Why are Hash Tables always doubled?

To maintain consistent performance, the hash table has to be resized - be it growing or shrinking. The trigger to resize depends on the load factor, which is defined as the ratio of the number of keys that the hash table holds to the total number of slots.

When should we resize?

The Hash Table is resized when the load factor hits a certain threshold. If we get too aggressive or too lenient, we would not be able to get the optimal efficiency. Hence, we have to find a sweet spot.

We typically grow the hash table when the load factor hits 0.5 and shrink when we hit 0.125.

Why do we always double?

We have heard and seen so many times, that when a Hash Table is required to grow, we always double the underlying array; but why? Can we not just increase it by 1 every time we are trying to insert?

Resizing by 1 every time

Let’s take an example: say, we grow the array by 1 every time we insert an element in the Hash Table. Let’s compute the time it requires to fill n elements.

Inserting the 1st element is: allocating an array of size 1, and inserting 1 element; so in all O(1) operations.

Inserting the 2nd element is: allocating an array of size 2, copying 1 element from the old array, and then inserting the 2nd element; so in all O(2) operations.

Hence, inserting the nth element is: allocating an array of size n, copying n-1 elements from the old array, and then inserting the nth element; so in all O(n) operations.

Total operations to insert n elements = 1 + 2 + … + n = (n(n-1))/2 which is O(n^2).

Doubling every time

If we double every time, inserting n elements requires O(n) time, as it is spacing out an expensive resize operation. We would be inserting n/2 elements before resizing the array to 2n.

Note: For a detailed amortized analysis, please refer to the video attached here, where I have explained the reasoning in depth.

Why is a hash table array always a power of 2?

For a power of 2, the MOD and the bitwise AND spit out the same result and given that the bitwise AND is a magnitude faster than the MOD, we get the best performance out of our Hash Tables when we use AND

(i % 2^k) == (i & (2^k) - 1)

This is why the length of the underlying array is always a power of 2, making our most-frequent operation efficient.

Shrinking the Hash Table

To ensure we are not wasting space, we trigger the shrink when we do not utilize the underlying array enough. While triggering a shrink, we also need to ensure that we are not aggressive enough that we have to grow immediately after the shrink.

Hence, we shrink the hash table when the load factor hits 1/8 i.e. in a table of length 64 if we are only holding 8 keys, we trigger a shrink and that reduces the length to 32.

Note: To understand why we do it at load factor = 1/8, please refer to the video.

Here's the video ⤵