Consider an agent for playing Connect-4 on a c x r board (c columns and r rows).

1. Formulate the search problem, that is,

• find a representation (data structure) for states
• find a representation (data structure) for actions
• write down the initial state in your representation
• develop a function computing a list of legal moves of each agent
• develop a function computing the successor state resulting from executing a move in a state
• develop a function deciding when a terminal state is reached
• develop a function for deciding whether an agent has won the game

All of this can be done on paper (or in a text file). You don't actually have to program it! Just write down pseudo-code.

2. Estimate the memory requirement for you state data structure (in bytes relative to c and r). Suppose you want to solve the game by searching the state space. How does the size of your data structure influence the applicability of breadth-first search, depth-first search and iterative deepening search? What is the largest board (c x r) that you could solve using each of the three algorithms assuming you have 2GB of memory available? For the sake of simplicity, you can assume a square board, i.e. c=r.

3. For each of functions above (legal moves, successor state, …), determine its (worst-case) time complexity in terms of c and r.