Consider the 8-puzzle problem. Trace out the A* algorithm given the initial and goal states below. You are supposed to show the generated search tree until the search generates the goal state. For each state show the value of the evaluation function f(n) = g(n) + h(n). Recall that g(n) gives the path cost from the initial state to node n. Moreover, for this problem the step cost is 1 for any action (moving the empty tile). As a heuristic let h(n) be the number of misplaced tiles. Hence f(initial-state) = 0 + 3 = 3. The # symbol denotes the empty tile. Initial State Goal State 1 2 3 1 2 3 # 4 6 4 5 6 7 5 8 7 8 #

Write the PYTHON programming to solve with breadth-first search and build node-arcs with python code for the attached problem:

There are many applications of Shortest Path Algorithm. Consider the problem of solving a jumbled Rubik's Cube in the fewest number of moves. I claim that this problem can be solved using a Shortest Path Algorithm. Determine whether this statement is TRUE or FALSE. NOTE: if you want to check if this statement is TRUE, think about how the Rubik's Cube Problem can be represented as a graph. What are the vertices? Which pairs of vertices are connected with edges? What is your source vertex and what is your destination vertex? How would Dijkstra's Algorithm enable you to find the optimal sequence of moves to solve a jumbled cube in the fewest number of moves?

Given a linked list L storing n integers, present an algorithm (either in words or in a pseudocode) that decides whether L contains any 0 or not. The output of your algorithm should be either Yes or No. What is the running time of your algorithm in the worst-case, using O notation?