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Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Transcribed Image Text:**Understanding HashMap: Properties and Performance**
**Introduction to HashMap**
`java.util.HashMap` is a type of data structure that utilizes a separate-chaining hash table. It operates with a load factor, defined as the ratio of the number of key-value pairs \( n \) to the array length \( m \). This load factor is typically maintained between 0.5 and 2.0 to optimize performance.
**Performance Characteristics**
When analyzing the performance of a `HashMap`, consider the following properties associated with its operations:
1. **Equals Method**:
- \(\Theta(1)\) calls to `equals()` in a typical call to `put()`. This implies constant time complexity for equality checks when inserting elements.
2. **HashCode Method (Get Operation)**:
- \(\Theta(1)\) calls to `hashCode()` in a typical call to `get()`. This suggests that generally, retrieving elements by key can be performed in constant time.
3. **HashCode Method (Resizing Operation)**:
- \(\Theta(\log n)\) calls to `hashCode()` in a call to `put()` that triggers a resizing operation. Resizing may require rehashing existing elements, incurring logarithmic time complexity.
4. **Memory Usage**:
- Uses \(\Theta(n)\) memory in the worst case. This indicates linear space complexity relative to the number of key-value pairs.
Understanding these properties helps in evaluating `HashMap` efficiency in different scenarios, such as handling large datasets, and aids in deciding its suitability for specific applications.
Expert Solution
Step 1
A hash function h maps keys of a given type to integers underlying in a fixed interval [0, . . . , N − 1]. We call h(x) as hash value of x.
Examples:
- h(x) = x mod N is a hash function for integer keys.
- h((x, y)) = (5 · x + 7 · y) mod N is a hash function for pairs of integers.
A hash table consists of a hash function h and an array (called table) of size N.
Collision occur when different elements are mapped to the same cell. Keys k1, k2 with h(k1) = h(k2) are said to collide.
Collision can be handled by using any one of these ways:
- chaining
- linear probing
- double hashing
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