A hash function f defined as f(key) = key mod 7, with linear probing used to…

In open addressing with linear probing, a key's home slot is given by h(key) = key mod m, where m is the table size. If that slot already holds another key, the search moves forward one slot at a time, h(key)+1, h(key)+2, and so on (wrapping past the last index back to 0), stopping at the first empty slot found.

1. Insert 37: h(37) = 37 mod 7 = 2. Slot 2 is empty, so 37 is placed at slot 2.

2. Insert 38: h(38) = 38 mod 7 = 3. Slot 3 is empty, so 38 is placed at slot 3.

3. Insert 72: h(72) = 72 mod 7 = 2. Slot 2 already holds 37, so probe slot 3, which already holds 38, so probe slot 4, which is empty; 72 is placed at slot 4.

4. Insert 48: h(48) = 48 mod 7 = 6. Slot 6 is empty, so 48 is placed at slot 6.

5. Insert 98: h(98) = 98 mod 7 = 0. Slot 0 is empty, so 98 is placed at slot 0.

6. Insert 11: h(11) = 11 mod 7 = 4. Slot 4 already holds 72, so probe the next slot, slot 5, which is empty; 11 is placed at slot 5.

Recount the final table: slot 0 holds 98, slot 2 holds 37, slot 3 holds 38, slot 4 holds 72, slot 5 holds 11, and slot 6 holds 48 - six keys in six distinct slots out of seven, a load factor of 6/7, with no slot reused. Independently, 11 = 7x1 + 4 confirms the home slot is 4; since slot 4 is already occupied by 72, the next slot in the probe order, slot 5, is where 11 comes to rest.

So the key 11 is stored at index 5.