Function with varying number of For Loops (python)

Question

My problem is difficult to explain.

I want to create a function that contains nested for loops,
the amount of which is proportional to an argument passed to the function.

Here's a hypothetical example:

Function(2)

...would involve...

for x in range (y):
    for x in range (y):
        do_whatever()

Another example...

  Function(6)

...would involve...

for x in range (y):
    for x in range (y):
        for x in range (y):
            for x in range (y):
                for x in range (y):
                    for x in range (y):
                        whatever()

The variables of the for loop (y) are NOT actually used in the nested code.

Your first thought might be to create ONE for loop, with a range that is to the power of the number argument...
THIS CAN NOT WORK because the product would be HUGE. I have instances required where there are 8 nested for loops.
The product is too large for a range in a for loop.

There are other arguments needed to be passed to the function, but I can handle that myself.

Here's the code (it creates the Snowflake Fractal)

from turtle import *
length = 800
speed(0)

def Mini(length):
    for x in range (3):
        forward(length)
        right(60)

penup()
setpos(-500, 0)
pendown()   

choice = input("Enter Complexity:")

if choice == 1:
    for x in range (3):
        forward(length)
        left(120)

elif choice == 2:
    for x in range (3):
        Mini(length/3)
        left(120)

if choice == 3:
    for x in range (6):
        Mini(length/9)
        right(60)
        Mini(length/9)
        left(120)

if choice == 4:
    for y in range (6):
        for x in range (2):
            Mini(length/27)
            right(60)
            Mini(length/27)
            left(120)
        right(180)
        for x in range (2):
            Mini(length/27)
            right(60)
            Mini(length/27)
            left(120)

if choice == 5:
    for a in range (6):
        for z in range (2):
            for y in range (2):
                for x in range (2):
                    Mini(length/81)
                    right(60)
                    Mini(length/81)
                    left(120)
                right(180)
                for x in range (2):
                    Mini(length/81)
                    right(60)
                    Mini(length/81)
                    left(120)
            right(180)
        right(180)

if choice == 6:
    for c in range (6):
        for b in range (2):
            for a in range (2):
                for z in range (2):
                    for y in range (2):
                        for x in range (2):
                            Mini(length/243)
                            right(60)
                            Mini(length/243)
                            left(120)
                        right(180)
                        for x in range (2):
                            Mini(length/243)
                            right(60)
                            Mini(length/243)
                            left(120)
                    right(180)
                right(180)
            right(180)
        right(180)

if choice == 7:
    for a in range (6):
        for b in range(2):
            for c in range (2):
                for d in range (2):
                    for e in range (2):
                        for f in range (2):
                            for y in range (2):
                                for x in range (2):
                                    Mini(length/729)
                                    right(60)
                                    Mini(length/729)
                                    left(120)
                                right(180)
                                for x in range (2):
                                    Mini(length/729)
                                    right(60)
                                    Mini(length/729)
                                    left(120)
                            right(180)
                        right(180)
                    right(180)
                right(180)
            right(180)
        right(180)

I'd appreciate any help you can give me at all,
though if you suggest a different method (such as recursion),
please don't just paste the code; instead, suggests some ideas that could put me in the right direction.

(The algorithm is for a Specialist Math Assignment)

---

specs:
Python 2.7.1
Turtle
IDLE
Windows7

Answer 1

I'm not clear why you can't use the product of the bounds and do

for x in range(y exp n)

where n is the # of loops.... You say y exp n will be huge, but I'm sure python can handle it.

However, that being said, what about some sort of recursive algorithm?

def loop_rec(y, n):
    if n >= 1:
        for x in range(y):
            loop_rec(y, n - 1)
    else:
       whatever()

Answer 2

This problem can be solved by recursion. I am just writing an algorithm here, since I believe this can be a general problem.

function Recurse (y, number) 
   if (number > 1)
      Recurse ( y, number - 1 )
   else
      for x in range (y)
          whatever()

Answer 3

Recursion will be your best bet. Consider what it should do in the base case and in the recursive case.

Code left out, as per request.

Answer 4

Here you go. Let ranges be your ranges, operate on result when you need to.

ranges=((1,4),(0,3),(3,6))
from operator import mul
operations=reduce(mul,(p[1]-p[0] for p in ranges))-1
result=[i[0] for i in ranges]
pos=len(ranges)-1
increments=0
print result
while increments < operations:
    if result[pos]==ranges[pos][1]-1:
        result[pos]=ranges[pos][0]
        pos-=1
    else:
        result[pos]+=1
        increments+=1
        pos=len(ranges)-1 #increment the innermost loop
        print result

[1, 0, 3]
[1, 0, 4]
[1, 0, 5]
[1, 1, 3]
[1, 1, 4]
[1, 1, 5]
[1, 2, 3]
[1, 2, 4]
[1, 2, 5]
[2, 0, 3]
[2, 0, 4]
[2, 0, 5]
[2, 1, 3]
[2, 1, 4]
[2, 1, 5]
[2, 2, 3]
[2, 2, 4]
[2, 2, 5]
[3, 0, 3]
[3, 0, 4]
[3, 0, 5]
[3, 1, 3]
[3, 1, 4]
[3, 1, 5]
[3, 2, 3]
[3, 2, 4]
[3, 2, 5]
[1, 0, 4]

Testing with the following would give the same result:

for x in range(*ranges[0]):
    for y in range(*ranges[1]):
        for z in range(*ranges[2]):
            print [x,y,z]

Answer 5

A nice implementation of the varying number of For Loops problem:

def for_recursive(number_of_loops, range_list, execute_function, current_index=0, iter_list = []):

if iter_list == []:
    iter_list = [0]*number_of_loops

if current_index == number_of_loops-1:
    for iter_list[current_index] in range_list[current_index]:
        execute_function(iter_list)
else:
    for iter_list[current_index] in range_list[current_index]:
        for_recursive(number_of_loops, iter_list = iter_list, range_list = range_list,  current_index = current_index+1, execute_function = execute_function) 

An example of how to use it:

def do_whatever(index_list):
    return print(index_list)


for_recursive(range_list = [range(0,3), range(0,3) , range(1,3)], execute_function = do_whatever , number_of_loops=3)

The code returns the same that this code:

for i in range(0,3):
    for j in range(0,3):
        for k in range(1,3):
            print([i,j,k])

Answer 6

Have you considered xrange ?

for x in xrange(y ** n):
    whatever()

And if you overshoot even xrange limit, you can use itertool

import itertools
for x in itertools.product(xrange(y), repeat=n):
   whatever()

(previous itertool answer incorrectly used n for the range instead of y)

Answer 7

Here is another option for iterative solution, seems simpler to me. The idea is to use an analogy with a 10 or X-based numbering system. Where you basically increase your number/count by one each time but the representation changes according to the base. I.e. if the base is 10, then the number changes 1 .. 9 10 11 .. 19 20... Imagine that we want to loop on i,j,k from 0 .. 9 for each. We run the loop for counter in range(101010) and take the digits as the values of the number. E.g. 731 means i=7,j=3, k=1. To make the case more general, where the range for each i/j/... is different - we take modulo that range:

`

ranges = [2,3,4]
lenr = len(ranges)
for i in range(2*3*4):
    perm = []
    d, r  = i, 0
    for rng_i in (1, lenr):
        d, r = divmod(d, ranges[lenr - rng_i])
        perm.append(r)
    perm.extend([0]*(lenr-len(perm)))   # pad with zeros
    print (list(reversed(perm)))        # need to reverse as appended from right

Output will be:

[0, 0, 0]
[0, 0, 1]
[0, 0, 2]
[0, 0, 3]
[0, 1, 0]
[0, 1, 1]
[0, 1, 2]
[0, 1, 3]
[0, 0, 0]
[0, 0, 1]
[0, 0, 2]
[0, 0, 3]
[0, 1, 0]
[0, 1, 1]
[0, 1, 2]
[0, 1, 3]
[0, 0, 0]
[0, 0, 1]
[0, 0, 2]
[0, 0, 3]
[0, 1, 0]
[0, 1, 1]
[0, 1, 2]
[0, 1, 3]

`

Answer 8

My reply is late, but supposing that you want to do multiple loops, e.g. print some range multiple times. Then the correct version of this recursion is:

def loop_rec(y, number):
   if (number > 1):
      loop_rec( y, number - 1 )
      for i in range(y): 
         print(i, end=' ')        
   else:      
      for i in range(y):
         print(i, end=' ')

loop_rec(4,3)

This will create three for loops with the range(4)

If you want to play around with dynamic range, here are some variants:

def loop_rec(y, number):
if (number > 1):
    loop_rec( y+1, number - 1 )
    for i in range(y): 
        print(i, end=' ')
    print(' ;')
else:      
    for i in range(y):
        print(i, end=' ')
    print(';')

loop_rec(6,4)

which will print out:

0 1 2 3 4 5 6 7 8 ;
0 1 2 3 4 5 6 7  ;
0 1 2 3 4 5 6  ;
0 1 2 3 4 5  ;

or

def loop_rec(y, number):
if (number > 1):
    loop_rec( y-1, number - 1 )
    for i in range(y): 
        print(i, end=' ')
    print(' ;')
else:      
    for i in range(y):
        print(i, end=' ')
    print(';')
loop_rec(6,4)

which will output:

0 1 2 ;
0 1 2 3  ;
0 1 2 3 4  ;
0 1 2 3 4 5  ;

A better variant which is using only one for loop (less typing) is the following:

def loop_rec(y, number):
    if (number >= 1):
        loop_rec( y+1, number - 1 )
        for i in range(y): 
            print(i, end=' ')
        print('')
    else:      
        return

loop_rec(1,5)

will output:

0 1 2 3 4 
0 1 2 3 
0 1 2 
0 1 
0