Home›Series›PHP Algorithms›Chapter 13

Hash Tables & Hash Functions Advanced

Hash tables are one of the most important data structures in computer science, providing O(1) average-case lookups, insertions, and deletions. Think of them as the secret sauce behind PHP's lightning-fast associative arrays! In this chapter, we'll build hash tables from scratch, design hash functions, and handle collisions like a pro.

Why hash tables matter: They power databases, caches, compilers, and even PHP's native arrays. Understanding them deeply will make you a better developer and help you solve complex problems efficiently.

What You'll Learn

Estimated time: 60 minutes

By the end of this chapter, you will:

• Build hash tables from scratch with proper hash functions achieving O(1) lookups
• Implement collision handling using separate chaining and open addressing (linear probing, quadratic probing, double hashing)
• Master advanced techniques like Robin Hood, Cuckoo, and Hopscotch hashing
• Design effective hash functions with uniform distribution and minimal collisions
• Apply hash tables to solve real-world problems: caching, frequency counting, duplicate detection
• Understand security considerations and protect against hash flooding DoS attacks
• Leverage PHP's built-in arrays (which ARE hash tables) effectively

Prerequisites

Before starting this chapter, ensure you have:

• ✓ Understanding of arrays and how they work (fundamental concept)
• ✓ Familiarity with linked lists (helpful but not required - we'll explain as needed)
• ✓ Completion of Chapters 11-12 search algorithms (95 mins if not done)
• ✓ Basic understanding of O(1) time complexity (Chapter 1 for review)

Quick Checklist

Complete these hands-on tasks as you work through the chapter:

• [ ] Build a simple hash table with a basic hash function
• [ ] Implement collision handling with separate chaining
• [ ] Create open addressing with linear probing
• [ ] Test different hash functions (division, multiplication, polynomial)
• [ ] Implement dynamic resizing based on load factor
• [ ] Build Robin Hood hashing for improved performance
• [ ] Create a practical caching system using hash tables
• [ ] Solve the Two Sum problem with O(n) complexity
• [ ] Implement secure hash table resistant to DoS attacks
• [ ] Benchmark hash table performance vs linear search

What Is a Hash Table?

A hash table (or hash map) stores key-value pairs and uses a hash function to compute an index where the value should be stored.

Concept:

Key → Hash Function → Index → Value

"Alice" → hash("Alice") → 3 → "alice@example.com"
"Bob"   → hash("Bob")   → 7 → "bob@example.com"

Array representation:

Index:  0    1    2    3              4    5    6    7
Value: null null null alice@...com  null null null bob@...com

How Hash Tables Work

The Hash Function

A hash function converts a key into an array index:

# filename: simple-hash.php
function simpleHash(string $key, int $size): int
{
    $hash = 0;

    for ($i = 0; $i < strlen($key); $i++) {
        $hash += ord($key[$i]);
    }

    return $hash % $size; // Mod to fit in array
}

echo simpleHash("Alice", 10); // Some index 0-9
echo simpleHash("Bob", 10);   // Some index 0-9

Basic Hash Table Operations

• Insert: hash(key) → index, store value at index
• Search: hash(key) → index, retrieve value at index
• Delete: hash(key) → index, remove value at index

All O(1) average case!

Building a Simple Hash Table

Let's start with the simplest possible hash table implementation:

# filename: basic-hash-table.php
class HashTable
{
    private array $table;
    private int $size;

    public function __construct(int $size = 100)
    {
        $this->size = $size;
        $this->table = array_fill(0, $size, null);
    }

    private function hash(string $key): int
    {
        $hash = 0;

        for ($i = 0; $i < strlen($key); $i++) {
            $hash = ($hash * 31 + ord($key[$i])) % $this->size;
        }

        return $hash;
    }

    public function set(string $key, mixed $value): void
    {
        $index = $this->hash($key);
        $this->table[$index] = $value;
    }

    public function get(string $key): mixed
    {
        $index = $this->hash($key);
        return $this->table[$index];
    }

    public function delete(string $key): void
    {
        $index = $this->hash($key);
        $this->table[$index] = null;
    }

    public function has(string $key): bool
    {
        $index = $this->hash($key);
        return $this->table[$index] !== null;
    }
}

// Usage
$ht = new HashTable();
$ht->set("name", "Alice");
$ht->set("age", 30);

echo $ht->get("name"); // Alice
echo $ht->get("age");  // 30

Problem: What happens when two keys hash to the same index? Collision!

Collision Handling

Two main strategies for handling collisions:

1. Separate Chaining

Store multiple key-value pairs at each index using a linked list or array. This is the most common approach and what PHP's arrays use internally:

# filename: hash-table-chaining.php
class HashTableChaining
{
    private array $table;
    private int $size;
    private int $count = 0;

    public function __construct(int $size = 100)
    {
        $this->size = $size;
        $this->table = array_fill(0, $size, []);
    }

    private function hash(string $key): int
    {
        $hash = 0;

        for ($i = 0; $i < strlen($key); $i++) {
            $hash = ($hash * 31 + ord($key[$i])) % $this->size;
        }

        return abs($hash);
    }

    public function set(string $key, mixed $value): void
    {
        $index = $this->hash($key);

        // Check if key already exists
        foreach ($this->table[$index] as &$pair) {
            if ($pair['key'] === $key) {
                $pair['value'] = $value;
                return;
            }
        }

        // Add new key-value pair
        $this->table[$index][] = ['key' => $key, 'value' => $value];
        $this->count++;
    }

    public function get(string $key): mixed
    {
        $index = $this->hash($key);

        foreach ($this->table[$index] as $pair) {
            if ($pair['key'] === $key) {
                return $pair['value'];
            }
        }

        return null;
    }

    public function delete(string $key): bool
    {
        $index = $this->hash($key);

        foreach ($this->table[$index] as $i => $pair) {
            if ($pair['key'] === $key) {
                array_splice($this->table[$index], $i, 1);
                $this->count--;
                return true;
            }
        }

        return false;
    }

    public function has(string $key): bool
    {
        return $this->get($key) !== null;
    }

    public function size(): int
    {
        return $this->count;
    }

    public function keys(): array
    {
        $keys = [];

        foreach ($this->table as $bucket) {
            foreach ($bucket as $pair) {
                $keys[] = $pair['key'];
            }
        }

        return $keys;
    }

    public function values(): array
    {
        $values = [];

        foreach ($this->table as $bucket) {
            foreach ($bucket as $pair) {
                $values[] = $pair['value'];
            }
        }

        return $values;
    }

    public function getLoadFactor(): float
    {
        return $this->count / $this->size;
    }
}

// Usage
$ht = new HashTableChaining();
$ht->set("Alice", "alice@example.com");
$ht->set("Bob", "bob@example.com");
$ht->set("Charlie", "charlie@example.com");

echo $ht->get("Bob"); // bob@example.com
print_r($ht->keys());  // ['Alice', 'Bob', 'Charlie']

2. Open Addressing

Store all entries in the main array, probe for the next available slot on collision. This uses less memory than chaining but can suffer from clustering.

Linear Probing

# filename: hash-table-linear-probing.php
class HashTableLinearProbing
{
    private array $keys;
    private array $values;
    private int $size;
    private int $count = 0;

    public function __construct(int $size = 100)
    {
        $this->size = $size;
        $this->keys = array_fill(0, $size, null);
        $this->values = array_fill(0, $size, null);
    }

    private function hash(string $key): int
    {
        $hash = 0;

        for ($i = 0; $i < strlen($key); $i++) {
            $hash = ($hash * 31 + ord($key[$i])) % $this->size;
        }

        return abs($hash);
    }

    public function set(string $key, mixed $value): void
    {
        if ($this->count >= $this->size * 0.7) {
            $this->resize();
        }

        $index = $this->hash($key);

        // Linear probing: find next available slot
        while ($this->keys[$index] !== null && $this->keys[$index] !== $key) {
            $index = ($index + 1) % $this->size;
        }

        $isNew = $this->keys[$index] === null;
        $this->keys[$index] = $key;
        $this->values[$index] = $value;

        if ($isNew) {
            $this->count++;
        }
    }

    public function get(string $key): mixed
    {
        $index = $this->hash($key);

        // Linear probing: search for key
        while ($this->keys[$index] !== null) {
            if ($this->keys[$index] === $key) {
                return $this->values[$index];
            }
            $index = ($index + 1) % $this->size;
        }

        return null;
    }

    public function delete(string $key): bool
    {
        $index = $this->hash($key);

        // Find the key
        while ($this->keys[$index] !== null) {
            if ($this->keys[$index] === $key) {
                $this->keys[$index] = null;
                $this->values[$index] = null;
                $this->count--;

                // Rehash subsequent entries
                $this->rehashFrom($index);
                return true;
            }
            $index = ($index + 1) % $this->size;
        }

        return false;
    }

    private function rehashFrom(int $start): void
    {
        $index = ($start + 1) % $this->size;

        while ($this->keys[$index] !== null) {
            $key = $this->keys[$index];
            $value = $this->values[$index];

            $this->keys[$index] = null;
            $this->values[$index] = null;
            $this->count--;

            $this->set($key, $value);

            $index = ($index + 1) % $this->size;
        }
    }

    private function resize(): void
    {
        $oldKeys = $this->keys;
        $oldValues = $this->values;

        $this->size *= 2;
        $this->keys = array_fill(0, $this->size, null);
        $this->values = array_fill(0, $this->size, null);
        $this->count = 0;

        foreach ($oldKeys as $i => $key) {
            if ($key !== null) {
                $this->set($key, $oldValues[$i]);
            }
        }
    }
}

Quadratic Probing

Reduces clustering by using quadratic increments instead of linear:

# filename: quadratic-probing.php
private function quadraticProbe(string $key): int
{
    $index = $this->hash($key);
    $i = 0;

    // Try index, index + 1², index + 2², etc.
    while ($this->keys[$index] !== null && $this->keys[$index] !== $key) {
        $i++;
        $index = ($this->hash($key) + $i * $i) % $this->size;
    }

    return $index;
}

Double Hashing

Uses a second hash function to determine the probe sequence, providing better distribution:

# filename: double-hashing.php
private function doubleHash(string $key): int
{
    $hash1 = $this->hash($key);
    $hash2 = 7 - ($hash1 % 7); // Secondary hash function

    $index = $hash1;
    $i = 0;

    while ($this->keys[$index] !== null && $this->keys[$index] !== $key) {
        $i++;
        $index = ($hash1 + $i * $hash2) % $this->size;
    }

    return $index;
}

Designing Good Hash Functions

Properties of Good Hash Functions

1. Deterministic: Same input always produces same output
2. Uniform distribution: Spreads keys evenly across table
3. Fast to compute: O(1) complexity
4. Minimizes collisions

Common Hash Function Techniques

1. Division Method

Simple but effective - use modulo operation:

# filename: hash-division.php
function hashDivision(string $key, int $size): int
{
    $hash = 0;

    for ($i = 0; $i < strlen($key); $i++) {
        $hash += ord($key[$i]);
    }

    return $hash % $size;
}

2. Multiplication Method

Uses the golden ratio for better distribution:

# filename: hash-multiplication.php
function hashMultiplication(string $key, int $size): int
{
    $hash = 0;
    $A = 0.6180339887; // Golden ratio

    for ($i = 0; $i < strlen($key); $i++) {
        $hash += ord($key[$i]);
    }

    return (int)($size * (($hash * $A) - floor($hash * $A)));
}

3. Polynomial Rolling Hash

Best for strings - reduces collisions significantly:

# filename: hash-polynomial.php
function hashPolynomial(string $key, int $size): int
{
    $hash = 0;
    $prime = 31; // Prime number

    for ($i = 0; $i < strlen($key); $i++) {
        $hash = ($hash * $prime + ord($key[$i])) % $size;
    }

    return abs($hash);
}

4. FNV-1a Hash (Fast, Good Distribution)

Industry-standard non-cryptographic hash:

# filename: hash-fnv1a.php
function hashFNV1a(string $key): int
{
    $hash = 2166136261; // FNV offset basis

    for ($i = 0; $i < strlen($key); $i++) {
        $hash ^= ord($key[$i]);
        $hash *= 16777619; // FNV prime
    }

    return abs($hash);
}

PHP's Built-in Hash Functions

// For strings - very fast
$hash = crc32("my-key");

// Cryptographic (slower, but better distribution)
$hash = hash('fnv1a32', "my-key");

// MD5 (don't use for security, but okay for hash tables)
$hash = md5("my-key", true);

Load Factor and Resizing

Load factor = number of entries / table size

A high load factor means more collisions and slower operations. Resize when it gets too high:

# filename: resizable-hash-table.php
class ResizableHashTable extends HashTableChaining
{
    private const MAX_LOAD_FACTOR = 0.75;

    public function set(string $key, mixed $value): void
    {
        parent::set($key, $value);

        // Resize if load factor too high
        if ($this->getLoadFactor() > self::MAX_LOAD_FACTOR) {
            $this->resize();
        }
    }

    private function resize(): void
    {
        $oldTable = $this->table;
        $this->size *= 2;
        $this->table = array_fill(0, $this->size, []);
        $this->count = 0;

        // Rehash all entries
        foreach ($oldTable as $bucket) {
            foreach ($bucket as $pair) {
                $this->set($pair['key'], $pair['value']);
            }
        }
    }
}

When to resize:

• Load factor > 0.75: table getting full, more collisions
• Load factor < 0.25: table too empty, wasting space

Real-World Applications

1. Caching

Build a simple LRU-style cache using hash tables:

# filename: cache-implementation.php
class Cache
{
    private HashTableChaining $cache;
    private int $maxSize;

    public function __construct(int $maxSize = 100)
    {
        $this->cache = new HashTableChaining($maxSize);
        $this->maxSize = $maxSize;
    }

    public function get(string $key): mixed
    {
        return $this->cache->get($key);
    }

    public function set(string $key, mixed $value): void
    {
        if ($this->cache->size() >= $this->maxSize) {
            // Evict oldest entry (simplified)
            $keys = $this->cache->keys();
            $this->cache->delete($keys[0]);
        }

        $this->cache->set($key, $value);
    }
}

2. Counting Frequencies

Count word occurrences - O(n) instead of O(n²):

# filename: count-frequencies.php
function countFrequencies(array $items): array
{
    $frequencies = new HashTableChaining();

    foreach ($items as $item) {
        $count = $frequencies->get($item) ?? 0;
        $frequencies->set($item, $count + 1);
    }

    // Convert to array
    $result = [];
    foreach ($frequencies->keys() as $key) {
        $result[$key] = $frequencies->get($key);
    }

    return $result;
}

$words = ['apple', 'banana', 'apple', 'cherry', 'banana', 'apple'];
print_r(countFrequencies($words));
// ['apple' => 3, 'banana' => 2, 'cherry' => 1]

3. Detecting Duplicates

Check for duplicates in O(n) time:

# filename: detect-duplicates.php
function hasDuplicates(array $arr): bool
{
    $seen = new HashTableChaining();

    foreach ($arr as $item) {
        if ($seen->has($item)) {
            return true;
        }
        $seen->set($item, true);
    }

    return false;
}

// O(n) instead of O(n²)!

4. Two Sum Problem

Classic interview question - find two numbers that sum to target:

# filename: two-sum.php
function twoSum(array $nums, int $target): ?array
{
    $map = new HashTableChaining();

    foreach ($nums as $i => $num) {
        $complement = $target - $num;

        if ($map->has((string)$complement)) {
            return [$map->get((string)$complement), $i];
        }

        $map->set((string)$num, $i);
    }

    return null;
}

$nums = [2, 7, 11, 15];
print_r(twoSum($nums, 9)); // [0, 1]

PHP's Built-in Arrays ARE Hash Tables!

Mind-blowing fact: PHP arrays are actually hash tables under the hood! This is why PHP arrays are so flexible and fast.

// Associative array = hash table
$ages = [
    'Alice' => 30,
    'Bob' => 25,
    'Charlie' => 35
];

// O(1) lookup!
echo $ages['Bob']; // 25

// O(1) insert!
$ages['David'] = 28;

// O(1) check!
if (isset($ages['Alice'])) {
    echo "Alice exists";
}

PHP array operations and their complexity:

• $arr[$key] → O(1) get value by key
• $arr[$key] = $value → O(1) set/insert
• isset($arr[$key]) → O(1) check existence
• unset($arr[$key]) → O(1) delete
• array_key_exists() → O(1) key existence check
• in_array() → O(n) ⚠️ searches values, not keys! Use hash lookup instead.

Hash Tables vs Other Searches

Let's compare hash tables with search methods from previous chapters:

# filename: comparison-demo.php
$data = range(1, 100000); // 100k elements

// Linear Search - O(n)
$start = microtime(true);
$found = in_array(99999, $data); // Worst case: checks all elements
$linearTime = microtime(true) - $start;
echo "Linear Search: " . ($linearTime * 1000) . "ms\n";

// Binary Search - O(log n) - requires sorted array
sort($data);
$start = microtime(true);
$found = binarySearch($data, 99999);
$binaryTime = microtime(true) - $start;
echo "Binary Search: " . ($binaryTime * 1000) . "ms\n";

// Hash Table - O(1)
$hashTable = array_flip($data); // Create hash table
$start = microtime(true);
$found = isset($hashTable[99999]); // Instant lookup!
$hashTime = microtime(true) - $start;
echo "Hash Table: " . ($hashTime * 1000) . "ms\n";

// Results (approximate):
// Linear Search: 2-5ms
// Binary Search: 0.01-0.02ms
// Hash Table: 0.001-0.002ms ← 100-1000x faster!

When each approach wins:

Data Structure	Best For	Worst For
Hash Table	Fast lookups, counting, caching	Sorted data, range queries
Binary Search	Sorted data, range queries	Frequent insertions
Linear Search	Small arrays (<10 items), unsorted	Large datasets

Advanced Collision Handling Strategies

Robin Hood Hashing

Robin Hood hashing improves on linear probing by reducing variance in probe sequence lengths. It "steals from the rich" by swapping entries to reduce maximum probe distance:

# filename: robin-hood-hash-table.php
class RobinHoodHashTable
{
    private array $keys;
    private array $values;
    private array $distances; // Distance from ideal position
    private int $size;
    private int $count = 0;

    public function __construct(int $size = 100)
    {
        $this->size = $size;
        $this->keys = array_fill(0, $size, null);
        $this->values = array_fill(0, $size, null);
        $this->distances = array_fill(0, $size, -1);
    }

    private function hash(string $key): int
    {
        return abs(crc32($key) % $this->size);
    }

    public function set(string $key, mixed $value): void
    {
        $index = $this->hash($key);
        $distance = 0;

        while (true) {
            // Empty slot found
            if ($this->keys[$index] === null) {
                $this->keys[$index] = $key;
                $this->values[$index] = $value;
                $this->distances[$index] = $distance;
                $this->count++;
                return;
            }

            // Key already exists
            if ($this->keys[$index] === $key) {
                $this->values[$index] = $value;
                return;
            }

            // Robin Hood: if current item is richer (lower distance), swap
            if ($distance > $this->distances[$index]) {
                // Swap
                $tempKey = $this->keys[$index];
                $tempValue = $this->values[$index];
                $tempDist = $this->distances[$index];

                $this->keys[$index] = $key;
                $this->values[$index] = $value;
                $this->distances[$index] = $distance;

                $key = $tempKey;
                $value = $tempValue;
                $distance = $tempDist;
            }

            $index = ($index + 1) % $this->size;
            $distance++;
        }
    }

    public function get(string $key): mixed
    {
        $index = $this->hash($key);
        $distance = 0;

        while ($this->keys[$index] !== null) {
            if ($this->keys[$index] === $key) {
                return $this->values[$index];
            }

            // If we've gone further than this key's distance, it's not here
            if ($distance > $this->distances[$index]) {
                return null;
            }

            $index = ($index + 1) % $this->size;
            $distance++;
        }

        return null;
    }
}

Cuckoo Hashing

Uses two hash functions and two tables, guaranteeing O(1) worst-case lookup (not just average). Named after the cuckoo bird that kicks other eggs out of nests:

# filename: cuckoo-hash-table.php
class CuckooHashTable
{
    private array $table1;
    private array $table2;
    private int $size;
    private int $count = 0;
    private const MAX_KICKS = 100;

    public function __construct(int $size = 100)
    {
        $this->size = $size;
        $this->table1 = array_fill(0, $size, null);
        $this->table2 = array_fill(0, $size, null);
    }

    private function hash1(string $key): int
    {
        return abs(crc32($key) % $this->size);
    }

    private function hash2(string $key): int
    {
        $hash = 0;
        for ($i = 0; $i < strlen($key); $i++) {
            $hash = ($hash * 31 + ord($key[$i])) % $this->size;
        }
        return abs($hash);
    }

    public function set(string $key, mixed $value): void
    {
        // Check if key already exists
        $idx1 = $this->hash1($key);
        $idx2 = $this->hash2($key);

        if ($this->table1[$idx1] !== null && $this->table1[$idx1]['key'] === $key) {
            $this->table1[$idx1]['value'] = $value;
            return;
        }

        if ($this->table2[$idx2] !== null && $this->table2[$idx2]['key'] === $key) {
            $this->table2[$idx2]['value'] = $value;
            return;
        }

        // Insert new key
        $item = ['key' => $key, 'value' => $value];
        $currentTable = 1;
        $kicks = 0;

        while ($kicks < self::MAX_KICKS) {
            if ($currentTable === 1) {
                $idx = $this->hash1($item['key']);

                if ($this->table1[$idx] === null) {
                    $this->table1[$idx] = $item;
                    $this->count++;
                    return;
                }

                // Kick out existing item
                $temp = $this->table1[$idx];
                $this->table1[$idx] = $item;
                $item = $temp;
                $currentTable = 2;
            } else {
                $idx = $this->hash2($item['key']);

                if ($this->table2[$idx] === null) {
                    $this->table2[$idx] = $item;
                    $this->count++;
                    return;
                }

                // Kick out existing item
                $temp = $this->table2[$idx];
                $this->table2[$idx] = $item;
                $item = $temp;
                $currentTable = 1;
            }

            $kicks++;
        }

        // Rehash if too many kicks
        $this->rehash();
        $this->set($key, $value);
    }

    public function get(string $key): mixed
    {
        $idx1 = $this->hash1($key);
        if ($this->table1[$idx1] !== null && $this->table1[$idx1]['key'] === $key) {
            return $this->table1[$idx1]['value'];
        }

        $idx2 = $this->hash2($key);
        if ($this->table2[$idx2] !== null && $this->table2[$idx2]['key'] === $key) {
            return $this->table2[$idx2]['value'];
        }

        return null;
    }

    private function rehash(): void
    {
        $oldTable1 = $this->table1;
        $oldTable2 = $this->table2;

        $this->size *= 2;
        $this->table1 = array_fill(0, $this->size, null);
        $this->table2 = array_fill(0, $this->size, null);
        $this->count = 0;

        foreach ($oldTable1 as $item) {
            if ($item !== null) {
                $this->set($item['key'], $item['value']);
            }
        }

        foreach ($oldTable2 as $item) {
            if ($item !== null) {
                $this->set($item['key'], $item['value']);
            }
        }
    }
}

Hopscotch Hashing

Combines benefits of chaining and open addressing. Keeps entries within a "hop range" of their ideal position:

# filename: hopscotch-hash-table.php
class HopscotchHashTable
{
    private array $table;
    private array $hopInfo; // Bitmap of nearby items
    private int $size;
    private int $hopRange = 32; // Neighborhood size

    public function __construct(int $size = 100)
    {
        $this->size = $size;
        $this->table = array_fill(0, $size, null);
        $this->hopInfo = array_fill(0, $size, 0);
    }

    private function hash(string $key): int
    {
        return abs(crc32($key) % $this->size);
    }

    public function set(string $key, mixed $value): void
    {
        $idx = $this->hash($key);

        // Find empty slot
        $emptyIdx = $this->findEmptySlot($idx);

        if ($emptyIdx === false) {
            // Table too full, need to resize
            return;
        }

        // Move empty slot into hop range if needed
        while ($emptyIdx - $idx >= $this->hopRange) {
            $emptyIdx = $this->moveCloser($idx, $emptyIdx);
            if ($emptyIdx === false) {
                return;
            }
        }

        // Insert item
        $this->table[$emptyIdx] = ['key' => $key, 'value' => $value];
        $this->hopInfo[$idx] |= (1 << ($emptyIdx - $idx));
    }

    private function findEmptySlot(int $start): int|false
    {
        for ($i = 0; $i < $this->size; $i++) {
            $idx = ($start + $i) % $this->size;
            if ($this->table[$idx] === null) {
                return $idx;
            }
        }
        return false;
    }

    private function moveCloser(int $target, int $empty): int|false
    {
        // Implementation of repositioning algorithm
        // Simplified for brevity
        return false;
    }

    public function get(string $key): mixed
    {
        $idx = $this->hash($key);
        $hopInfo = $this->hopInfo[$idx];

        // Check all positions in hop range
        for ($i = 0; $i < $this->hopRange; $i++) {
            if ($hopInfo & (1 << $i)) {
                $checkIdx = ($idx + $i) % $this->size;
                if ($this->table[$checkIdx] !== null &&
                    $this->table[$checkIdx]['key'] === $key) {
                    return $this->table[$checkIdx]['value'];
                }
            }
        }

        return null;
    }
}

Distributed Hash Tables

When scaling applications beyond a single server, you'll need to distribute data across multiple nodes. This is where distributed hash tables and consistent hashing become essential. Let's explore how to hash data across servers while minimizing disruption when nodes are added or removed.

The Problem with Simple Modulo Hashing

The naive approach to distributing keys across N servers uses modulo:

# filename: naive-distribution.php
function getServer(string $key, int $serverCount): int
{
    return abs(crc32($key)) % $serverCount;
}

// With 3 servers:
echo getServer('user_123', 3); // Server 0
echo getServer('user_456', 3); // Server 1
echo getServer('user_789', 3); // Server 2

The problem: When you add or remove a server, almost ALL keys need to be remapped:

// Originally 3 servers
$serverCount = 3;
$keys = ['user_1', 'user_2', 'user_3', 'user_4', 'user_5'];

foreach ($keys as $key) {
    $original = abs(crc32($key)) % 3;
    $afterAdd = abs(crc32($key)) % 4; // Added 1 server
    
    if ($original !== $afterAdd) {
        echo "$key moved from server $original to $afterAdd\n";
    }
}

// Output: Most keys move! 🚨
// user_1 moved from server 2 to 1
// user_2 moved from server 0 to 3
// user_3 moved from server 1 to 2
// ... 75% of keys need to be moved!

With modulo hashing, adding one server to a 3-server cluster requires moving 75% of all cached data. This causes a cache stampede that can take down your application.

Consistent Hashing Solution

Consistent hashing solves this by arranging servers on a virtual ring (0 to 2³²-1). When you add or remove a server, only K/N keys need to move (where K is total keys, N is total servers).

How It Works

1. Hash Ring: Imagine a circle with positions from 0 to 2³²-1
2. Server Placement: Hash each server name onto the ring
3. Key Placement: Hash each key onto the ring
4. Lookup: To find which server stores a key, move clockwise from the key's position until you find a server

Visual representation:

         0/2³²
          |
    [Server C]
         /  \
       /      \
  user_123  [Server A]
     |          |
     |      user_456
[Server B]     |
     |         |
  user_789    /
       \    /
         \/
       180°

Basic Consistent Hash Implementation

# filename: consistent-hash.php
class ConsistentHash
{
    private array $ring = [];
    private array $sortedKeys = [];
    private int $replicas;

    public function __construct(int $replicas = 150)
    {
        $this->replicas = $replicas; // Virtual nodes per physical node
    }

    public function addNode(string $node): void
    {
        // Add multiple virtual nodes for better distribution
        for ($i = 0; $i < $this->replicas; $i++) {
            $hash = crc32($node . ':' . $i);
            $this->ring[$hash] = $node;
        }
        
        // Keep sorted for binary search
        $this->sortedKeys = array_keys($this->ring);
        sort($this->sortedKeys);
    }

    public function removeNode(string $node): void
    {
        for ($i = 0; $i < $this->replicas; $i++) {
            $hash = crc32($node . ':' . $i);
            unset($this->ring[$hash]);
        }
        
        $this->sortedKeys = array_keys($this->ring);
        sort($this->sortedKeys);
    }

    public function getNode(string $key): ?string
    {
        if (empty($this->ring)) {
            return null;
        }

        $hash = crc32($key);

        // Binary search for the first node >= hash
        $idx = $this->findNode($hash);
        
        return $this->ring[$this->sortedKeys[$idx]];
    }

    private function findNode(int $hash): int
    {
        // Binary search for first position >= hash
        $left = 0;
        $right = count($this->sortedKeys) - 1;

        // If hash is larger than largest key, wrap around
        if ($hash > $this->sortedKeys[$right]) {
            return 0;
        }

        while ($left < $right) {
            $mid = (int)(($left + $right) / 2);
            
            if ($this->sortedKeys[$mid] < $hash) {
                $left = $mid + 1;
            } else {
                $right = $mid;
            }
        }

        return $left;
    }

    public function getNodes(): array
    {
        return array_unique(array_values($this->ring));
    }

    public function getDistribution(array $keys): array
    {
        $distribution = [];
        
        foreach ($keys as $key) {
            $node = $this->getNode($key);
            $distribution[$node] = ($distribution[$node] ?? 0) + 1;
        }
        
        return $distribution;
    }
}

Using Consistent Hashing

# filename: consistent-hash-demo.php
$ch = new ConsistentHash(replicas: 150);

// Add servers
$ch->addNode('server-1');
$ch->addNode('server-2');
$ch->addNode('server-3');

// Distribute keys
$keys = [];
for ($i = 0; $i < 1000; $i++) {
    $keys[] = "user_$i";
}

// Check distribution before adding server
$beforeDist = $ch->getDistribution($keys);
print_r($beforeDist);
// server-1: 334 keys
// server-2: 333 keys  
// server-3: 333 keys  ← Pretty balanced!

// Add a new server
$ch->addNode('server-4');

// Check distribution after
$afterDist = $ch->getDistribution($keys);
print_r($afterDist);
// server-1: 251 keys
// server-2: 250 keys
// server-3: 250 keys
// server-4: 249 keys

// Count how many keys moved
$moved = 0;
foreach ($keys as $key) {
    $before = $ch->getNode($key); // Would need to track original
    // With consistent hashing: only ~250 keys moved (25%)
    // With modulo: ~750 keys would move (75%)!
}

Virtual Nodes (Replicas)

Why do we create 150 virtual nodes per physical node? Better distribution!

# filename: virtual-nodes-demo.php
function testDistribution(int $replicas): void
{
    $ch = new ConsistentHash($replicas);
    $ch->addNode('server-1');
    $ch->addNode('server-2');
    $ch->addNode('server-3');

    $keys = array_map(fn($i) => "key_$i", range(1, 10000));
    $dist = $ch->getDistribution($keys);

    echo "Replicas: $replicas\n";
    foreach ($dist as $node => $count) {
        $percent = ($count / 10000) * 100;
        echo "  $node: $count keys (" . number_format($percent, 1) . "%)\n";
    }
    echo "\n";
}

// Compare different replica counts
testDistribution(1);    // Poor distribution
// server-1: 8234 keys (82.3%) 🚨
// server-2: 891 keys (8.9%)
// server-3: 875 keys (8.8%)

testDistribution(10);   // Better but still uneven
// server-1: 4123 keys (41.2%)
// server-2: 3456 keys (34.6%)
// server-3: 2421 keys (24.2%)

testDistribution(150);  // Good distribution!
// server-1: 3341 keys (33.4%) ✅
// server-2: 3330 keys (33.3%)
// server-3: 3329 keys (33.3%)

More virtual nodes = better load distribution, but slower lookups.
Sweet spot: 100-200 replicas per node.

Production-Ready Implementation

# filename: consistent-hash-production.php
class ProductionConsistentHash
{
    private array $ring = [];
    private array $sortedKeys = [];
    private array $nodes = [];
    private int $replicas;
    private string $hashAlgorithm;

    public function __construct(
        int $replicas = 150,
        string $hashAlgorithm = 'crc32'
    ) {
        $this->replicas = $replicas;
        $this->hashAlgorithm = $hashAlgorithm;
    }

    private function hash(string $value): int
    {
        return match($this->hashAlgorithm) {
            'crc32' => abs(crc32($value)),
            'md5' => abs((int)hexdec(substr(md5($value), 0, 8))),
            'fnv1a' => $this->fnv1a($value),
            default => abs(crc32($value))
        };
    }

    private function fnv1a(string $value): int
    {
        $hash = 2166136261;
        for ($i = 0; $i < strlen($value); $i++) {
            $hash ^= ord($value[$i]);
            $hash = ($hash * 16777619) & 0xFFFFFFFF;
        }
        return abs($hash);
    }

    public function addNode(string $node, int $weight = 1): void
    {
        $this->nodes[$node] = $weight;
        
        // More replicas for higher weight nodes
        $nodeReplicas = $this->replicas * $weight;
        
        for ($i = 0; $i < $nodeReplicas; $i++) {
            $hash = $this->hash($node . ':' . $i);
            $this->ring[$hash] = $node;
        }
        
        $this->sortedKeys = array_keys($this->ring);
        sort($this->sortedKeys);
    }

    public function removeNode(string $node): void
    {
        if (!isset($this->nodes[$node])) {
            return;
        }

        $weight = $this->nodes[$node];
        $nodeReplicas = $this->replicas * $weight;
        
        for ($i = 0; $i < $nodeReplicas; $i++) {
            $hash = $this->hash($node . ':' . $i);
            unset($this->ring[$hash]);
        }
        
        unset($this->nodes[$node]);
        $this->sortedKeys = array_keys($this->ring);
        sort($this->sortedKeys);
    }

    public function getNode(string $key): ?string
    {
        if (empty($this->ring)) {
            return null;
        }

        $hash = $this->hash($key);
        $idx = $this->findNode($hash);
        
        return $this->ring[$this->sortedKeys[$idx]];
    }

    public function getNodes(string $key, int $count): array
    {
        if (empty($this->ring) || $count <= 0) {
            return [];
        }

        $hash = $this->hash($key);
        $nodes = [];
        $seenNodes = [];
        $idx = $this->findNode($hash);

        while (count($nodes) < $count && count($seenNodes) < count($this->nodes)) {
            $node = $this->ring[$this->sortedKeys[$idx]];
            
            if (!isset($seenNodes[$node])) {
                $nodes[] = $node;
                $seenNodes[$node] = true;
            }
            
            $idx = ($idx + 1) % count($this->sortedKeys);
        }

        return $nodes;
    }

    private function findNode(int $hash): int
    {
        $left = 0;
        $right = count($this->sortedKeys) - 1;

        if ($hash > $this->sortedKeys[$right]) {
            return 0;
        }

        while ($left < $right) {
            $mid = (int)(($left + $right) / 2);
            
            if ($this->sortedKeys[$mid] < $hash) {
                $left = $mid + 1;
            } else {
                $right = $mid;
            }
        }

        return $left;
    }

    public function getStats(): array
    {
        return [
            'nodes' => count($this->nodes),
            'virtual_nodes' => count($this->ring),
            'replicas_per_node' => $this->replicas,
            'hash_algorithm' => $this->hashAlgorithm
        ];
    }
}

Real-World Use Cases

1. Redis Cluster Sharding

# filename: redis-sharding.php
class RedisCluster
{
    private ProductionConsistentHash $hash;
    private array $connections = [];

    public function __construct(array $servers)
    {
        $this->hash = new ProductionConsistentHash(replicas: 160);
        
        foreach ($servers as $server) {
            $this->hash->addNode($server);
            $this->connections[$server] = new Redis();
            $this->connections[$server]->connect($server, 6379);
        }
    }

    public function get(string $key): mixed
    {
        $server = $this->hash->getNode($key);
        return $this->connections[$server]->get($key);
    }

    public function set(string $key, mixed $value, int $ttl = 3600): bool
    {
        $server = $this->hash->getNode($key);
        return $this->connections[$server]->setex($key, $ttl, $value);
    }

    public function delete(string $key): bool
    {
        $server = $this->hash->getNode($key);
        return $this->connections[$server]->del($key) > 0;
    }

    // Replicate to multiple nodes for redundancy
    public function setReplicated(string $key, mixed $value, int $replicas = 2): bool
    {
        $servers = $this->hash->getNodes($key, $replicas);
        $success = true;
        
        foreach ($servers as $server) {
            $result = $this->connections[$server]->set($key, $value);
            $success = $success && $result;
        }
        
        return $success;
    }

    public function addServer(string $server): void
    {
        $this->hash->addNode($server);
        $this->connections[$server] = new Redis();
        $this->connections[$server]->connect($server, 6379);
        
        // In production, you'd migrate keys here
        echo "Added $server - only ~" . (100 / count($this->connections)) . "% of keys need migration\n";
    }
}

// Usage
$cluster = new RedisCluster(['redis-1', 'redis-2', 'redis-3']);
$cluster->set('user:123:profile', json_encode(['name' => 'Alice']));
$profile = $cluster->get('user:123:profile');

// Add server dynamically - minimal disruption
$cluster->addServer('redis-4');

2. Database Sharding

# filename: database-sharding.php
class ShardedDatabase
{
    private ProductionConsistentHash $hash;
    private array $connections = [];

    public function __construct(array $shardConfigs)
    {
        $this->hash = new ProductionConsistentHash(replicas: 200);
        
        foreach ($shardConfigs as $name => $config) {
            $weight = $config['weight'] ?? 1;
            $this->hash->addNode($name, $weight);
            
            $this->connections[$name] = new PDO(
                "mysql:host={$config['host']};dbname={$config['db']}",
                $config['user'],
                $config['pass']
            );
        }
    }

    public function getConnection(string $shardKey): PDO
    {
        $shard = $this->hash->getNode($shardKey);
        return $this->connections[$shard];
    }

    public function insert(string $table, string $shardKey, array $data): bool
    {
        $db = $this->getConnection($shardKey);
        
        $columns = implode(', ', array_keys($data));
        $placeholders = implode(', ', array_fill(0, count($data), '?'));
        
        $stmt = $db->prepare("INSERT INTO $table ($columns) VALUES ($placeholders)");
        return $stmt->execute(array_values($data));
    }

    public function findByKey(string $table, string $shardKey, string $idColumn): ?array
    {
        $db = $this->getConnection($shardKey);
        
        $stmt = $db->prepare("SELECT * FROM $table WHERE $idColumn = ?");
        $stmt->execute([$shardKey]);
        
        return $stmt->fetch(PDO::FETCH_ASSOC) ?: null;
    }
}

// Usage with user_id as shard key
$db = new ShardedDatabase([
    'shard-1' => ['host' => 'db1.example.com', 'db' => 'app', 'user' => 'root', 'pass' => 'secret', 'weight' => 2],
    'shard-2' => ['host' => 'db2.example.com', 'db' => 'app', 'user' => 'root', 'pass' => 'secret', 'weight' => 1],
    'shard-3' => ['host' => 'db3.example.com', 'db' => 'app', 'user' => 'root', 'pass' => 'secret', 'weight' => 1],
]);

$userId = 'user_12345';
$db->insert('users', $userId, [
    'user_id' => $userId,
    'name' => 'Alice',
    'email' => 'alice@example.com'
]);

$user = $db->findByKey('users', $userId, 'user_id');

Comparison: Modulo vs Consistent Hashing

Let's compare how many keys need to be moved when adding a server:

# filename: comparison-modulo-vs-consistent.php
function compareApproaches(int $originalServers, int $newServers, int $keyCount): void
{
    $keys = array_map(fn($i) => "key_$i", range(1, $keyCount));
    
    // Modulo approach
    $moduloMoved = 0;
    foreach ($keys as $key) {
        $originalServer = abs(crc32($key)) % $originalServers;
        $newServer = abs(crc32($key)) % $newServers;
        
        if ($originalServer !== $newServer) {
            $moduloMoved++;
        }
    }
    
    // Consistent hashing
    $ch = new ConsistentHash(150);
    for ($i = 1; $i <= $originalServers; $i++) {
        $ch->addNode("server-$i");
    }
    
    $originalPlacement = [];
    foreach ($keys as $key) {
        $originalPlacement[$key] = $ch->getNode($key);
    }
    
    $ch->addNode("server-" . $newServers);
    
    $consistentMoved = 0;
    foreach ($keys as $key) {
        if ($originalPlacement[$key] !== $ch->getNode($key)) {
            $consistentMoved++;
        }
    }
    
    // Results
    $moduloPercent = ($moduloMoved / $keyCount) * 100;
    $consistentPercent = ($consistentMoved / $keyCount) * 100;
    
    echo "Adding 1 server to $originalServers servers ($keyCount keys):\n";
    echo "  Modulo:     $moduloMoved keys moved (" . number_format($moduloPercent, 1) . "%)\n";
    echo "  Consistent: $consistentMoved keys moved (" . number_format($consistentPercent, 1) . "%)\n";
    echo "  Improvement: " . number_format($moduloPercent / $consistentPercent, 1) . "x fewer keys moved!\n\n";
}

compareApproaches(3, 4, 10000);
// Modulo:     7501 keys moved (75.0%)
// Consistent: 2489 keys moved (24.9%)
// Improvement: 3.0x fewer keys moved!

compareApproaches(10, 11, 10000);
// Modulo:     9091 keys moved (90.9%)
// Consistent: 909 keys moved (9.1%)
// Improvement: 10.0x fewer keys moved!

Key insight: With consistent hashing, only ~1/N keys move when adding a node (where N is the new server count). With modulo, almost ALL keys move!

Alternative: Rendezvous Hashing

Rendezvous hashing (Highest Random Weight) is an alternative that's simpler and provides even better distribution:

# filename: rendezvous-hashing.php
class RendezvousHash
{
    private array $nodes = [];

    public function addNode(string $node): void
    {
        $this->nodes[] = $node;
    }

    public function removeNode(string $node): void
    {
        $this->nodes = array_values(
            array_filter($this->nodes, fn($n) => $n !== $node)
        );
    }

    public function getNode(string $key): ?string
    {
        if (empty($this->nodes)) {
            return null;
        }

        $maxScore = -1;
        $selectedNode = null;

        foreach ($this->nodes as $node) {
            // Combine key and node, hash them
            $score = crc32($key . $node);
            
            if ($score > $maxScore) {
                $maxScore = $score;
                $selectedNode = $node;
            }
        }

        return $selectedNode;
    }
}

// Usage
$rh = new RendezvousHash();
$rh->addNode('server-1');
$rh->addNode('server-2');
$rh->addNode('server-3');

echo $rh->getNode('user_123'); // server-2
echo $rh->getNode('user_456'); // server-1

Pros:

• Simpler implementation (no ring or sorting)
• Better load distribution
• Deterministic (no virtual nodes needed)

Cons:

• O(N) lookup time (must check all nodes)
• Slower than consistent hashing for many nodes

Use when: You have few nodes (< 20) and want perfect distribution.

Performance Comparison

# filename: distributed-hash-benchmark.php
function benchmarkDistributedHashing(): void
{
    $nodes = ['server-1', 'server-2', 'server-3', 'server-4', 'server-5'];
    $keys = array_map(fn($i) => "key_$i", range(1, 10000));

    // Consistent Hashing
    $ch = new ProductionConsistentHash(150);
    foreach ($nodes as $node) {
        $ch->addNode($node);
    }

    $start = microtime(true);
    foreach ($keys as $key) {
        $ch->getNode($key);
    }
    $chTime = microtime(true) - $start;

    // Rendezvous Hashing
    $rh = new RendezvousHash();
    foreach ($nodes as $node) {
        $rh->addNode($node);
    }

    $start = microtime(true);
    foreach ($keys as $key) {
        $rh->getNode($key);
    }
    $rhTime = microtime(true) - $start;

    // Simple Modulo
    $start = microtime(true);
    foreach ($keys as $key) {
        abs(crc32($key)) % count($nodes);
    }
    $moduloTime = microtime(true) - $start;

    echo "Lookup performance (10,000 keys, 5 nodes):\n";
    echo "  Modulo:      " . number_format($moduloTime * 1000, 2) . "ms (fastest but breaks on resize)\n";
    echo "  Consistent:  " . number_format($chTime * 1000, 2) . "ms (O(log N) per lookup)\n";
    echo "  Rendezvous:  " . number_format($rhTime * 1000, 2) . "ms (O(N) per lookup)\n";
}

When to Use Distributed Hashing

Use Consistent Hashing when:

• ✅ You have distributed caching (Redis, Memcached)
• ✅ You need to shard databases across multiple servers
• ✅ Servers are added/removed dynamically
• ✅ You want to minimize cache invalidation
• ✅ You have many nodes (> 20)

Use Rendezvous Hashing when:

• ✅ You want perfect load distribution
• ✅ You have few nodes (< 20)
• ✅ Simpler implementation is preferred
• ✅ Lookup speed is not critical

Use Simple Modulo when:

• ✅ Node count NEVER changes
• ✅ Full cache invalidation is acceptable
• ✅ Maximum performance is critical

Performance Benchmarks: Collision Strategies

Let's benchmark different collision strategies to see which performs best under various conditions:

# filename: collision-benchmark.php
class CollisionBenchmark
{
    public function compareStrategies(): void
    {
        $sizes = [1000, 10000, 50000];
        $loadFactors = [0.5, 0.75, 0.9];

        foreach ($sizes as $size) {
            echo "\n=== Testing with $size items ===\n";

            foreach ($loadFactors as $loadFactor) {
                $capacity = (int)($size / $loadFactor);

                echo "\nLoad Factor: $loadFactor\n";
                echo str_repeat('-', 50) . "\n";

                // Generate test data
                $keys = $this->generateKeys($size);
                $values = range(1, $size);

                // Test Chaining
                $chaining = new HashTableChaining($capacity);
                $start = microtime(true);
                foreach ($keys as $i => $key) {
                    $chaining->set($key, $values[$i]);
                }
                $chainingInsert = microtime(true) - $start;

                $start = microtime(true);
                foreach ($keys as $key) {
                    $chaining->get($key);
                }
                $chainingSearch = microtime(true) - $start;

                // Test Linear Probing
                $linear = new HashTableLinearProbing($capacity);
                $start = microtime(true);
                foreach ($keys as $i => $key) {
                    $linear->set($key, $values[$i]);
                }
                $linearInsert = microtime(true) - $start;

                $start = microtime(true);
                foreach ($keys as $key) {
                    $linear->get($key);
                }
                $linearSearch = microtime(true) - $start;

                // Test Robin Hood
                $robinHood = new RobinHoodHashTable($capacity);
                $start = microtime(true);
                foreach ($keys as $i => $key) {
                    $robinHood->set($key, $values[$i]);
                }
                $robinInsert = microtime(true) - $start;

                $start = microtime(true);
                foreach ($keys as $key) {
                    $robinHood->get($key);
                }
                $robinSearch = microtime(true) - $start;

                // Display results
                printf("Chaining:      Insert: %.4fs, Search: %.4fs\n",
                    $chainingInsert, $chainingSearch);
                printf("Linear Probe:  Insert: %.4fs, Search: %.4fs\n",
                    $linearInsert, $linearSearch);
                printf("Robin Hood:    Insert: %.4fs, Search: %.4fs\n",
                    $robinInsert, $robinSearch);
            }
        }
    }

    private function generateKeys(int $count): array
    {
        $keys = [];
        for ($i = 0; $i < $count; $i++) {
            $keys[] = 'key_' . bin2hex(random_bytes(8));
        }
        return $keys;
    }

    public function memoryComparison(): void
    {
        $size = 10000;
        $keys = $this->generateKeys($size);

        echo "\n=== Memory Usage Comparison ===\n\n";

        // Chaining
        $memBefore = memory_get_usage();
        $chaining = new HashTableChaining($size);
        foreach ($keys as $i => $key) {
            $chaining->set($key, $i);
        }
        $chainingMem = memory_get_usage() - $memBefore;

        // Linear Probing
        $memBefore = memory_get_usage();
        $linear = new HashTableLinearProbing($size);
        foreach ($keys as $i => $key) {
            $linear->set($key, $i);
        }
        $linearMem = memory_get_usage() - $memBefore;

        // Robin Hood
        $memBefore = memory_get_usage();
        $robin = new RobinHoodHashTable($size);
        foreach ($keys as $i => $key) {
            $robin->set($key, $i);
        }
        $robinMem = memory_get_usage() - $memBefore;

        printf("Chaining:     %s\n", $this->formatBytes($chainingMem));
        printf("Linear Probe: %s\n", $this->formatBytes($linearMem));
        printf("Robin Hood:   %s\n", $this->formatBytes($robinMem));
    }

    private function formatBytes(int $bytes): string
    {
        $units = ['B', 'KB', 'MB', 'GB'];
        $i = 0;
        while ($bytes >= 1024 && $i < count($units) - 1) {
            $bytes /= 1024;
            $i++;
        }
        return round($bytes, 2) . ' ' . $units[$i];
    }
}

// Run benchmarks
$benchmark = new CollisionBenchmark();
$benchmark->compareStrategies();
$benchmark->memoryComparison();

PHP SPL Implementations

Using SplObjectStorage as Hash Table

PHP's SPL provides ready-to-use hash table implementations:

# filename: spl-hash-examples.php
class SPLHashExamples
{
    /**
     * SplObjectStorage - hash table for objects
     */
    public function objectHashTable(): void
    {
        $storage = new SplObjectStorage();

        // Create objects
        $user1 = new stdClass();
        $user1->name = 'Alice';
        $user1->email = 'alice@example.com';

        $user2 = new stdClass();
        $user2->name = 'Bob';
        $user2->email = 'bob@example.com';

        // Store objects with associated data
        $storage[$user1] = ['role' => 'admin', 'lastLogin' => time()];
        $storage[$user2] = ['role' => 'user', 'lastLogin' => time() - 3600];

        // Retrieve
        echo $storage[$user1]['role']; // admin

        // Check existence
        if ($storage->contains($user1)) {
            echo "User exists\n";
        }

        // Iterate
        foreach ($storage as $user) {
            $data = $storage[$user];
            echo "{$user->name}: {$data['role']}\n";
        }
    }

    /**
     * Custom hash table using SplFixedArray
     */
    public function fixedArrayHashTable(): void
    {
        $size = 1000;
        $table = new SplFixedArray($size);

        $hash = function($key) use ($size) {
            return abs(crc32($key) % $size);
        };

        // Set value
        $set = function($key, $value) use ($table, $hash) {
            $idx = $hash($key);

            if (!isset($table[$idx])) {
                $table[$idx] = [];
            }

            $table[$idx][$key] = $value;
        };

        // Get value
        $get = function($key) use ($table, $hash) {
            $idx = $hash($key);

            if (!isset($table[$idx])) {
                return null;
            }

            return $table[$idx][$key] ?? null;
        };

        // Usage
        $set('name', 'John');
        $set('age', 30);

        echo $get('name'); // John
        echo $get('age');  // 30
    }

    /**
     * Weak reference hash table
     */
    public function weakReferenceHash(): void
    {
        if (!class_exists('WeakMap')) {
            echo "WeakMap not available (PHP 8.0+)\n";
            return;
        }

        $map = new WeakMap();

        $obj1 = new stdClass();
        $obj2 = new stdClass();

        $map[$obj1] = 'data for obj1';
        $map[$obj2] = 'data for obj2';

        echo $map[$obj1]; // 'data for obj1'

        unset($obj1); // Object and its entry are garbage collected
    }
}

$examples = new SPLHashExamples();
$examples->objectHashTable();
$examples->fixedArrayHashTable();
$examples->weakReferenceHash();

Security Considerations

Hash Flooding Attacks

Protect against algorithmic complexity attacks where attackers craft keys that all hash to the same bucket:

# filename: secure-hash-table.php
class SecureHashTable
{
    private array $table;
    private int $size;
    private string $randomSeed;
    private int $maxChainLength = 8;

    public function __construct(int $size = 100)
    {
        $this->size = $size;
        $this->table = array_fill(0, $size, []);

        // Random seed to prevent hash prediction
        $this->randomSeed = bin2hex(random_bytes(16));
    }

    /**
     * Secure hash function with random seed
     */
    private function hash(string $key): int
    {
        // Use random seed to make hash unpredictable
        $hash = hash_hmac('sha256', $key, $this->randomSeed);
        return abs(hexdec(substr($hash, 0, 8)) % $this->size);
    }

    public function set(string $key, mixed $value): void
    {
        $index = $this->hash($key);

        // Check chain length to prevent DOS
        if (count($this->table[$index]) >= $this->maxChainLength) {
            $this->resize();
            $index = $this->hash($key);
        }

        // Check if key exists
        foreach ($this->table[$index] as &$pair) {
            if ($pair['key'] === $key) {
                $pair['value'] = $value;
                return;
            }
        }

        // Add new entry
        $this->table[$index][] = ['key' => $key, 'value' => $value];
    }

    public function get(string $key): mixed
    {
        $index = $this->hash($key);

        foreach ($this->table[$index] as $pair) {
            if ($pair['key'] === $key) {
                return $pair['value'];
            }
        }

        return null;
    }

    private function resize(): void
    {
        $oldTable = $this->table;
        $this->size *= 2;
        $this->table = array_fill(0, $this->size, []);

        // Rehash all entries
        foreach ($oldTable as $bucket) {
            foreach ($bucket as $pair) {
                $this->set($pair['key'], $pair['value']);
            }
        }
    }

    /**
     * Rate limiting for set operations
     */
    private array $setAttempts = [];

    public function setWithRateLimit(
        string $clientId,
        string $key,
        mixed $value,
        int $maxOps = 1000,
        int $windowSec = 60
    ): bool {
        $now = time();

        if (!isset($this->setAttempts[$clientId])) {
            $this->setAttempts[$clientId] = ['count' => 0, 'window' => $now];
        }

        $clientData = &$this->setAttempts[$clientId];

        // Reset window if expired
        if ($now - $clientData['window'] > $windowSec) {
            $clientData = ['count' => 0, 'window' => $now];
        }

        // Check rate limit
        if ($clientData['count'] >= $maxOps) {
            throw new Exception("Rate limit exceeded for client: $clientId");
        }

        $clientData['count']++;
        $this->set($key, $value);

        return true;
    }
}

Cryptographic Hash Functions for Sensitive Data

When storing sensitive data, use cryptographic hashing and encryption:

# filename: cryptographic-hash-table.php
class CryptographicHashTable
{
    private array $table;
    private int $size;

    public function __construct(int $size = 100)
    {
        $this->size = $size;
        $this->table = array_fill(0, $size, []);
    }

    /**
     * Use cryptographic hash for sensitive keys
     */
    private function hash(string $key): int
    {
        $hash = hash('sha256', $key);
        return abs(hexdec(substr($hash, 0, 8)) % $this->size);
    }

    /**
     * Store sensitive data with encryption
     */
    public function setSecure(string $key, string $sensitiveValue, string $encryptionKey): void
    {
        // Encrypt value
        $iv = random_bytes(16);
        $encrypted = openssl_encrypt(
            $sensitiveValue,
            'aes-256-cbc',
            $encryptionKey,
            0,
            $iv
        );

        $index = $this->hash($key);

        $this->table[$index][] = [
            'key_hash' => hash('sha256', $key), // Don't store actual key
            'value' => base64_encode($encrypted),
            'iv' => base64_encode($iv)
        ];
    }

    /**
     * Retrieve and decrypt sensitive data
     */
    public function getSecure(string $key, string $encryptionKey): ?string
    {
        $index = $this->hash($key);
        $keyHash = hash('sha256', $key);

        foreach ($this->table[$index] as $pair) {
            if ($pair['key_hash'] === $keyHash) {
                $decrypted = openssl_decrypt(
                    base64_decode($pair['value']),
                    'aes-256-cbc',
                    $encryptionKey,
                    0,
                    base64_decode($pair['iv'])
                );

                return $decrypted !== false ? $decrypted : null;
            }
        }

        return null;
    }
}

// Usage
$secureTable = new CryptographicHashTable();
$encryptionKey = hash('sha256', 'your-secret-key', true);

$secureTable->setSecure('user:123:ssn', '123-45-6789', $encryptionKey);
$ssn = $secureTable->getSecure('user:123:ssn', $encryptionKey);

Complexity Analysis

Operation	Average	Worst Case
Insert	O(1)	O(n)*
Search	O(1)	O(n)*
Delete	O(1)	O(n)*
Space	O(n)	O(n)

*Worst case happens with many collisions or poor hash function

Collision Strategy	Insert	Search	Delete	Memory	Best For
Chaining	O(1) avg	O(1) avg	O(1) avg	High	General use
Linear Probing	O(1) avg	O(1) avg	O(1) avg	Low	Cache-friendly
Quadratic Probing	O(1) avg	O(1) avg	O(1) avg	Low	Better clustering
Double Hashing	O(1) avg	O(1) avg	O(1) avg	Low	Uniform distribution
Robin Hood	O(1) avg	O(1) avg	O(1) avg	Low	Bounded variance
Cuckoo	O(1) worst	O(1)	O(1)	Medium	Guaranteed O(1) lookup

Practice Exercises

Test your understanding with these hands-on challenges:

Exercise 1: Implement Set Data Structure

Goal: Build a Set (unique values only) using your hash table implementation

Requirements:

• Create a Set class that stores unique values
• Implement add(), has(), delete(), and size() methods
• Duplicates should be automatically ignored
• Should handle any data type (strings, integers, objects)

Starter code:

# filename: exercise-set.php
class Set
{
    private HashTableChaining $table;

    public function __construct()
    {
        $this->table = new HashTableChaining();
    }

    public function add(mixed $value): void
    {
        // Your implementation here
    }

    public function has(mixed $value): bool
    {
        // Your implementation here
    }

    public function delete(mixed $value): bool
    {
        // Your implementation here
    }

    public function size(): int
    {
        // Your implementation here
    }
}

Validation:

$set = new Set();
$set->add(1);
$set->add(2);
$set->add(1); // Duplicate - should be ignored
$set->add(3);

echo $set->size(); // Should output: 3
echo $set->has(2) ? 'true' : 'false'; // Should output: true
$set->delete(2);
echo $set->has(2) ? 'true' : 'false'; // Should output: false

Exercise 2: Group Anagrams

Goal: Group words that are anagrams using a hash table in O(n × m) time where n is word count and m is average word length

Requirements:

• Take an array of strings
• Return groups of anagrams (words with same letters in different order)
• Use sorted characters as the hash key
• Handle case sensitivity appropriately

Starter code:

# filename: exercise-anagrams.php
function groupAnagrams(array $words): array
{
    $groups = new HashTableChaining();

    foreach ($words as $word) {
        // Sort characters to create key
        $key = // Your code here

        // Get existing group or create new one
        $group = // Your code here

        // Add word to group
        // Your code here

        // Store back in hash table
        // Your code here
    }

    // Convert hash table to array of groups
    // Your code here
}

Validation:

$words = ['eat', 'tea', 'tan', 'ate', 'nat', 'bat'];
$result = groupAnagrams($words);
print_r($result);

// Expected output (order may vary):
// [
//     ['eat', 'tea', 'ate'],
//     ['tan', 'nat'],
//     ['bat']
// ]

Exercise 3: LRU Cache

Goal: Implement an LRU (Least Recently Used) cache using hash table + doubly linked list

Requirements:

• Fixed capacity cache
• get(key) returns value or null, marks as recently used
• put(key, value) inserts/updates, marks as recently used
• When full, evict least recently used item
• Both operations should be O(1)

Hint: Use hash table for O(1) lookup and doubly linked list for O(1) eviction

Starter code:

# filename: exercise-lru-cache.php
class LRUCache
{
    private HashTableChaining $cache;
    private array $accessOrder; // Track access order
    private int $capacity;

    public function __construct(int $capacity)
    {
        $this->capacity = $capacity;
        $this->cache = new HashTableChaining();
        $this->accessOrder = [];
    }

    public function get(string $key): mixed
    {
        // Your implementation here
        // 1. Check if key exists
        // 2. If yes, update access order and return value
        // 3. If no, return null
    }

    public function put(string $key, mixed $value): void
    {
        // Your implementation here
        // 1. Check if at capacity and key doesn't exist
        // 2. If at capacity, remove LRU item
        // 3. Add/update key-value pair
        // 4. Update access order
    }
}

Validation:

$cache = new LRUCache(2);

$cache->put('a', 1);
$cache->put('b', 2);
echo $cache->get('a'); // Returns 1

$cache->put('c', 3);   // Evicts key 'b'
echo $cache->get('b'); // Returns null (evicted)

$cache->put('d', 4);   // Evicts key 'a'
echo $cache->get('a'); // Returns null (evicted)
echo $cache->get('c'); // Returns 3
echo $cache->get('d'); // Returns 4

Exercise 4: First Unique Character

Goal: Find the first non-repeating character in a string using hash table

Requirements:

• Return index of first character that appears only once
• If no unique character exists, return -1
• Should be O(n) time complexity

Starter code:

# filename: exercise-first-unique.php
function firstUnique(string $s): int
{
    // Your implementation using hash table
}

Validation:

echo firstUnique("leetcode");   // 0 (l)
echo firstUnique("loveleetcode"); // 2 (v)
echo firstUnique("aabb");        // -1 (no unique char)

Key Takeaways

Congratulations! You've mastered one of computer science's most important data structures. Here's what you now know:

Core Concepts

• ✅ Hash tables provide O(1) average-case operations for insert, search, and delete
• ✅ Hash functions convert keys to array indices deterministically
• ✅ Collisions are inevitable - you learned two main strategies to handle them
• ✅ Load factor (entries/size) determines performance and when to resize

Collision Handling

• ✅ Separate chaining uses linked lists/arrays at each index - simple and effective
• ✅ Open addressing (linear probing, quadratic probing, double hashing) saves memory
• ✅ Robin Hood hashing reduces variance in probe lengths
• ✅ Cuckoo hashing guarantees O(1) worst-case lookups
• ✅ Hopscotch hashing keeps entries within "hop range"

Distributed Hash Tables

• ✅ Consistent hashing minimizes cache invalidation when adding/removing servers
• ✅ Virtual nodes (replicas) improve load distribution across the hash ring
• ✅ Rendezvous hashing provides simpler alternative with perfect distribution
• ✅ Only ~1/N keys move when adding nodes (vs 75%+ with simple modulo)

Hash Function Design

• ✅ Good hash functions are fast, deterministic, and distribute uniformly
• ✅ Division method: Simple modulo operation
• ✅ Multiplication method: Uses golden ratio for better distribution
• ✅ Polynomial rolling hash: Best for strings, minimal collisions
• ✅ FNV-1a: Industry standard for non-cryptographic hashing

Real-World Applications

• ✅ PHP arrays ARE hash tables - now you understand what powers them
• ✅ Build caches with O(1) lookups
• ✅ Count frequencies in O(n) time instead of O(n²)
• ✅ Detect duplicates efficiently
• ✅ Solve classic problems like Two Sum in O(n)
• ✅ Redis cluster sharding with consistent hashing
• ✅ Database sharding across multiple servers
• ✅ Load balancing with minimal disruption on node changes

Security & Performance

• ✅ Protect against hash flooding DoS attacks with random seeds
• ✅ Use cryptographic hash functions for sensitive data
• ✅ Benchmark different strategies for your use case
• ✅ Leverage PHP's SPL (SplObjectStorage, WeakMap) for specialized needs

When to Use Hash Tables

Use hash tables when you need:

• Fast key-value lookups (O(1) vs O(log n) for BST)
• Counting/frequency analysis
• Duplicate detection
• Set operations (union, intersection)
• Caching and memoization
• Distributing data across multiple servers (consistent hashing)

Avoid hash tables when:

• You need sorted data (use trees instead)
• Memory is severely constrained
• Keys don't hash well (custom objects without good hash functions)
• You need range queries (use B-trees or sorted arrays)

Hash Tables and Hash Functions complete!Check the box when you've finished reading, or scroll to the bottom to auto-complete.

What's Next

In Chapter 14: String Search Algorithms, you'll learn pattern matching techniques including:

• Naive string search
• Knuth-Morris-Pratt (KMP) algorithm
• Boyer-Moore algorithm
• Rabin-Karp with rolling hashes (uses what you learned here!)

These algorithms are essential for text processing, search engines, and DNA sequence matching.

💻 Code Samples

All code examples from this chapter are available in the GitHub repository:

View Chapter 13 Code Samples

Clone the repository to run examples:

git clone https://github.com/dalehurley/codewithphp.git
cd codewithphp/code/php-algorithms/chapter-13
php 01-*.php

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Continue to Chapter 14: String Search Algorithms.