PHP associative arrays are implemented as ordered hash tables, enabling efficient key-value operations; 1. Insertion: average O(1), worst O(n) due to collisions or resizing; 2. Lookup: average O(1), worst O(n) with collisions; 3. Deletion: average O(1), worst O(n) if many collisions; 4. Key checks (isset/array_key_exists): average O(1), worst O(n); 5. Iteration: O(n) in all cases; 6. array_merge: O(m n); 7. array_keys/array_values: O(n); practical use favors isset() for non-null checks, avoids untrusted keys, minimizes large merges, and treats arrays as fast hash maps with rare but possible performance degradation under adversarial conditions.

PHP associative arrays—also known as associative arrays or simply arrays—are actually ordered hash tables under the hood. This makes them incredibly versatile, allowing key-value storage with mixed key types (strings and integers) and dynamic resizing. When analyzing time complexity, it's essential to understand that PHP arrays are implemented as hash tables, which directly affects the performance of common operations.

Below is an analysis of the time complexity for key operations in PHP associative arrays, based on the underlying hash table implementation.

1. Insertion (Adding an Element)

Operation: $array[$key] = $value;

• Average Case: O(1)
  Insertion involves computing the hash of the key and placing the key-value pair in the appropriate bucket. With a good hash function and sufficient capacity, this is constant time.

• Worst Case: O(n)
  In rare cases, such as a hash collision attack or when the array resizes (rehashing all elements), insertion can degrade to O(n). However, resizing is amortized over many insertions, so average performance remains O(1).

  

Note: PHP uses a mechanism called "incremental rehashing" during expansion, which helps reduce performance spikes.

2. Lookup (Accessing by Key)

Operation: $value = $array[$key];

• Average Case: O(1)
  Hash computation and direct bucket access make lookups very fast.

• Worst Case: O(n)
  Occurs when all keys collide in the same bucket (e.g., due to malicious input or poor hash distribution). In practice, this is mitigated by PHP's internal protections against collision attacks (e.g., SipHash used in PHP 7 ).

3. Deletion (Unset by Key)

Operation: unset($array[$key]);

• Average Case: O(1)
  Finding the element via hash and removing it is typically constant time.

• Worst Case: O(n)
  Only if there are many hash collisions in the target bucket. Otherwise, deletion is efficient.

Note: unset() doesn't immediately compact memory. The internal hash table marks the entry as deleted, which may affect iteration but not lookup performance significantly.

4. Key Existence Check

Operation: array_key_exists($key, $array) or isset($array[$key])

• isset($array[$key]): O(1) average
  Fast hash-based lookup. Returns false for null values (so not suitable if you need to distinguish null from absence).

• array_key_exists($key, $array): O(1) average
  Also hash-based, but returns true even if the value is null.

• Worst Case: O(n) due to collisions (same as lookup).

5. Iteration (Using foreach)

Operation: foreach ($array as $key => $value)

• Time Complexity: O(n)
  Iterating over all elements takes linear time, as each element is visited exactly once, regardless of key distribution.

Note: PHP arrays maintain internal ordering (insertion order), so iteration order is predictable.

6. Array Merging

Operation: array_merge($a, $b)

• Time Complexity: O(m n)
  Where m and n are the number of elements in the two arrays. Each element is copied, and string keys are rehashed. Numeric keys are reindexed, which adds overhead.

Note: Merging large arrays can be expensive due to rehashing and memory allocation.

7. Getting All Keys or Values

Operations: array_keys($array), array_values($array)

• Time Complexity: O(n)
  Both functions must traverse the entire array and return a new array with keys or values.

Summary of Time Complexities

Practical Implications

• Use isset() for fast key checks when you don’t need to distinguish null from absence.
• Avoid using associative arrays with untrusted keys in security-sensitive contexts (though PHP mitigates hash flooding).
• For large datasets, consider object storage or specialized data structures if performance becomes a bottleneck.
• Repeated merging or copying of large arrays can be costly—consider references or lazy evaluation.

In most real-world applications, PHP associative arrays perform efficiently due to optimized hash table implementation. While worst-case scenarios exist, they are rare in practice. Understanding these complexities helps in writing scalable PHP code, especially in performance-critical applications.

Basically, treat PHP arrays as fast hash maps—great for average-case O(1) operations, but be mindful of edge cases.

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