What is the significance of load factor of a Hash Table?

The load factor of a hash table is a critical metric that significantly impacts its performance and efficiency. It is defined as the ratio of the number of elements (entries) in the hash table to the total number of slots (buckets) available in the table. Mathematically, it is expressed as:

$$ \text{Load Factor} = \frac{\text{Number of Elements}}{\text{Number of Buckets}} $$

Significance of Load Factor

1. Performance Optimization:

   • Lookup Time: The load factor directly influences the average time complexity for search, insertion, and deletion operations in a hash table. A lower load factor generally means fewer collisions, leading to faster average lookup times, typically $$O(1)$$ [1][2][8].
   • Collision Handling: As the load factor increases, the likelihood of collisions also increases. Collisions occur when multiple keys hash to the same index. Effective collision resolution strategies, such as separate chaining or open addressing, are essential to maintain performance [5][7][12].

2. Space-Time Trade-off:

   • Space Efficiency: A higher load factor implies better space utilization since more elements are stored in fewer buckets. However, this comes at the cost of increased collisions and potentially slower operations [2][4][7].
   • Time Efficiency: To maintain efficient operations, hash tables often resize (rehash) when the load factor exceeds a certain threshold. This resizing process involves creating a larger table and rehashing all existing elements, which can be time-consuming but is necessary to keep the load factor within an optimal range [6][13][14].

3. Resizing and Rehashing:

   • Thresholds: Different implementations of hash tables set different thresholds for the maximum load factor. For example, Java's HashMap typically uses a load factor of 0.75, meaning the table is resized when it is 75% full [13][14].
   • Rehashing: When the load factor exceeds the threshold, the hash table is resized, usually by doubling its size, and all elements are rehashed to new positions. This process helps maintain low collision rates and efficient operation [6][12][13].

4. Impact on Different Collision Resolution Methods:

   • Separate Chaining: Hash tables using separate chaining are less sensitive to high load factors because each bucket can store multiple elements using linked lists. However, very high load factors can still degrade performance as the linked lists grow longer [5][7][8].
   • Open Addressing: Hash tables using open addressing (e.g., linear probing, quadratic ...