A robot moves around in a confined space (shown in diagram below) which can be represented using a 10 X 10 grid of cells where the cells marked 'X' are unsurpassable walls (thus the diagram shows walls surrounding the space and also a wall inside the space). At any given time the robot is located inside a non-wall cell and faces one of four directions - north, south, east or west. The robot can act in one of two ways - (i) turn to face one of two directions from whichever direction it was facing by rotating 90 degress clockwise or counter-clockwise (i.e. from facing north it can face east or west, from facing east it can face north or south etc.) or (ii) move to the next non-wall cell it is facing. Additionally, as shown in the diagram, the robot starts in the cell labeled 'S' facing East and its goal is to reach the cell labeled 'G' (it does not matter what direction it faces once it lands inside G).

Your task is to -

(a) create a correct way of representing the state of the robot

(b) write down an optimal path (as a sequence of states) from the starting state to goal state assuming that the cost of a turn and a move are both 1

(c) write down an optimal path (as a sequence of states) from the starting state to goal state assuming that the cost of a turn is 2 and the cost of a move is 1.