**Understanding Alpha-Beta Pruning in Game Trees**In the provided game tree structure, each node is represented by a letter (denoting the node's name) and a number (representing the minimax value). The goal is to apply alpha-beta pruning to efficiently determine which nodes' exact values are unnecessary to compute, given that the right child is added to the frontier first and the left child is expanded (or a utility is returned if it's a terminal node).### Tree Structure1. **Root Node (MIN level):** - **M**2. **Level 1 (MAX level):** - **L (Value: 11)** - **K**3. **Level 2 (MIN level):** - **J (Under K)** - **I (Under K)**4. **Level 3 (MAX level for J):** - **H (Value: 13)** - **G** - **F (Value: 7)**5. **Level 4 (MIN level under G and I):** - **D (Value: 14 under G)** - **C (Value: 9 under G)**6. **Level 3 (MAX level under I):** - **F (Continued, with values not needed at this level)** - **E (Value: 5)** 7. **Level 4 (Terminal nodes under G and I):** - **B (Value: 12 under F)** - **A (Value: 5 under E and F)**### Alpha-Beta Pruning Process- Start pruning from the root and progress towards the leaves, eliminating branches based on the minimax values derived from the left and right children. Note: Right child is added to the frontier first.**Nodes Determined Unnecessary by Alpha-Beta Pruning:**Crossed out nodes (i.e., nodes that would be pruned in this traversal based on alpha-beta logic):- **C**- **E**These nodes are pruned as they are not required to determine the outcome under the given rules for alpha-beta pruning, where the right child is prioritized in the expansion.This approach optimizes the minimax algorithm by ignoring branches that need not be considered, enhancing the efficiency of decision-making in games with extensive utility trees. The image is a list with checkboxes and letters next to each line. The items, in order of appearance, are:- □ L- □ C- □ B- □ E- □ I- □ D- □ M- □ H- □ G- □ A- □ J- □ F- □ KThere are no graphs or diagrams to explain.

Given : The game tree. The task is to find the set of nodes selected in alpha-beta pruning.Explanation : Number of levels in tree = 5 At level 4, the node with maximum value at level 5 is selected : Selected nodes are = D(14), B(12) At level 3, the node with a minimum value at level 4 is selected : Selected nodes are = H(13) , F(5) At level 2, the node with a maximum value at level 3 is selected : Selected nodes are = J(13) At level 1, the node with a minimum value at level 1 is selected : Selected nodes are = L(11) Final Answer : D, B, H, F, J, L

Engineering

Computer Science

Consider the game tree in the following figure, where the letter next to the node is the name and the number below the node is the minmax value. Cross out the node(s) whose exact value(s) the alpha-beta pruning method never determines, assuming that the right child is added to the frontier first and the left child is expanded or returns utility (if terminal node) fırst. Select all nodes with the node names that will be crossed out by the above pruning. MIN ▼ M МАX A L A K 11 MIN МАX ΔΗ A E 13 7 ▼ D V B ▼ A 14 9. 12

Consider the game tree in the following figure, where the letter next to the node is the name and the number below the node is the minmax value. Cross out the node(s) whose exact value(s) the alpha-beta pruning method never determines, assuming that the right child is added to the frontier first and the left child is expanded or returns utility (if terminal node) fırst. Select all nodes with the node names that will be crossed out by the above pruning. MIN ▼ M МАX A L A K 11 MIN МАX ΔΗ A E 13 7 ▼ D V B ▼ A 14 9. 12

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Binomial Heap

A binomial heap is a group of binomial trees. This data structure acts as a priority queue and implements the merge operation faster.

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**Understanding Alpha-Beta Pruning in Game Trees**

In the provided game tree structure, each node is represented by a letter (denoting the node's name) and a number (representing the minimax value). The goal is to apply alpha-beta pruning to efficiently determine which nodes' exact values are unnecessary to compute, given that the right child is added to the frontier first and the left child is expanded (or a utility is returned if it's a terminal node).

### Tree Structure

1. **Root Node (MIN level):**
- **M**

2. **Level 1 (MAX level):**
- **L (Value: 11)**
- **K**

3. **Level 2 (MIN level):**
- **J (Under K)**
- **I (Under K)**

4. **Level 3 (MAX level for J):**
- **H (Value: 13)**
- **G**
- **F (Value: 7)**

5. **Level 4 (MIN level under G and I):**
- **D (Value: 14 under G)**
- **C (Value: 9 under G)**

6. **Level 3 (MAX level under I):**
- **F (Continued, with values not needed at this level)**
- **E (Value: 5)**

7. **Level 4 (Terminal nodes under G and I):**
- **B (Value: 12 under F)**
- **A (Value: 5 under E and F)**

### Alpha-Beta Pruning Process

- Start pruning from the root and progress towards the leaves, eliminating branches based on the minimax values derived from the left and right children. Note: Right child is added to the frontier first.

**Nodes Determined Unnecessary by Alpha-Beta Pruning:**

Crossed out nodes (i.e., nodes that would be pruned in this traversal based on alpha-beta logic):

- **C**
- **E**

These nodes are pruned as they are not required to determine the outcome under the given rules for alpha-beta pruning, where the right child is prioritized in the expansion.

This approach optimizes the minimax algorithm by ignoring branches that need not be considered, enhancing the efficiency of decision-making in games with extensive utility trees.

The image is a list with checkboxes and letters next to each line. The items, in order of appearance, are:

- □ L
- □ C
- □ B
- □ E
- □ I
- □ D
- □ M
- □ H
- □ G
- □ A
- □ J
- □ F
- □ K

There are no graphs or diagrams to explain.

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