Consider a double hashing scheme in which the primary hash function is $h_1(k) = k \bmod 23$, and the secondary hash function is $h_2(k) = 1 + (k \bmod 19)$. Assume that the table size is 23. Then the address returned by probe 1 in the probe sequence (assume that the probe sequence begins at probe 0) for key value $k = 90$ is ________.

In double hashing, the hash function for probe $i$ (where $i = 0, 1, 2, \dots$) is given by:

Given:

• Table size $m = 23$

• Key $k = 90$

• $h_1(k) = k \bmod 23$

• $h_2(k) = 1 + (k \bmod 19)$

Compute $h_1(90)$ and $h_2(90)$:

• $h_1(90) = 90 \bmod 23 = 90 - (3 \times 23) = 90 - 69 = 21$

• $h_2(90) = 1 + (90 \bmod 19) = 1 + (90 - 4 \times 19) = 1 + (90 - 76) = 1 + 14 = 15$

For probe 1 ($i = 1$):

Thus, the address returned by probe 1 is 13.