Task $2$: N$-$Queens Problem $-$ Simulated Annealing

$N-$ Queens problem is to place $n-$ queens in such a manner on an $nx$ chessboard that no

queens attack each other by being in the same row, column or diagonal. For $n=1,$ the problem

has a trivial solution, and no solution exists for $n=2$ and $n=3.$ So first we will consider the $4$

queens' problem and then generate it to $(n>4)$ queens' problem.

$($a$)$ Write a Java$/$Python program that solves the above problem using the Simulated

Annealing algorithm.

Make sure that your program is well$-$documented $($i$.$e$.,$ writing enough comments that

clearly explain your code$)$ and executable with no syntax$/$compiling errors.

$($b$)$ Explain in some details how your solution would improve the performance as compared

to the classical search algorithm such as DFS$?$