To implement Depth$-$First Search $($DFS$),$ Uniform$-$Cost Search $($UCS$),$ Best$-$First Search $($BFS$),$ and $A^{**}$ Algorithm to solve the following $8-$puzzle problem $($i$.$e$.$ find the goal$)$:

$8-$puzzle Problem:

The $8-$puzzle consists of eight numbered, movable tiles set in a $33$ frame. One tile of the $8-$puzzle is always empty thus making it possible to move an adjacent numbered file into the empty tile position. Start with a random state $($Do not make it a fixed starting state$).$ The goal state is listed below.

$\backslash$table$[[1,2,3],[8,,4],[7,6,5]]$

The program is to solve the initial configuration and find the goal configuration. A solution to the problem is an appropriate sequence of moves. You must write your own codes for the algorithms. Make sure your submission meets all of the requirements and free of plagiarism.

Your program should be able to address any initial configuration and provide a table of statistics below in your PDF file.

$\backslash$table$[[$Algorithm$,\backslash$table$[[$Average number of nodes$],[$visited $($you need repeat each$],[$algorithm several times with$],[$different initial configuration$)]],\backslash$table$[[$Give the best run$],[$time$,$ the worst run$],[$time$,$ and average run$],[$time when you run$],[$your program: run$],[$each algorithm at$],[$least for $5$ times$]],\backslash$table$[[$Your comment on these$],[$algorithms$]]],[$DFS$,\backslash$table$[[$Best:$],[$Worst:$],[$Average:$]],\backslash$table$[[$Best:$],[$Worst:$],[$Average:$]],],[\backslash$table$[[$UCS $($using the$],[$depth as the$],[$cost$)]],\backslash$table$[[$Best:$],[$Worst:$],[$Average:$]],\backslash$table$[[$Best:$],[$Worst:$],[$Average:$]],],[\backslash$table$[[$BFS $($using$],[$Manhattan$],[$distance as the$],[$heuristics$)]],\backslash$table$[[$Best:$],[$Worst:$],[$Average:$]],\backslash$table$[[$Best:$],[$Worst:$],[$Average:$]],],[\backslash$table$[[$A$*{?}^{**}($using$],[$Nilsson$\text{'}$s$],[$Sequence as the$],[$heuristics$)]],\backslash$table$[[$Best:$],[$Worst:$],[$Average:$]],\backslash$table$[[$Best:$],[$Worst:$],[$Average:$]],]]$

You may write your code in a contemporary language of your choice; typical languages would include C$/$C$++,$ Python, Java, Ada, Pascal, Smalltalk, Lisp, and Prolog. A GUI interface is preferred.