java Eight Queens

A puzzler for chess buffs is the Eight Queens problem, which asks: Is it possible

to place eight queens on an empty chessboard so that no queen is $$attacking$$

any other $($i$.$e$.,$ no two queens are in the same row, in the same column or along

the same diagonal$)?$ For example, if a queen is placed in the upper$-$left corner of

the board, no other queens could be placed in any of the marked squares shown

in Fig. $1.$

Solve the problem recursively. $[$Hint: Your solution should begin with the first

column and look for a location in that column where a queen can be placed$$

initially, place the queen in the first row. The solution should then recursively

search the remaining columns. In the first few columns, there will be several

locations where a queen may be placed. Take the first available location. If a

column is reached with no possible location for a queen, the program should

return to the previous column, and move the queen in that column to a new row.

This continuous backing up and trying new alternatives is an example of

recursive backtracking.$]$

Fig$\mathrm{.}1$ Squares eliminated by placing a queen in the upper$-$left corner of a

chessboard.

$2.$ Recursive File and Directory Manipulation

Using the String$-$processing capabilities of textbook Chapter $14,$ the file and

directory capabilities of Section $15\mathrm{.}3$ and a Map Section $16\mathrm{.}10,$ create an

application that recursively walks a directory structure supplied by the user and

reports the number of files of each file type $($such as $.$java, $.$txt$,.$class, $.$docx, etc.$)$

that exist in the specified directory path. Display the filename extensions in

sorted order. Next, investigate method walk of class the Files. This method

returns a stream that walks a directory and its subdirectories and returns the

contents to you as a stream. Then, reimplement the first part of this exercise,

using lambdas and streams, rather than recursion.

$3.$ Calculating Factorials with Lambdas and Streams

Reimplement the factorial methods of Figs. $18\mathrm{.}318\mathrm{.}4$ in the textbook page $761$

to calculate factorials using lambdas and streams, rather than recursion.

Submission requirements:

Your submission must include a document with the logic for each problem in this

assignment as well as each problem$$s source code.