What approaches can be applied to hash tables to efficiently handle increasing object counts and reduce search time?

For efficient operation of a hash table when increasing the number of objects and the need to reduce search time, several approaches are used:

• Dynamic resizing (rehashing): when a certain fill threshold (load factor) is reached, the size of the table is increased and elements are redistributed to new indices, which reduces the number of collisions.

• Choosing a good hash function: the function should evenly distribute keys across the table, minimizing collisions.

• Using collision resolution methods:

  • Open addressing (linear or quadratic probing, double hashing).
  • Chaining (each cell contains a linked list or another structure for storing collisions).

• Optimizing the collision storage structure: for example, with a large number of collisions in chains, balanced trees can be used instead of lists.

• Parallel hash tables: for multi-threaded applications, structures with locking or lock-free implementations are used.

Example of dynamic resizing in Swift:

class HashTable<Key: Hashable, Value> {
    private var buckets: [[(Key, Value)]]
    private(set) var count = 0
    private var capacity: Int
    private let loadFactorThreshold = 0.75

    init(capacity: Int = 16) {
        self.capacity = capacity
        self.buckets = Array(repeating: [], count: capacity)
    }

    private func index(for key: Key) -> Int {
        return abs(key.hashValue) % capacity
    }

    func insert(_ key: Key, value: Value) {
        if Double(count) / Double(capacity) > loadFactorThreshold {
            resize()
        }
        let idx = index(for: key)
        for i in 0..<buckets[idx].count {
            if buckets[idx][i].0 == key {
                buckets[idx][i].1 = value
                return
            }
        }
        buckets[idx].append((key, value))
        count += 1
    }

    func get(_ key: Key) -> Value? {
        let idx = index(for: key)
        return buckets[idx].first(where: { $0.0 == key })?.1
    }

    private func resize() {
        capacity *= 2
        var newBuckets = Array(repeating: [(Key, Value)](), count: capacity)
        for bucket in buckets {
            for (key, value) in bucket {
                let idx = abs(key.hashValue) % capacity
                newBuckets[idx].append((key, value))
            }
        }
        buckets = newBuckets
    }
}