MySQL: Cartesian Product and Left Join

1. Example as below:

# 1. Goods table
select * from goods;
+----------+--------+------------+
| goods_id | cat_id | goods_name |
+----------+--------+------------+
|        1 |      1 | CDMA Phone |
|        2 |      1 | GSM Phone  |
|        3 |      1 | 3G Phone   |
+----------+--------+------------+

# 2. Cat table
select * from cat;
+--------+--------------+
| cat_id | cat_name     |
+--------+--------------+
|      1 | Mobile Phone |
+--------+--------------+

# 3. How to combine cat_name into goods table?

# First approach:
# Using JAVA, select all from goods and get cat_id, then search cat table and get cat_name. Combine results.
# Using m*n times SQL

# Second approach:
# Using join(left join)
# select goods_id, goods_name, cat.cat_name from *** where goods.cat_id = cat.cat_id;
# But how to realize this?

2. Set/Collection in Math

1) Properties of Set: Orderless, Uniquity

# Orderless
#{1, 2, 3} == {2, 3, 1} == {1, 3, 2}
# Uniquity
# {1, 2, 3, 3} is not a Set

2) Regard a table as a set, and a row in a table as an element in a set.

So seriously speaking, there can not be two same rows in a single table.

But actually, there can be two same rows in a single table because there is a rowId for each row in a table. And the rowId is not visible. It is generated by MySQL automatically and can not be accessed by user.

3. Cartesian Product in Math

# Eg 1

# What's the cartesian product of the two following sets?
# Q: {2, 3, 4} X {4, 7}
# A:  {8, 14, 12, 21, 16, 28}--->Wrong!
# A: {{2, 4}, {2, 7}, {3, 4}, {3, 7}, {4, 4}, {4, 7}}--->Bingo!

#Eg 2

# What's the cartesian product of the two following sets
# Q: {chicken, duck} X {cat, dog, camel}
# A: {{chicken, cat}, {chicken, dog}, {chicken, camel}, {duck, cat}, {duck, dog}, {duck, camel}}

1) Cartesian product is also called Set multiple.

2) Cartesian product is actually a total combination of the two sets.

Q: Let set A have M elements which are unique in set A; Let set B have N elements which are unique in set B. So how many element will we get after cartesian product of A and B?

A: The number is M*N. And if we put these M*N elements in a set there will not be duplicate elements to worry about

. Q: If table A have 9 columns and table B have 5 columns. What's the cartesian product of the two tables?

A: There will be 9*5=45 columns.

Eg:

Cartesian product of two tables (Refer from IBM red brick warehouse website)

Join of two tables

State table Region table City State City Area Jacksonville Miami Nashville

FL		Jacksonville	South
FL	Miami	South
TN	New Orleans	South

Example query

select * from state, region;

Cartesian product (join predicate not specified)

City State City Area Jacksonville Jacksonville Jacksonville Miami Miami Miami Nashville Nashville Nashville

FL	Jacksonville	South
FL	Miami	South
FL	New Orleans	South
FL	Jacksonville	South
FL	Miami	South
FL	New Orleans	South
TN	Jacksonville	South
TN	Miami	South
TN	New Orleans	South

#Cartesian product of two tables
select * from goods, cat;
+----------+--------+------------+--------+--------------+
| goods_id | cat_id | goods_name | cat_id | cat_name     |
+----------+--------+------------+--------+--------------+
|        1 |      1 | CDMA Phone |      1 | Mobile Phone |
|        2 |      1 | GSM Phone  |      1 | Mobile Phone |
|        3 |      1 | 3G Phone   |      1 | Mobile Phone |
+----------+--------+------------+--------+--------------+

#A possible solution to the question raised at begining
select * from goods, cat where goods.cat_id = cat.cat_id;
+----------+--------+------------+--------+--------------+
| goods_id | cat_id | goods_name | cat_id | cat_name     |
+----------+--------+------------+--------+--------------+
|        1 |      1 | CDMA Phone |      1 | Mobile Phone |
|        2 |      1 | GSM Phone  |      1 | Mobile Phone |
|        3 |      1 | 3G Phone   |      1 | Mobile Phone |
+----------+--------+------------+--------+--------------+
#Two Steps:
#1. Get cartesian product of two tables
#2. Apply filters to the result set. 

#A more elegant way by using left join
select * from goods left join cat on goods.cat_id = cat.cat_id;
+----------+--------+------------+--------+--------------+
| goods_id | cat_id | goods_name | cat_id | cat_name     |
+----------+--------+------------+--------+--------------+
|        1 |      1 | CDMA Phone |      1 | Mobile Phone |
|        2 |      1 | GSM Phone  |      1 | Mobile Phone |
|        3 |      1 | 3G Phone   |      1 | Mobile Phone |
+----------+--------+------------+--------+--------------+

#Remove duplicate columns
select goods.cat_id, goods_id, goods_name from goods left join cat on goods.cat_id = cat.cat_id;
+--------+----------+------------+
| cat_id | goods_id | goods_name |
+--------+----------+------------+
|      1 |        1 | CDMA Phone |
|      1 |        2 | GSM Phone  |
|      1 |        3 | 3G Phone   |
+--------+----------+------------+

1) Regard the result of cartesian product or left join as a real table and not as a result set.

2) We can use where, group by, having, order by, limit on this result table.

Eg.

select goods.cat_id, goods_id, goods_name from goods left join cat on goods.cat_id = cat.cat_id where goods_id >= 2;
+--------+----------+------------+
| cat_id | goods_id | goods_name |
+--------+----------+------------+
|      1 |        2 | GSM Phone  |
|      1 |        3 | 3G Phone   |
+--------+----------+------------+