The keys 5, 28, 19, 15, 26, 33, 12, 17, 10 are inserted into a hash table using the hash function $h(k) = k \bmod 9$. The collisions are resolved by chaining. After all the keys are inserted, the length of the longest chain is _______. (answer in integer)

Compute the hash value $h(k) = k \bmod 9$ for each key:

• $h(5) = 5 \bmod 9 = 5$

• $h(28) = 28 \bmod 9 = 1$

• $h(19) = 19 \bmod 9 = 1$

• $h(15) = 15 \bmod 9 = 6$

• $h(26) = 26 \bmod 9 = 8$

• $h(33) = 33 \bmod 9 = 6$

• $h(12) = 12 \bmod 9 = 3$

• $h(17) = 17 \bmod 9 = 8$

• $h(10) = 10 \bmod 9 = 1$

Distribution of keys into the slots:

• Slot 1: $\{28, 19, 10\}$ (Chain length = 3)

• Slot 3: $\{12\}$ (Chain length = 1)

• Slot 5: $\{5\}$ (Chain length = 1)

• Slot 6: $\{15, 33\}$ (Chain length = 2)

• Slot 8: $\{26, 17\}$ (Chain length = 2)

The maximum number of keys hashed to any single slot is in slot 1, which contains 3 keys.

Therefore, the length of the longest chain is 3.