Hash Table Load Factor and Resizing Mechanism

Description:
The load factor is a crucial performance parameter in hash tables, defined as the ratio of the current number of elements to the total number of slots in the hash table (i.e., Load Factor = Number of Elements / Hash Table Size). It measures the "fullness" of the hash table. When the load factor becomes too high, the probability of hash collisions increases significantly, causing the time complexity of operations like search and insertion to degrade (from O(1) to O(n) in the worst case). Therefore, when the load factor exceeds a predefined threshold, the hash table triggers a resizing (Rehashing) operation. This involves creating a larger new array and rehashing all existing key-value pairs into the new array, thereby reducing the load factor and maintaining operational efficiency.

Solution Process:

1. Understanding the Role of Load Factor

   • The load factor directly affects the trade-off between space utilization and time efficiency in a hash table.
   • If the load factor is too low (e.g., 0.1), it indicates many empty slots, leading to significant space waste, but the probability of collisions is low, and operations are fast.
   • If the load factor is too high (e.g., 0.9), space utilization is high, but collisions occur frequently, causing chains (or the collision resolution structure) to lengthen and performance to degrade.
   • Therefore, a reasonable threshold (e.g., Java HashMap's default of 0.75) must be set to balance space and efficiency.

2. Resizing Trigger Condition

   • Assume the current hash table size is capacity, the number of stored elements is size, and the load factor threshold is loadFactorThreshold (e.g., 0.75).
   • Resizing is triggered when, after inserting a new element, the condition size / capacity > loadFactorThreshold is met.
   • Example: Table size is 10, threshold is 0.75. When inserting the 8th element (8/10 = 0.8 > 0.75), resizing is required.

3. Specific Steps of Resizing

   • Allocate a New Array: The new size is typically double the original size (or another prime number to reduce hash value clustering). For example, if the original size is 10, the new size becomes 20.
   • Rehash: Iterate through each slot in the original hash table and perform the following operations for each key-value pair:
     1. Recalculate the slot index for the key in the new array using the hash function (newIndex = hash(key) % newCapacity).
     2. Insert the key-value pair into the corresponding position in the new array (the collision resolution strategy remains unchanged, e.g., separate chaining still appends to a linked list).
   • Release the Original Array: After all elements are migrated, the original array is reclaimed, and the hash table instance is updated to reference the new array.

4. Performance Analysis of Resizing

   • The time complexity of the resizing operation is O(n) because it requires traversing all elements.
   • However, since resizing does not occur frequently, amortized analysis shows that the average time complexity of insertion operations remains O(1).
   • Optimization strategy: Pre-allocate space during resizing to avoid frequent insertions and deletions near the threshold causing repeated resizing.

5. Example Illustration

   • Initial state: Table size is 4, threshold is 0.75, current number of elements is 0.
   • After inserting 3 elements, load factor = 3/4 = 0.75, no resizing.
   • Before inserting the 4th element, check: 4/4 = 1.0 > 0.75, trigger resizing.
   • New table size becomes 8. Rehash the original 3 elements into the new table, then insert the 4th element.
   • The load factor is now reduced to 4/8 = 0.5, and performance is restored.

Through these steps, the hash table can automatically adjust its size when the load factor becomes too high, ensuring efficient operations.