The state of the board is stored in a list. The list stores values for the

# board in the following positions:

#

# $-------------$

# $|0|3|6|$

# $-------------$

# $|1|4|7|$

# $-------------$

# $|2|5|8|$

# $-------------$

#

# The goal is defined as:

#

# $-------------$

# $|1|2|3|$

# $-------------$

# $|8|0|4|$

# $-------------$

# $|7|6|5|$

# $-------------$

goal$\_$state $=[1,8,7,2,0,6,3,4,5]$

$$python$$

Please use the following search algorithms to solve the $8-$puzzle problem.

Uniform$-$Cost Search

Input: A state of random layout with $1,2,3,...,8,$ blank. Goal state:

Output for each algorithm:

$($a$)$ The number of movements $($state changes$)$ from the initial state to the

goal state.

$($b$)$ The maximum number of states ever saved in the memory during the process.

$($c$)$ Please explain the strategy you used in each search algorithm.