume that the size of disk can only be 1 to 9. We use 0 to represent empy rod, and s1s2::sk represents that there are k disks in this rod and their size are s1, s2 … sk from top to bottom(si 6= sj ; 8i; j and k 9).

For example, the following status can be represented as 123 0 0

Another example as follows can be represented as 24 0 1 0

Output: Print the list of successor states reachable in one step from the given input. Each line of output represents a state, the outputs follow the same format. The successors should not include the initial state itself or duplicates.

Here are some examples of running the program from the command line. The inputs and outputs are space-separated with no comma. Please follow the same input/output format.

Example1:

$java Hanoi 123 0 0 2310

As we can only move between adjacent rods. Only the disk of size 1 can be moved from the 1st rod to the 2nd rod.

Example 2:

$java Hanoi 24 0 1 0 4210

24001

24100

The disk of size 2 and disk of size 1 can be moved to the adjacent rods. The order of outputs does not matter. The following outputs are also correct.

4210

24100

24001

Problem 2. Transforming Number[30]

In this problem, we are given two Integers X and Y. Write a program Number.java to count the least steps we need to convert X to Y use the following rules:

Increase X by 1. Decrease X by 1. Multiply X by 3.

Get the square of X.

You may assume that 0 X < 100, 0 Y < 100, and X 6= Y . During the transformation process,

all numbers can not be less than 0 or greater than 99. That is, if the transformation is X > X1 > X2 > Xk::: > Y , we have 0 Xi < 100 and i = 1; :::k.

The input and output formats are as follow:

Input: two integers X Y

Output: one integer k. Indicate that the least number of steps is k to transform X to Y following the above rules.

Example 1: $java Number 1 5

3

The least number of steps is 3. We can transform like 1 > 2 > 6 > 5, that needs three steps.

However, we cannot do it in less than 3 steps.

Example 2:

$java Number 1 19

4

We can transform the number like 1 > 2 > 6 > 18 > 19. That needs 4 steps.

The transform path may not be unique. However, we only output the least number of steps.

Hint: use the breath rst search to solve this problem.