Load factor and rehashing in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the sentence to define load factor in hash tables.

Data Structures Theory

Load factor is defined as the ratio of [1] to the number of buckets in a hash table.

Drag options to blanks, or click blank then click option'

Abucket size

Bnumber of collisions

Cnumber of elements stored

Dhash function complexity

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing load factor with number of collisions.

Using bucket size instead of number of elements.

The load factor measures how full the hash table is by dividing the number of stored elements by the number of buckets.

2fill in blank

medium

Complete the sentence to explain when rehashing is typically triggered.

Data Structures Theory

Rehashing is usually triggered when the load factor exceeds [1] to maintain efficient operations.

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A2.0

B1.0

C0.5

D0.75

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing 1.0 or higher, which is less common.

Selecting a very low value like 0.5 which is too strict.

Rehashing often happens when the load factor goes beyond 0.75 to keep the hash table efficient and reduce collisions.

3fill in blank

hard

Fix the error in the explanation of rehashing.

Data Structures Theory

Rehashing means [1] the hash table size and recalculating the positions of existing elements.

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Aincreasing

Breducing

Ckeeping

Dignoring

Attempts:

3 left

💡 Hint

Common Mistakes

Thinking rehashing reduces the table size.

Assuming rehashing keeps the size the same.

Rehashing involves increasing the hash table size to reduce collisions and redistribute elements.

4fill in blank

hard

Fill both blanks to describe the effect of rehashing on load factor and performance.

Data Structures Theory

After rehashing, the load factor becomes [1] and the average lookup time [2].

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Alower

Bhigher

Cdecreases

Dincreases

Attempts:

3 left

💡 Hint

Common Mistakes

Assuming load factor increases after rehashing.

Thinking lookup time increases after rehashing.

Rehashing lowers the load factor by increasing table size, which decreases average lookup time by reducing collisions.

5fill in blank

hard

Fill all three blanks to complete the explanation of rehashing steps.

Data Structures Theory

Rehashing involves creating a new table with [1] buckets, then [2] each element from the old table, and finally [3] them into the new table.

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Adouble the size

Bremoving

Cinserting

Dhalving the size

Attempts:

3 left

💡 Hint

Common Mistakes

Thinking the new table is smaller.

Confusing removing with inserting steps.

Rehashing creates a new larger table (often double size), removes each element from the old table, and inserts them into the new table to redistribute keys.

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