Load factor and rehashing in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Load Factor in Hash Tables

What does the load factor in a hash table represent?

A The ratio of the number of stored elements to the total number of buckets

B The number of collisions that have occurred during insertions

C The maximum number of elements the hash table can store

D The total number of buckets in the hash table

💡 Hint

Think about how full the hash table is compared to its capacity.

The load factor is the ratio of stored elements to buckets, indicating how full the hash table is. It helps decide when to resize the table.

❓ Reasoning

intermediate

Effect of High Load Factor on Hash Table Performance

What is the most likely effect of a high load factor on a hash table's performance?

A No effect on performance as load factor only affects memory usage

B Faster search times due to more elements being stored

C Increased number of collisions leading to slower search and insertion

D Decreased memory usage with no impact on speed

💡 Hint

Consider what happens when many elements share the same bucket.

A high load factor means more elements per bucket, causing more collisions and slower operations.

🧠 Conceptual

advanced

Purpose of Rehashing in Hash Tables

Why is rehashing performed in a hash table?

A To reduce the load factor by increasing the number of buckets and redistribute elements

B To delete all elements and reset the hash table

C To convert the hash table into a linked list for easier traversal

D To compress the stored data to save memory

💡 Hint

Think about what happens when the table becomes too full.

Rehashing increases the number of buckets and redistributes elements to keep operations efficient.

🔍 Analysis

advanced

Identifying When Rehashing Should Occur

Given a hash table with 100 buckets and 75 stored elements, should rehashing be triggered if the load factor threshold is 0.7?

A No, because the load factor is below 1

B Yes, because the load factor is 0.75 which exceeds the threshold

C No, because 75 elements is less than 100 buckets

D Yes, because the number of buckets is too small regardless of load factor

💡 Hint

Calculate the load factor and compare it to the threshold.

Load factor = 75/100 = 0.75, which is greater than 0.7, so rehashing should occur.

❓ Comparison

expert

Comparing Rehashing Strategies

Which rehashing strategy is generally more efficient in maintaining hash table performance as it grows?

A Keeping the number of buckets fixed and only re-inserting elements

B Reducing the number of buckets to save memory and re-inserting elements

C Increasing the number of buckets by one and re-inserting all elements

D Doubling the number of buckets and re-inserting all elements

💡 Hint

Consider how the size increase affects load factor and performance.

Doubling buckets quickly reduces load factor and keeps operations efficient, while small increases cause frequent rehashing.

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