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Min Max Algorithm in Artificial Intelligence
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- 2. Mini-max algorithmis a recursive or backtracking algorithm which is used in decision-making and game theory. Mini-Max algorithm uses recursion to search through the game- tree. In this algorithm two players play the game, one is called MAX and other is called MIN.
- 3. Both theplayers fight it as the opponent player gets the minimum benefit while they get the maximum benefit. The minimax algorithm performs a depth-first search algorithm for the exploration of the complete game tree. The minimax algorithm proceeds all the way down to the terminal node of the tree, then backtrack the tree as the recursion.
- 4. Workin g An exampleof game-tree which is representing the two-player game. In this example, there are two players one is called Maximizer and other is called Minimizer. Maximizer will try to get the Maximum possible score, and Minimizer will try to get the minimum possible score.
- 5. This algorithmapplies DFS, so in this game-tree, we have to go all the way through the leaves to reach the terminal nodes. At the terminal node, the terminal values are given so we will compare those value and backtrack the tree until the initial state occurs.
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- 8. Ia.rimizer linilnizer laximiz.er Terminal node -1 4 26 -3 -5 0 T erminal value
- 9. 4 linimizer 7 - .la.'.imize1· Terminal node -1 4 2 6 -3 -5 T erminal alue
- 10. Propertie s Complete-Min-Max algorithm is Complete. It will definitely find a solution (if exist), in the finite search tree. Optimal- Min-Max algorithm is optimal if both opponents are playing optimally. Time complexity- As it performs DFS for the game-tree, so the time complexity of Min-Max algorithm is O(bm), where b is branching factor of the game-tree, and m is the maximum depth of the tree. Space Complexity- Space complexity of Mini-max algorithm is also similar to DFS which is O(bm).
- 11. Limitation The maindrawback of the minimax algorithm is that it gets really slow for complex games such as Chess, go, etc. This type of games has a huge branching factor, and the player has lots of choices to decide. This limitation of the minimax algorithm can be improved from alpha-beta pruning.