Why is a hash table lookup only O(1) time when searching for a key is O(n)?

Question

Technically speaking, based on posts I\'ve read here, Hash table is indeed O(n) time lookup in the worst case. But I don\'t get how the internal mechanics guarantee it to be

Answer 1

Great question!

Assume

1. We want to map strings to values
2. hashFunction(string) => hashedIndex : int in O(1)
3. valueArray : [any] stores values
4. valueIndex : int is the first empty index in valueArray
5. lookupArray : [int] stores each valueIndex at hashedIndex
6. array lookups are O(1).

// Setting a value

valueArray[valueIndex] = value 

hashedIndex = hashFunction(string)

lookupArray[hashedIndex] = valueIndex


// Looking up a value

hashedIndex = hashFunction(string) // O(1)

valueIndex = lookupArray[hashedIndex]; // O(1) array lookup

value = valueArray[valueIndex]; // O(1) array lookup

Lots of details omitted to answer your question clearly.

Hope that helps!