Part $3$: The N$-$Puzzle Problem

In Part $3,$ you will apply the three uniformed search algorithms to simplified versions of the $15-$puzzle. Specifically, we will consider the $(3$x$3)9-$puzzle and the $(3$x$4)12-$puzzle.

$3.$A $-$ Create $9-$Puzzle Environment

Create an instance of the NPuzzle environment with $3$ rows and $3$ columns. Set scramble$=200$ and random$\_$state$=1.$ Use the display$()$ method to display the initial state of the environment.

$3.$B $-$ Solving $9-$Puzzle

Apply the depth$-$first search, breadth$-$first search, and uniform$-$cost search algorithms to the environment created in $3.$B$.$ Set a time limit of $2$ minutes for each algorithm. Store the solutions and the resulting log information into variables. Leave display$\_$results with its default value of True.

$3.$C $-$ Visualizing Solution

Identify the $9-$puzzle solution with the lowest path cost. If there is a tie, then select either solution. Call the generate$\_$gif$()$ method for the selected solution. This will display a gif animation of the solution to the puzzle.

$3.$D $-$ Create $12-$Puzzle Environment

Create an instance of the NPuzzle environment with $3$ rows and $4$ columns. Set scramble$=200$ and random$\_$state$=1.$ Use the display$()$ method to display the initial state of the environment.

$3.$E $-$ Solving $12-$Puzzle

Apply the depth$-$first search, breadth$-$first search, and uniform$-$cost search algorithms to the environment created in $3.$D$.$ Set a time limit of $2$ minutes for each algorithm. Store the solutions and the resulting log information into variables. Leave display$\_$results with its default value of True.