Simple solution
SELECT magic_word
FROM gob
WHERE 'shazam' LIKE (magic_word || '%')
ORDER BY magic_word DESC
LIMIT 1;
This works because the longest match sorts last - so I sort DESC
and pick the first match.
I am assuming from your example that you want to match left-anchored, from the beginning of the string. If you want to match anywhere in the string (which is more expensive and even harder to back up with an index), use:
...
WHERE 'shazam' LIKE ('%' || magic_word || '%')
...
SQL Fiddle.
Performance
The query is not sargable. It might help quite a bit if you had additional information, like a minimum length that you could base an index on, to reduce the number of rows to consider. It needs to be criteria that gets you less than ~ 5% of the table to be effective. So, initials (a natural minimum pick) may or may not be useful. But two or three letters at the start might help quite a bit.
In fact you could optimize this iteratively. Something along the line of:
Try a partial index of words with 15 letters+
If not found, try 12 letters+
If not found, try 9 letters+
...
A simple case of what I outlined in this related answer on dba.SE:
Another approach would be to use a trigram index. You'd need the additional module pg_trgm
for that. Normally you would search with a short pattern in a table with longer strings. But trigrams work for your reverse approach, too, with some limitations. Obviously you couldn't match a string with just two characters in the middle of a longer string using trigrams ... Test for corner cases.
There are a number of answers here on SO with more information. Example:
Advanced solution
Consider the solution under this closely related question for a whole table of search strings. Implemented with a recursive CTE: