The Min-Max algorithm is one of the fundamental algorithms used in Artificial Intelligence, particularly in game-playing and decision-making systems. It is commonly applied to two-player, zero-sum games such as Tic-Tac-Toe, Chess, Checkers, and Connect Four. The basic idea of the algorithm is that one player tries to maximize the score or utility, while the other player tries to minimize it. Therefore, the two players are generally referred to as the MAX player and the MIN player. The Min-Max algorithm represents the possible moves of a game in the form of a game tree. Each node of the tree represents a particular game state, and each branch represents a possible move. The leaf nodes represent terminal states or states at which the search is stopped. A numerical utility value is assigned to these terminal states. The MAX player selects the move with the highest utility value, whereas the MIN player selects the move with the lowest utility value. By working backward from the terminal states to the current state, the algorithm determines the best possible move. The algorithm assumes that both players play optimally. MAX assumes that MIN will always choose the move that is worst for MAX, while MIN assumes that MAX will always choose the move that is best for MAX. Thus, the algorithm considers the opponent's best possible response before selecting a move. A simple Python implementation of the Min-Max algorithm is given below: ```python def minimax(depth, node_index, maximizing_player, values, height): # Base condition: if the leaf node is reached if depth == height: return values[node_index] if maximizing_player: return max( minimax(depth + 1, node_index * 2, False, values, height), minimax(depth + 1, node_index * 2 + 1, False, values, height) ) else: return min( minimax(depth + 1, node_index * 2, True, values, height), minimax(depth + 1, node_index * 2 + 1, True, values, height) ) # Terminal node values values = [3, 5, 2, 9, 12, 5, 23, 23] # Calculate the height of the binary