Hash Table Concept and Hash Functions in DSA Python - Execution Trace

Concept Flow - Hash Table Concept and Hash Functions

Start: Insert key-value pair

↓

Apply hash function on key

↓

Get index from hash value

↓

Check bucket at index

↓

Insert pair

↓

Done

↓

Insert pair

↓

Done

Shows how a key-value pair is inserted into a hash table using a hash function to find the index, then inserting or handling collisions.

Execution Sample

DSA Python

hash_table = [None] * 5
key = 'cat'
hash_value = hash(key)
index = hash_value % 5
hash_table[index] = (key, 'meow')

Inserts the key 'cat' with value 'meow' into a hash table of size 5 using a hash function.

Execution Table

Step	Operation	Key	Hash Value	Index	Bucket State	Visual State
1	Start insertion	cat			[None, None, None, None, None]	None -> None -> None -> None -> None
2	Compute hash	cat	e.g. 123456789			None -> None -> None -> None -> None
3	Calculate index	cat	123456789	4		None -> None -> None -> None -> None
4	Check bucket at index 4	cat	123456789	4	Empty	None -> None -> None -> None -> None
5	Insert ('cat', 'meow')	cat	123456789	4	Occupied	None -> None -> None -> None -> ('cat', 'meow')
6	Done	cat	123456789	4	Occupied	None -> None -> None -> None -> ('cat', 'meow')

💡 Insertion complete as bucket at index 4 was empty.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 5	Final
hash_table	[None, None, None, None, None]	[None, None, None, None, None]	[None, None, None, None, None]	[None, None, None, None, ('cat', 'meow')]	[None, None, None, None, ('cat', 'meow')]
key	cat	cat	cat	cat	cat
hash_value		123456789	123456789	123456789	123456789
index			4	4	4

Key Moments - 3 Insights

Why do we use the modulo operator (%) on the hash value?

Because the hash value can be very large, modulo limits it to the size of the hash table, giving a valid index (see Step 3 in execution_table).

What happens if the bucket at the computed index is already occupied?

We handle collisions by methods like chaining or probing (shown in concept_flow branch 'Handle collision'), but in this example, the bucket was empty (Step 4).

Why do we store key-value pairs instead of just values?

Because different keys can hash to the same index, storing pairs helps verify the correct key during lookup or collision handling.

Visual Quiz - 3 Questions

Look at the execution_table, what is the index computed for key 'cat'?

A 4

B 2

C 3

D 0

💡 Hint

Check the 'Index' column at Step 3 in the execution_table.

At which step does the hash table get updated with the new key-value pair?

A Step 2

B Step 4

C Step 5

D Step 6

💡 Hint

Look for the step where 'Insert' operation happens and bucket state changes to 'Occupied'.

If the hash table size changed to 3, how would the index for 'cat' change?

A It would remain the same as before

B It would be hash('cat') % 3

C It would be hash('cat') % 5

D It would be 0

💡 Hint

Index depends on modulo with table size, see Step 3 in execution_table.

Concept Snapshot

Hash Table stores key-value pairs.
Hash function converts key to a number.
Modulo operator limits index to table size.
Insert at computed index.
Handle collisions if bucket occupied.
Fast average lookup and insertion.

Full Transcript

A hash table stores data as key-value pairs. To insert, we apply a hash function to the key, which gives a large number. We then use modulo with the table size to get a valid index. If the bucket at that index is empty, we insert the pair. If occupied, we handle collisions by chaining or probing. This process allows fast data access by key.

Practice

1. What is the main purpose of a hash function in a hash table?

easy

A. To encrypt the data stored in the table

B. To sort the keys in ascending order

C. To convert a key into an index for storing data

D. To count the number of elements in the table

Solution

1. Step 1: Understand the role of a hash function

   A hash function takes a key and converts it into a number that can be used as an index in the hash table.

2. Step 2: Compare with other options

   Sorting keys, encrypting data, or counting elements are not the main roles of a hash function in a hash table.

3. Final Answer:

   To convert a key into an index for storing data -> Option C

4. Quick Check:

   Hash function = key to index [OK]

Hint: Hash function maps keys to indexes fast [OK]

Common Mistakes:

• Thinking hash function sorts keys
• Confusing hash function with encryption
• Assuming hash function counts elements

2. Which of the following is the correct syntax to define a simple hash function in Python that returns the remainder of a key divided by 10?

easy

A. def hash_func(key): return key % 10

B. def hash_func(key): return key / 10

C. def hash_func(key): return key * 10

D. def hash_func(key): return key + 10

Solution

1. Step 1: Identify the correct modulus operation

   The hash function should return the remainder when key is divided by 10, which is done using the modulus operator '%'.

2. Step 2: Check syntax correctness

   def hash_func(key): return key % 10 uses 'return key % 10' which is correct syntax and logic. Other options use division, multiplication, or addition which do not produce the remainder.

3. Final Answer:

   def hash_func(key): return key % 10 -> Option A

4. Quick Check:

   Use % for remainder in hash function [OK]

Hint: Use % operator for remainder in hash functions [OK]

Common Mistakes:

• Using division instead of modulus
• Multiplying or adding instead of modulus
• Incorrect function syntax

3. What will be the output of the following code?

def simple_hash(key):
    return key % 5

hash_table = [None] * 5
keys = [12, 22, 17]
for key in keys:
    index = simple_hash(key)
    hash_table[index] = key
print(hash_table)

medium

A. [None, None, 12, 17, 22]

B. [None, None, 17, None, None]

C. [None, 22, 12, None, 17]

D. [None, 12, 22, 17, None]

Solution

1. Step 1: Calculate hash indexes for each key

   12 % 5 = 2, 22 % 5 = 2, 17 % 5 = 2. All three keys map to the same index 2.

2. Step 2: Trace the assignments

   The code assigns directly to hash_table[index] with no collision handling, so later keys overwrite earlier ones at index 2: 12 -> 22 -> 17. Final state: [None, None, 17, None, None].

3. Final Answer:

   [None, None, 17, None, None] -> Option B

4. Quick Check:

   All keys hash to index 2, last key stored [OK]

Hint: Check hash index for each key carefully [OK]

Common Mistakes:

• Assuming keys store at different indexes without collision
• Ignoring overwriting in hash table
• Miscomputing modulus

4. Identify the error in the following hash function code:

def hash_func(key):
    return key // 10

hash_table = [None] * 10
index = hash_func(25)
hash_table[index] = 25
print(hash_table)

medium

A. No error, code runs correctly

B. hash_table size is too small for keys

C. Function should return key * 10 instead

D. Using integer division instead of modulus causes wrong indexing

Solution

1. Step 1: Understand the hash function logic

   The function uses integer division '//' which divides key by 10 and returns the quotient, not the remainder.

2. Step 2: Check impact on indexing

   For key=25, 25 // 10 = 2, which is a valid index but this is not a typical hash function behavior. Usually, modulus '%' is used to get remainder for index within table size.

3. Step 3: Identify the error

   Using '//' can cause indexes outside the hash table size if keys are large. Modulus '%' should be used to ensure index is within table size.

4. Final Answer:

   Using integer division instead of modulus causes wrong indexing -> Option D

5. Quick Check:

   Use % for index, not // [OK]

Hint: Use % to keep index within table size [OK]

Common Mistakes:

• Confusing integer division with modulus
• Ignoring table size limits
• Assuming code runs without error

5. You want to design a hash function for strings that returns an index between 0 and 9 for a hash table of size 10. Which of the following functions correctly implements this?

hard

A. def hash_func(s): return sum(ord(c) for c in s) % 10

B. def hash_func(s): return len(s) * 10

C. def hash_func(s): return ord(s[0])

D. def hash_func(s): return s.count('a')

Solution

1. Step 1: Understand the requirement

   The hash function must return an integer index between 0 and 9 for any string input.

2. Step 2: Analyze each option

   def hash_func(s): return sum(ord(c) for c in s) % 10 sums ASCII values of all characters and uses modulus 10 to keep index in range 0-9. def hash_func(s): return len(s) * 10 multiplies length by 10, which can exceed 9. def hash_func(s): return ord(s[0]) returns ASCII of first char, which can be larger than 9. def hash_func(s): return s.count('a') counts 'a's, which can be any number, possibly larger than 9.

3. Step 3: Choose correct function

   Only def hash_func(s): return sum(ord(c) for c in s) % 10 guarantees index in 0-9 range for any string.

4. Final Answer:

   def hash_func(s): return sum(ord(c) for c in s) % 10 -> Option A

5. Quick Check:

   Sum ASCII % table size for string hash [OK]

Hint: Sum ASCII codes and mod by table size [OK]

Common Mistakes:

• Using string length times 10 as index
• Using ASCII code directly without modulus
• Using character count without range check