Load factor and rehashing in Data Structures Theory - Mini Project: Build & Apply

Understanding Load Factor and Rehashing in Hash Tables

📖 Scenario: Imagine you have a small library where you keep books in boxes. Each box can hold a few books. When a box gets too full, you need to get bigger boxes to keep the books organized and easy to find.This is similar to how a hash table works in computers. We will learn about the load factor, which tells us how full the boxes are, and rehashing, which is the process of getting bigger boxes when needed.

🎯 Goal: You will build a simple example to understand how load factor is calculated and when rehashing happens in a hash table.

📋 What You'll Learn

Create a dictionary representing a hash table with a fixed size and some entries

Add a variable to store the maximum load factor allowed before rehashing

Calculate the current load factor based on the number of entries and table size

Add a condition to check if rehashing is needed and update the table size accordingly

💡 Why This Matters

🌍 Real World

Hash tables are used in many software applications to store and quickly find data, like phone books, databases, and caches.

💼 Career

Understanding load factor and rehashing helps software developers design efficient data structures that keep programs fast and responsive.

1

Create the initial hash table data

Create a dictionary called hash_table with these exact entries: 'apple': 1, 'banana': 2, 'cherry': 3. Also create a variable called table_size and set it to 5.

Data Structures Theory

# Create the hash_table dictionary and table_size variable
# Your code here

Hint

Use curly braces {} to create the dictionary with the exact keys and values.

Set table_size to 5 as an integer.

2

Set the maximum load factor

Create a variable called max_load_factor and set it to 0.7. This value means the hash table should rehash when it is more than 70% full.

Data Structures Theory

hash_table = {'apple': 1, 'banana': 2, 'cherry': 3}
table_size = 5
# Create max_load_factor variable
# Your code here

Hint

Use a decimal number for max_load_factor to represent 70%.

3

Calculate the current load factor

Create a variable called current_load_factor and set it to the number of entries in hash_table divided by table_size. Use len(hash_table) to get the number of entries.

Data Structures Theory

hash_table = {'apple': 1, 'banana': 2, 'cherry': 3}
table_size = 5
max_load_factor = 0.7
# Calculate current_load_factor
# Your code here

Hint

Use len(hash_table) to count entries and divide by table_size.

4

Check if rehashing is needed and update table size

Write an if statement that checks if current_load_factor is greater than max_load_factor. If true, double the table_size by multiplying it by 2.

Data Structures Theory

hash_table = {'apple': 1, 'banana': 2, 'cherry': 3}
table_size = 5
max_load_factor = 0.7
current_load_factor = len(hash_table) / table_size
# Check if rehashing is needed and update table_size
# Your code here

Hint

Use an if statement to compare the load factors and multiply table_size by 2 inside the block.

Practice

1. What does the load factor in a hash table represent?

easy

A. The ratio of stored elements to the total capacity of the table

B. The speed at which data is inserted into the table

C. The number of collisions that have occurred

D. The size of each element stored in the table

Solution

1. Step 1: Understand load factor definition

   Load factor is defined as the number of elements divided by the total slots in the hash table.

2. Step 2: Match definition to options

   The ratio of stored elements to the total capacity of the table correctly describes this ratio, while others describe unrelated concepts.

3. Final Answer:

   The ratio of stored elements to the total capacity of the table -> Option A

4. Quick Check:

   Load factor = elements / capacity [OK]

Hint: Load factor = elements ÷ table size [OK]

Common Mistakes:

• Confusing load factor with number of collisions
• Thinking load factor measures speed
• Mixing load factor with element size

2. Which of the following is the correct action when the load factor exceeds a threshold in a hash table?

easy

A. Delete random elements to reduce load

B. Reduce the size of the table to save memory

C. Rehash the table by increasing its size

D. Ignore and continue inserting elements

Solution

1. Step 1: Identify what happens when load factor is high

   A high load factor means the table is too full, causing more collisions and slower operations.

2. Step 2: Choose the correct response to high load factor

   Rehashing by increasing the table size reduces load factor and improves performance, which matches Rehash the table by increasing its size.

3. Final Answer:

   Rehash the table by increasing its size -> Option C

4. Quick Check:

   High load factor -> rehash with bigger table [OK]

Hint: Rehash by resizing when load factor is too high [OK]

Common Mistakes:

• Deleting elements randomly instead of resizing
• Ignoring the problem causing slowdowns
• Reducing table size which worsens collisions

3. Consider a hash table with capacity 10 and 7 elements inserted. If the load factor threshold is 0.7, what happens after inserting the 8th element?

medium

A. No rehashing occurs because load factor is still below threshold

B. Rehashing occurs because load factor exceeds threshold

C. Table size is reduced to maintain load factor

D. Insertion is rejected to keep load factor constant

Solution

1. Step 1: Calculate load factor after 7 elements

   Load factor = 7 / 10 = 0.7, which equals the threshold.

2. Step 2: Calculate load factor after 8 elements

   Load factor = 8 / 10 = 0.8, which exceeds the threshold of 0.7, triggering rehashing.

3. Final Answer:

   Rehashing occurs because load factor exceeds threshold -> Option B

4. Quick Check:

   Load factor > threshold -> rehash [OK]

Hint: Load factor > threshold triggers rehash [OK]

Common Mistakes:

• Assuming threshold is inclusive and no rehash needed
• Thinking table shrinks instead of grows
• Believing insertion is rejected

4. A hash table implementation does not rehash when the load factor exceeds the threshold. What is the most likely problem caused by this?

medium

A. Insertions and lookups will become slower due to collisions

B. The table will automatically shrink in size

C. The table will run out of memory quickly

D. Elements will be deleted automatically to reduce load

Solution

1. Step 1: Understand effect of no rehashing at high load

   Without rehashing, the table stays full, causing many collisions.

2. Step 2: Identify impact on operations

   More collisions slow down insertions and lookups, matching Insertions and lookups will become slower due to collisions.

3. Final Answer:

   Insertions and lookups will become slower due to collisions -> Option A

4. Quick Check:

   No rehash -> more collisions -> slower operations [OK]

Hint: No rehash means slower operations from collisions [OK]

Common Mistakes:

• Thinking memory runs out immediately
• Assuming table shrinks automatically
• Believing elements get deleted automatically

5. You have a hash table with capacity 16 and a load factor threshold of 0.75. After inserting 12 elements, you decide to rehash by doubling the capacity. What is the new load factor immediately after rehashing, before adding any new elements?

hard

A. 0.5

B. 0.75

C. 1.5

D. 0.375

Solution

1. Step 1: Calculate load factor before rehashing

   Load factor = 12 / 16 = 0.75, which triggers rehashing.

2. Step 2: Calculate load factor after doubling capacity

   New capacity = 16 * 2 = 32. Load factor = 12 / 32 = 0.375 immediately after rehash.

3. Final Answer:

   0.375 -> Option D

4. Quick Check:

   Load factor after resize = elements / new capacity = 12/32 = 0.375 [OK]

Hint: Load factor after resize = old elements ÷ new capacity [OK]

Common Mistakes:

• Using old capacity instead of new capacity
• Multiplying load factor by 2 incorrectly
• Confusing load factor with threshold