The quadratic probing strategy has a clustering problem related to the way it looks for open slots. Namely, when a collision occurs at bucket h(k), it checks buckets A[(h(k) +i2) mod N], for i = 1,2,…,N −1.a. Show that i2 mod N will assume at most (N + 1)/2 distinct values, for N prime, as i ranges from 1 to N −1. As a part of this justification, note that i2 mod N = (N −i)2 mod N for all i.b. A better strategy is to choose a prime N such that N mod 4 = 3 and then to check the buckets A[(h(k)±i2) mod N] as i ranges from 1 to (N −1)/2, alternating between plus and minus. Show that this alternate version is guaranteed to check every bucket in A.
The quadratic probing strategy has a clustering problem related to the way it looks for open…
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