Chaining Analysis

Expected number of steps to discover an item k is not in the hash table:

• We need to look at each item in the list T[h(k)].
• Under our uniform-hashing assumption, the h(k) slot looks like all the others.
• What's the expected number of keys in a slot?
• By ``linearity of expectation'', the expected number of keys in a slot j is equal to .

So, running time is proportional to the load factor: .