Load factor and rehashing in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the load factor in a hash table?

Load factor is the ratio of the number of stored elements to the total number of slots in the hash table. It shows how full the table is.

beginner

Why is load factor important in hash tables?

Load factor helps decide when to resize the hash table. A high load factor means more collisions, which slows down operations.

beginner

What does rehashing mean?

Rehashing means creating a new larger hash table and moving all existing elements into it using a new hash function or table size.

intermediate

When should rehashing be done?

Rehashing is done when the load factor exceeds a certain threshold, usually around 0.7 or 70%, to keep operations fast.

intermediate

What is the effect of rehashing on hash table performance?

Rehashing reduces collisions by increasing table size, which improves search, insert, and delete speeds but temporarily costs time to move elements.

What does a load factor of 1 mean in a hash table?

A The table has no collisions

B The table is empty

C The table is completely full

D Half of the table is full

A load factor of 1 means the number of elements equals the number of slots, so the table is full.

Why do we rehash a hash table?

A To change the data type of elements

B To delete all elements

C To make the table smaller

D To reduce the number of collisions

Rehashing increases the table size to reduce collisions and improve performance.

Which load factor value usually triggers rehashing?

A 0.7

B 0.5

C 0.1

D 1.5

A load factor around 0.7 is a common threshold to trigger rehashing.

What happens during rehashing?

A Elements are moved to a bigger table

B Elements are deleted

C Elements are sorted

D Elements are compressed

Rehashing moves elements to a larger table to reduce collisions.

What is a downside of rehashing?

A It deletes data

B It temporarily slows down operations

C It reduces table size

D It causes data loss

Rehashing takes time to move elements, causing a temporary slowdown.

Explain what load factor is and why it matters in hash tables.

Think about how full the table is and how that affects speed.

Describe the process and purpose of rehashing in hash tables.

Consider what happens when the table gets too full.

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