本次北美CS代写之AI入门课程代写主要是使用Java语言完成八皇后拼图Eight Queens Puzzle问题的求解，八皇后问题是将8个国际象棋皇后放置在8×8棋盘上的情况。

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If a homework has programming questions, please hand in the Java program. If a homework has written questions, please hand in a PDF file. Regardless, please zip all your files into hwX.zip where X is the homework number. Go to UW Canvas, choose your CS540 course, choose Assignment, click on Homework X: this is where you submit your zip file.

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All assignments are due at the beginning of class on the due date. One (1) day late, defined as a 24-hour period from the deadline (weekday or weekend), will result in 10% of the total points for the assignment deducted. So, for example, if a 100-point assignment is due on a Wednesday 9:30 a.m., and it is handed in between Wednesday 9:30 a.m. and Thursday 9:30 a.m., 10 points will be deducted. Two (2) days late, 25% off; three (3) days late, 50% off. No homework can be turned in more than three (3) days late. Written questions and program submission have the same deadline.

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### Collaboration Policy:

You are to complete this assignment individually. However, you are encouraged to discuss the general algorithms and ideas with classmates, TAs, and instructor in order to help you answer the questions. You are also welcome to give each other examples that are not on the assignment in order to demonstrate how to solve problems. But we require you to:

• not explicitly tell each other the answers

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In those cases where you work with one or more other people on the general discussion of the assignment and surrounding topics, we suggest that you specifically record on the assignment the names of the people you were in discussion with.

### Question 1: Eight Queens Puzzle [60 points]

This is a programming question. The solution to the programming problem should be coded in Java, and you are required to use only built-in libraries to complete this homework. Please submit a single zip file named hw4.zip, which should contain a source code file named EightQueen.java with no package statements, and make sure your program is runnable from command line on a department Linux machine. We provide a skeleton EightQueen.java code that you can optionally use, or you can write your own.

In this question you will implement heuristic search algorithms – hill climbing varieties and simulated annealing – for the eight queens puzzle.

The eight queens puzzle is the problem of placing eight chess queens on an 8 × 8 chessboard in such a way that no two queens attack each other. In other words, a solution requires that no two queens share the same row, column, or diagonal. For more background on the eight queens puzzle see https: //en.wikipedia.org/wiki/Eight_queens_puzzle.

Write a program EightQueen.java with the following command line format, where the command line input has variable length1:

$java EightQueen FLAG [seed] board

where FLAG is an integer that specifies the output of the program (see below). seed is a seed of a random number generator (only required in part c and e; discarded otherwise). board is a string of length 8 that specifies the board as an array where the index is the column and the value is the row. Each position in the string takes values in integer 0-7. To illustrate, the board below is represented as 13572064. Note that the board is a solution to the eight queens puzzle. That is, no two queens share the same row, column, or diagonal.

To solve this eight queens puzzle, we need to take steps to reduce the heuristic cost to zero. To evaluate which moves are best, we will calculate the heuristic costs of the board after one move. For simplicity, we will only move queens up or down vertically along individual columns.

When FLAG=200, perform calculation of all the heuristic costs of the board after one move, find moves (i.e. successors) with the lowest heuristic cost (the steepest moves), and print corresponding resulting boards after those moves. You will print the heuristic cost in the last line. If no move exists, you should simply produce no output at all.

Important: We ask you to implement the following order among successors. Whenever you append moves into a list, append them according to moves from small index to large index and from small value to large value. That is, the list is sorted by new queen position’s index and value in ascending order, with index having higher precedence than value. Recall that we are to represent the board as an array where the index is the column and the value is the row. This order will be used throughout the program, so that the output is well-defined. For example:

$java EightQueen 200 13572063 13572064 0

$java EightQueen 200 13572064 (note: produce no output)

$java EightQueen 200 01234567

Perform hill climbing (HC) algorithm by randomly choosing a steepest move from part b, print the corresponding board and its heuristic cost (space-separated) with a current iteration number (starting from 0 to XX) prefixed, then repeat the process for the number of iterations equal to XX. XX can be 00 to 99. For example, if FLAG=300, the cutoff is 0. In HC, you will do a goal test, but will NOT expand it. If FLAG=301, the cutoff is one. In HC, you will expand the initial state (i.e. put its moves into a stack in the order we specified in Part b). You will randomly select a move out, perform goal-check (and terminate the program if goal-check succeeds). But you will not expand any of these moves. If a solution is reached, the algorithm should stop and print the word ”Solved”.

When FLAG=3XX, command line argument seed is required. If seed = −1, you actually do not set the seed (this allows you to generate different random moves). Otherwise, you should set the seed to seed. To set the seed in Java, use the following code:

Random rng = new Random(); if (seed != -1) rng.setSeed(seed);

(Part d, 15 points)

We will look at an additional way to solve eight queens puzzle. So far, we had to go through every move and check every possible square. Now, we will perform first-choice hill climbing that, instead of trying to find the best move at each step, we will simply try to find a better move. In particular, we will choose the first move with a heuristic cost that is lower than a current heuristic cost. Again, we iterate through elements in the list from first to last in order specified in part b and c.

When FLAG=4XX, perform a first-choice hill climbing algorithm step, print the board and its heuristic cost (space-separated), then repeat the process for the number of iterations equal to XX. XX can be 00 to 99. If a solution is reached, the algorithm should stop and print the word ”Solved” in the last line. If the algorithm gets stuck on local optima, the algorithm should also terminate and print the word ”Local optimum” in the last line. A current board is at local optima if all heuristic costs of the board after one move are less than or equal to the current heuristic cost.

Perform simulated annealing algorithm2, print the board and its heuristic cost (space-separated), then repeat the process for the number of iterations equal to XX. XX can be 00 to 99. If a solution is reached, the algorithm should stop and print the word ”Solved” in the last line. For this part, we set the anneal rate and initial temperature to be 0.95 and 100, respectively.

When FLAG=5XX, command line argument seed is required and setting seed can be done like in part c. Recall that if seed = −1, you actually do not set the seed (this allows you to generate different random moves). Otherwise, you should set the seed to seed.

Important: We ask you to use only one instance of Random with the same sequence of method calls for each iteration, so that it generates and returns identical sequences of numbers, and the output is well-defined. Formally, define the sequence of method calls as (i1, i2, d1, i3, i4, d2, i5, i6, d3, …) where k is positive integers, dk is the kth nextDouble() call for the kth iteration, and ik is the kth nextInt() call. The new queen position picked at random at kth iteration is specified by i2k−1 as index and i2k as value. This should be done with:

Random rng = new Random(); if (seed != -1) rng.setSeed(seed);

…

for each iteration: int index = rng.nextInt(7); int value = rng.nextInt(7); double prob = rng.nextDouble();

…

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