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# Cartesian Product

## Preliminaries

```
# import pandas as pd
import pandas as pd
```

## Create Data

```
# Create two lists
i = [1,2,3,4,5]
j = [1,2,3,4,5]
```

## Calculate Cartesian Product (Method 1)

```
# List every single x in i with every single y (i.e. Cartesian product)
[(x, y) for x in i for y in j]
```

```
[(1, 1),
(1, 2),
(1, 3),
(1, 4),
(1, 5),
(2, 1),
(2, 2),
(2, 3),
(2, 4),
(2, 5),
(3, 1),
(3, 2),
(3, 3),
(3, 4),
(3, 5),
(4, 1),
(4, 2),
(4, 3),
(4, 4),
(4, 5),
(5, 1),
(5, 2),
(5, 3),
(5, 4),
(5, 5)]
```

## Calculate Cartesian Product (Method 2)

```
# An alternative way to do the cartesian product
# import itertools
import itertools
# for two sets, find the the cartisan product
for i in itertools.product([1,2,3,4,5], [1,2,3,4,5]):
# and print it
print(i)
```

```
(1, 1)
(1, 2)
(1, 3)
(1, 4)
(1, 5)
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(3, 5)
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(5, 1)
(5, 2)
(5, 3)
(5, 4)
(5, 5)
```

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