Q.Suppose a list has more than one element whose modulo division results in same remainder value. In such situations, what kind of hashing may be useful?

This is a plain theory question asking which hashing technique handles collisions when multiple elements hash to the same index.

When multiple elements produce the same hash value (same remainder after modulo division), a collision occurs. The question asks which hashing method is useful in such situations.

Separate chaining is the technique designed precisely for this scenario. Instead of storing a single element at each index of the hash table, separate chaining maintains a linked list (or any dynamic collection) at each bucket. When a collision occurs, the new element is simply appended to the list at that index.

For example, if we hash the keys {12, 22, 32} into a table of size 10 using hash(key) = key % 10, all three map to index 2. With separate chaining:

• Index 2 contains a linked list: 12 → 22 → 32
• Search, insert, and delete operations traverse this list. …

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Hashing maps keys to array indices using a hash function. When you use modulo division — say hash(key) = key % table_size — different keys can produce the same remainder. For example, if the table size is 10, both 23 and 43 hash to index 3. This is a collision.

The question asks which hashing technique handles collisions when modulo division is the hash function. Two main families exist:

Separate Chaining (Open Hashing)

Each slot in the hash table holds a linked list (or another dynamic structure like a Python list). When a collision occurs, the new element is simply appended to the list at that index.

Why it works well here:

• No limit on the number of elements that can hash to the same index.
• Simple to implement: insert, search, and delete operations just traverse the chain.
• The table never "fills up" in the traditional sense; performance degrades gracefully as chains grow longer.

Example: Hash table of size 5, inserting keys 12, 22, 32 (all hash to index 2):

Open Addressing (Closed Hashing)

When a collision occurs, the algorithm probes for the next available slot in the table itself using a sequence: linear probing ((h + i) % size), quadratic probing ((h + i²) % size), or double hashing. All elements live directly in the array, no auxiliary structures.

Trade-offs:

• The table can fill up (load factor α ≤ 1).
• Clustering can degrade performance (especially with linear probing).
• Deletion is more complex (requires tombstones or rehashing).

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Python Example: Separate Chaining

class HashTable:
    def __init__(self, size=10):
        self.size = size …