### Tree Traversals**Tree Structure:**- Root: A- Level 1: B, C- Level 2: D, E (under B), and F (under C)- Level 3: G, H (under D); I (under E); J, K (under F)- Level 4: L (under H); M, N (under I); O, P (under K)**Tasks:**1. **Preorder Traversal** - Visit the root, then the left subtree, followed by the right subtree. - Order: A, B, D, G, H, L, E, I, M, N, C, F, J, K, O, P2. **Inorder Traversal** - Visit the left subtree, the root, and then the right subtree. - Order: G, D, L, H, B, M, I, N, E, A, C, J, O, F, P, K3. **Postorder Traversal** - Visit the left subtree, the right subtree, and then the root. - Order: G, L, H, D, M, N, I, E, B, O, P, J, K, F, C, A### Graph and Minimum Spanning Tree**Graph Structure:**- Nodes: a, b, c, d, e, f, g, h, i, j, k- Edges with weights: - a-b (4), a-e (4), a-f (6) - b-e (3), b-c (5) - c-d (3), c-g (3) - d-h (4), e-j (3) - f-e (3), f-g (1) - g-h (6), g-k (2) - i-e (1), i-j (3) - j-k (4)**Objective:**Find a minimum spanning tree, minimizing the total edge weight while connecting all nodes.**Approach:**Using algorithms like Prim's or Kruskal's, ensure all nodes are connected with the minimum total edge weight, avoiding any cycles.

According to the Bartleby guideline, we are supposed to answer only first 3 sub part of the question…

D H B L E M N C (3) 1. Perform a preorder traversal of the tree diagrammed above. (3) 2. Perform an inorder traversal of the tree diagrammed above. (3) 3. Perform a postorder traversal of the tree diagrammed above. F O P K

D H B L E M N C (3) 1. Perform a preorder traversal of the tree diagrammed above. (3) 2. Perform an inorder traversal of the tree diagrammed above. (3) 3. Perform a postorder traversal of the tree diagrammed above. F O P K

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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Concept explainers

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.

Question

### Tree Traversals

**Tree Structure:**
- Root: A
- Level 1: B, C
- Level 2: D, E (under B), and F (under C)
- Level 3: G, H (under D); I (under E); J, K (under F)
- Level 4: L (under H); M, N (under I); O, P (under K)

**Tasks:**

1. **Preorder Traversal**
- Visit the root, then the left subtree, followed by the right subtree.
- Order: A, B, D, G, H, L, E, I, M, N, C, F, J, K, O, P

2. **Inorder Traversal**
- Visit the left subtree, the root, and then the right subtree.
- Order: G, D, L, H, B, M, I, N, E, A, C, J, O, F, P, K

3. **Postorder Traversal**
- Visit the left subtree, the right subtree, and then the root.
- Order: G, L, H, D, M, N, I, E, B, O, P, J, K, F, C, A

### Graph and Minimum Spanning Tree

**Graph Structure:**
- Nodes: a, b, c, d, e, f, g, h, i, j, k
- Edges with weights:
- a-b (4), a-e (4), a-f (6)
- b-e (3), b-c (5)
- c-d (3), c-g (3)
- d-h (4), e-j (3)
- f-e (3), f-g (1)
- g-h (6), g-k (2)
- i-e (1), i-j (3)
- j-k (4)

**Objective:**
Find a minimum spanning tree, minimizing the total edge weight while connecting all nodes.

**Approach:**
Using algorithms like Prim's or Kruskal's, ensure all nodes are connected with the minimum total edge weight, avoiding any cycles.

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