Collision Handling Using Chaining in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of inserting keys with chaining

What is the state of the hash table after inserting keys 10, 22, 31, 4, 15 using chaining with hash function h(key) = key % 10?

DSA Python

class HashTable:
    def __init__(self):
        self.size = 10
        self.table = [[] for _ in range(self.size)]

    def hash_function(self, key):
        return key % self.size

    def insert(self, key):
        index = self.hash_function(key)
        self.table[index].append(key)

ht = HashTable()
keys = [10, 22, 31, 4, 15]
for key in keys:
    ht.insert(key)

print(ht.table)

A [[], [10, 22, 31, 4, 15], [], [], [], [], [], [], [], []]

B [[10], [22], [31], [4], [15], [], [], [], [], []]

C [[10, 22, 31, 4, 15], [], [], [], [], [], [], [], [], []]

D [[10], [31], [22], [], [4], [15], [], [], [], []]

💡 Hint

Remember the hash function is key % 10, and collisions are handled by adding keys to the list at that index.

Hashes: 10%10=0, 22%10=2, 31%10=1, 4%10=4, 15%10=5. The table becomes [[10], [31], [22], [], [4], [15], [], [], [], []].

❓ Predict Output

intermediate

Output after deleting a key in chaining hash table

Given the hash table with chaining below, what is the state after deleting key 22? Initial table: [[10], [31], [22, 42], [], [4], [15], [], [], [], []] Hash function: h(key) = key % 10

DSA Python

class HashTable:
    def __init__(self):
        self.size = 10
        self.table = [[10], [31], [22, 42], [], [4], [15], [], [], [], []]

    def hash_function(self, key):
        return key % self.size

    def delete(self, key):
        index = self.hash_function(key)
        if key in self.table[index]:
            self.table[index].remove(key)

ht = HashTable()
ht.delete(22)
print(ht.table)

A [[10], [31], [], [], [4], [15], [], [], [], []]

B [[10], [31], [42], [], [4], [15], [], [], [], []]

C [[10], [31], [22, 42], [], [4], [15], [], [], [], []]

D [[10], [31], [42, 22], [], [4], [15], [], [], [], []]

💡 Hint

Deleting a key removes it from the list at the hashed index.

Key 22 is in the list at index 2. Removing it leaves [42] at index 2.

🔧 Debug

advanced

Identify the error in chaining insertion

What error does the following code raise when inserting keys 5 and 15? Code: class HashTable: def __init__(self): self.size = 10 self.table = [None] * self.size def hash_function(self, key): return key % self.size def insert(self, key): index = self.hash_function(key) self.table[index].append(key) ht = HashTable() ht.insert(5) ht.insert(15)

DSA Python

class HashTable:
    def __init__(self):
        self.size = 10
        self.table = [None] * self.size

    def hash_function(self, key):
        return key % self.size

    def insert(self, key):
        index = self.hash_function(key)
        self.table[index].append(key)

ht = HashTable()
ht.insert(5)
ht.insert(15)

A AttributeError: 'NoneType' object has no attribute 'append'

B IndexError: list index out of range

C TypeError: unsupported operand type(s) for %: 'str' and 'int'

D No error, code runs successfully

💡 Hint

Check how the table is initialized and what type each slot holds before insertion.

The table slots are initialized to None, so calling append on None raises AttributeError.

🧠 Conceptual

advanced

Why use chaining for collision handling?

Which of the following is the main advantage of using chaining to handle collisions in a hash table?

A It uses less memory than open addressing methods.

B It guarantees constant time lookup for all keys regardless of collisions.

C It allows multiple keys to be stored at the same index without overwriting existing keys.

D It avoids the need for a hash function.

💡 Hint

Think about what happens when two keys hash to the same index.

Chaining stores collided keys in a list at the same index, preventing overwriting.

❓ Predict Output

expert

Final hash table state after mixed operations with chaining

Given the hash table with chaining and hash function h(key) = key % 7, what is the state of the table after these operations? Operations: Insert 10 Insert 21 Insert 14 Insert 7 Delete 21 Insert 28 Delete 14 Initial table is empty with size 7.

DSA Python

class HashTable:
    def __init__(self):
        self.size = 7
        self.table = [[] for _ in range(self.size)]

    def hash_function(self, key):
        return key % self.size

    def insert(self, key):
        index = self.hash_function(key)
        self.table[index].append(key)

    def delete(self, key):
        index = self.hash_function(key)
        if key in self.table[index]:
            self.table[index].remove(key)

ht = HashTable()
operations = [
    ('insert', 10),
    ('insert', 21),
    ('insert', 14),
    ('insert', 7),
    ('delete', 21),
    ('insert', 28),
    ('delete', 14)
]

for op, key in operations:
    if op == 'insert':
        ht.insert(key)
    else:
        ht.delete(key)

print(ht.table)

A [[7, 28], [], [], [10], [], [], []]

B [[], [7], [], [10, 28], [], [], []]

C [[28], [7], [], [10], [], [], []]

D [[], [7], [], [10], [], [], [28]]

💡 Hint

Calculate the hash index for each key and update the table step-by-step.

Step-by-step (all colliding keys hash to index 0 except 10→3): Insert 10: [[], [], [], [10], [], [], []] Insert 21: [[21], [], [], [10], [], [], []] Insert 14: [[21, 14], [], [], [10], [], [], []] Insert 7: [[21, 14, 7], [], [], [10], [], [], []] Delete 21: [[14, 7], [], [], [10], [], [], []] Insert 28: [[14, 7, 28], [], [], [10], [], [], []] Delete 14: [[7, 28], [], [], [10], [], [], []]