does setting a column to index in a mysql table ensure O(1) look ups?

so when there's an index on a column, and you do a simple SELECT * FROM table WHERE indexed_column = value, is that a O(1) search? does it matter whether the cont开发者_运维知识库ents indexed are integers or string?

None of the lookups in MySQL's MyISAM or InnoDB storage engines are O(1) searches. Those storage engines use B+Trees to implement indexes. The best they can do is O(log₂n) searches.

The MEMORY storage engine uses a HASH index type by default, as well as the B+Tree index type. Only the HASH index can achieve O(1) lookups.

The data type of the indexed column doesn't change this in either case.

For more on MySQL indexes, read http://dev.mysql.com/doc/refman/5.1/en/mysql-indexes.html

It does not.

MySQL uses B-Trees as explained in this online book. Their complexity depends on the number of keys per node and therefore can do much better than O(log2n).

The number of keys per node used by MySQL depends on different factors as pointed out in this question.