To implement Uniform$-$Cost Search $($UCS$)$ 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 $3$x$3$ frame. One tile of the $8-$puzzle is always empty thus making it possible to move an adjacent numbered tile into the empty tile position. Start with a random state $($Do not make it a fixed starting state$).$ The goal state is listed below.

$123$

$84$

$765$

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. Algorithm Average number of nodes visited $($you need repeat each algorithm several times with different initial configuration$)$ Give the best run time, the worst run time, and average run time when you run your program: run each algorithm at least $5$ times Your comment on these algorithms

UCS $($using the depth as the cost$)$

Best:

Worst:

Average:

Average: A$*($using Manhattan distance as the heuristics$)$

Best:

Worst:

Average:

A$*($using Nilsson$$s Sequence as the heuristics$)$

Best:

Worst:

Average: