Question

Consider the Minimax Algorithm used in the area of Games as Adversarial Search.

If d represents the maximum depth of the Game Tree while n depicts the number of moves, the Time Complexity of minimax would be of the order ____________
a.O(n+d)
b.O(nᵈ)
c.O(nd)
d.O(dⁿ)

Answer 1

The time complexity of the minimax algorithm used in the area of games as adversarial search can be represented as O(b^d), where b is the branching factor and d is the maximum depth of the game tree.

Step-by-step explanation:

The Time Complexity of the minimax algorithm used in the area of games as adversarial search can be represented as O(b^d), where b is the branching factor (the number of possible moves at each level) and d is the maximum depth of the game tree.

In the case of the minimax algorithm, each level of the game tree represents one move by either the maximizing or minimizing player. At each level, the algorithm explores all possible moves and evaluates each move based on a heuristic evaluation function. Therefore, the number of nodes in the game tree can be expressed as b^d.

As a result, the time complexity of the minimax algorithm is O(b^d) since it needs to consider all possible moves at each level up to the maximum depth of the game tree.