Use the tree to encode "day". Use the tree to encode "candy". Use the tree to decode "1110101101". Use the tree to decode "111001101110010".
Use the tree to encode "day". Use the tree to encode "candy". Use the tree to decode "1110101101". Use the tree to decode "111001101110010".
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Transcription and Explanation for Educational Use**
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**Consider the following tree for a prefix code:**
[Image of a binary tree]
- Top vertex (root) branches into:
- Left (0): character 'a'
- Right (1): Next level vertex
- Second-level vertex (1) branches into:
- Left (0): character 'o'
- Right (1): Next level vertex
- Third-level vertex (1) branches into:
- Left (0): Next level vertex
- Right (1): character 'e'
- Fourth-level left vertex (0) branches into:
- Left (0): character 'c'
- Right (1): character 'n'
- Fourth-level right vertex (1) branches into:
- Left (0): character 'd'
- Right (1): character 'y'
**Figure 13:**
- A tree with 5 vertices.
- The top vertex branches into character 'a' on the left and another vertex on the right.
- The second-level vertex branches into 'o' on the left and another vertex on the right.
- The third-level vertex branches into two vertices:
- Left vertex in the fourth level: branches into 'c' on the left and 'n' on the right.
- Right vertex in the fourth level: branches into 'd' on the left and 'y' on the right.
- Weight of each edge branching left from a vertex is 0.
- Weight of each edge branching right from a vertex is 1.
**Exercises:**
1. **Use the tree to encode “day”:**
- 'd' = 110
- 'a' = 0
- 'y' = 111
- **Encoded: 1100111**
2. **Use the tree to encode “candy”:**
- 'c' = 1100
- 'a' = 0
- 'n' = 1101
- 'd' = 110
- 'y' = 111
- **Encoded: 110001101110111**
3. **Use the tree to decode “1110101101”:**
- 1 (right) -> 1 (right) -> 1 (right) -> 'e'
- 0 (left) -> 'a'
- 1 (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f2920b9-16cb-409a-b0d9-184574689b7b%2Fa1c0be6d-128c-44cd-92c4-c08b99861348%2Fypulfnv_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation for Educational Use**
---
**Consider the following tree for a prefix code:**
[Image of a binary tree]
- Top vertex (root) branches into:
- Left (0): character 'a'
- Right (1): Next level vertex
- Second-level vertex (1) branches into:
- Left (0): character 'o'
- Right (1): Next level vertex
- Third-level vertex (1) branches into:
- Left (0): Next level vertex
- Right (1): character 'e'
- Fourth-level left vertex (0) branches into:
- Left (0): character 'c'
- Right (1): character 'n'
- Fourth-level right vertex (1) branches into:
- Left (0): character 'd'
- Right (1): character 'y'
**Figure 13:**
- A tree with 5 vertices.
- The top vertex branches into character 'a' on the left and another vertex on the right.
- The second-level vertex branches into 'o' on the left and another vertex on the right.
- The third-level vertex branches into two vertices:
- Left vertex in the fourth level: branches into 'c' on the left and 'n' on the right.
- Right vertex in the fourth level: branches into 'd' on the left and 'y' on the right.
- Weight of each edge branching left from a vertex is 0.
- Weight of each edge branching right from a vertex is 1.
**Exercises:**
1. **Use the tree to encode “day”:**
- 'd' = 110
- 'a' = 0
- 'y' = 111
- **Encoded: 1100111**
2. **Use the tree to encode “candy”:**
- 'c' = 1100
- 'a' = 0
- 'n' = 1101
- 'd' = 110
- 'y' = 111
- **Encoded: 110001101110111**
3. **Use the tree to decode “1110101101”:**
- 1 (right) -> 1 (right) -> 1 (right) -> 'e'
- 0 (left) -> 'a'
- 1 (
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