Quadratic Probing

h(k,i) = (h(k) + c₁i + c₂ i²) mod m

• Only certain combination of c₁, c₂, and m use the entire hash table.
• h(k₁,0) = h(k₂,0) implies h(k₁,i) = h(k₂,i). This leads to secondary clustering.
• There are only m (<<m!) distinct probe sequences.

Example

h(k₁,i) = (h(k) + i + i²) mod m, c₁ = c₂ = 1

In this example, the probe sequence is

h(k)

h(k) + 2

h(k) + 6

h(k) + 12

...

What if m = 20?