Minimax algorithm ex.pptx
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The document describes the 4 main steps to solve a two-player game tree: 1) Generate the entire game tree and assign utility values to terminal nodes. 2) For the maximizer, compare each terminal node value to -infinity and select the maximum. 3) For the minimizer, compare each value to infinity and select the minimum. 4) For the maximizer, compare values from the previous step and select the maximum value for the root node.
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21CSC206T_UNIT3.pptx.pdf ARITIFICIAL INTELLIGENCE
1) Adversarial search involves searching game trees to find the best move in games with competitive players like tic-tac-toe and chess. Important concepts include pruning unwanted search tree portions and heuristic evaluation functions.
2) A game tree represents all possible game states, moves, and outcomes. Elements of game playing search include the initial state, players, legal moves, game results, end states, and payoffs for winning, losing, or drawing.
3) The minimax algorithm searches game trees to determine the best guaranteed outcome against an optimal opponent. It recursively evaluates nodes using the minimax rule to maximize the minimum payoff for the maximizing player.
1.game
Games provide well-defined test beds for developing AI techniques. They have clear rules and allow direct comparison of algorithms against humans. Game playing involves searching game trees to find optimal strategies, taking into account opponents' possible moves. The minimax algorithm and its improved version alpha-beta pruning are commonly used to search game trees and select the best next move.
cai
Minimax is an algorithm that is commonly used for game playing. It works by constructing a game tree that represents all possible future game states up to a certain depth, and uses an evaluation function to assign a value to each state. The minimax algorithm traverses the tree and "backs up" values from the leaves to the root by maximizing values at MAX nodes and minimizing values at MIN nodes. Alpha-beta pruning improves upon minimax by pruning branches that cannot affect the final output value.
Min Max Artificial Intelligence algorithm
The Mini-Max algorithm is a recursive algorithm used in decision making and game theory. It uses a depth-first search to explore the game tree, with one player trying to maximize their score (MAX) and the other trying to minimize it (MIN). At each node, it recursively evaluates the possible moves down to a terminal node, then backtracks to assign scores. It is complete, optimal if both players play optimally, and has time and space complexity of O(bm) for a branching factor b and maximum depth m. However, it is slow for complex games with large branching factors.
Lecture 8 dynamic programming
This document discusses algorithms for finding minimum and maximum elements in an array, including simultaneous minimum and maximum algorithms. It introduces dynamic programming as a technique for improving inefficient divide-and-conquer algorithms by storing results of subproblems to avoid recomputing them. Examples of dynamic programming include calculating the Fibonacci sequence and solving an assembly line scheduling problem to minimize total time.
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Minimax algorithm ex.pptx
- 1. EXAMPLE At the terminal node, the terminal values are given so we will compare those value and backtrack the tree until the initial state occurs. Following are the main steps involved in solving the two-player game tree: Step-1: In the first step, the algorithm generates the entire game-tree and apply the utility function to get the utility values for the terminal states. In the below tree diagram, let's take A is the initial state of the tree. Suppose maximizer takes first turn which has worst-case initial value =- infinity, and minimizer will take next turn which has worst-case initial value = +infinity.
- 2. • Step 2: Now, first we find the utilities value for the Maximizer, its initial value is -∞, so we will compare each value in terminal state with initial value of Maximizer and determines the higher nodes values. It will find the maximum among the all. • For node D max(-1,- -∞) => max(-1,4)= 4 • For Node E max(2, -∞) => max(2, 6)= 6 • For Node F max(-3, -∞) => max(-3,-5) = -3 • For node G max(0, -∞) = max(0, 7) = 7
- 3. • Step 3: In the next step, it's a turn for minimizer, so it will compare all nodes value with +∞, and will find the 3rd layer node values. • For node B= min(4,6) = 4 • For node C= min (-3, 7) = -3
- 4. • Step 4: Now it's a turn for Maximizer, and it will again choose the maximum of all nodes value and find the maximum value for the root node. In this game tree, there are only 4 layers, hence we reach immediately to the root node, but in real games, there will be more than 4 layers. • For node A max(4, -3)= 4