# How to iterate over alpha and numeric numbers

I would like to know how in Python I can iterate through a set of conditions.

- which has 2-6 lower alphabetic or numeric characters
- the first character is always a number

So the short progression will be:

`1a 1b 1c ... 1aa 1ab 1ac ... 2aaa 2aab 2aac etc.`

A terrible example that the first two can do is

```
##Loop through 1a-z0-9
start = '1'
l = 97
while l < 123:
num = start
num += chr(l)
print num
l += 1
l = 48
while l < 58:
num = start
num += chr(l)
print num
l += 1
```

I found itertools but can't find good examples to get away with.

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You can do this using `itertools.product`

and `itertools.chain`

. First, define strings of numbers and letters:

```
numbers = '0123456789'
alnum = numbers + 'abcdefghijklmnopqrstuvwxyz'
```

Using `itertools.product`

, you can get character tuples for strings of different lengths:

```
len2 = itertools.product(numbers, alnum) # length 2
len3 = itertools.product(numbers, alnum, alnum) # length 3
...
```

Concatenate iterators for all lengths together by appending tuples to strings. I would do it with a list:

`[''.join(p) for p in itertools.chain(len2, len3, len4, len5, len6)]`

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I would go with a product feature from itertools.

```
import itertools
digits = '0123456789'
alphanum = 'abcdef...z' + digits # this should contain all the letters and digits
for i in xrange(1, 6):
for tok in itertools.product(digits, itertools.product(alphanum, repeat=i)):
# do whatever you want with this token `tok` here.
```

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You can think of this problem in base 26 (ignoring the first number, we'll put this in a separate case.) So the letters we want to vary from 'a' to 'zzzzz' in base 26 would be 0 and (26.26 , 26,26,26) = 26 ^ 0 + 26 + 26 ^ 2 + 26 ^ 3 + 26 ^ 4 + 26 ^ 5. So now we have a bijection from numbers to letters, we just want to write a function that returns us from number to word

```
letters = 'abcdef..z'
def num_to_word( num ):
res = ''
while num:
res += letters[num%26]
num //= 26
return res
```

Now, to write our function that lists this

```
def generator():
for num in xrange(10):
for letter_num in xrange( sum( 26 ** i for i in xrange( 6 ) ) + 1 ):
tok = str(num) + num_to_word( letter_num )
yield tok
```

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allows you to do this using the first type of width search algorithm

```
starting from
Root:
have 10 children, i = 0,1,...,9
so , this root must have an iterator, 'i'
therefore this outermost loop will iterate 'i' from 0 to 9
i:
for each 'i', there are 5 children (ix , ixx, ixxx, ixxxx, ixxxxx)
( number of chars at the string )
so each i should have its own iterator 'j' representing number of chars
the loop inside Root loop will iterate 'j' from 1 to 5
j:
'j' will have 'j' number of children ( 1 -> x , 2 -> xx ,..., 5-> xxxxx)
so each j will have its own iterator 'k' representing each "character"
so, 'k' will be iterated inside this j loop, from 1 to j
( i=2, j=4, k = 3 will focus on 'A' at string "2xxAx" )
k:
each 'k' represents a character, so it iterates from 'a' to 'z'
each k should have a iterator(value) 'c' that iterates from 'a' to 'z' (or 97 to 122)
```

I think it will make more sense than what I wanted to show before. :) if you don't get this idea please tell me .. Interesting question by the way :)

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