Analyze the prove uniform hashing gives <=1/(1-alpha) expected unsuccessful probes.
Examples
Input:"test_input_1"
Output:"output_1"
Input:"test_input_2"
Output:"output_2"
Hints
Recall that uniform hashing assumes each key is equally likely to hash to any of the m slots, independent of other keys.
Model the unsuccessful search as a sequence of independent trials, where each trial fails with probability α (load factor) until the first success occurs.
Recognize that the expected number of trials follows a geometric distribution with success probability (1 - α), and derive the expectation using the formula for the geometric distribution.