Generalizing increasing number of nested loop algorithm

Question

Sorry for the terrible title, but I have no clue on how to generalize (or simplify) my loop case here.

I have a program that iterates to a sequence of integer, for example dimension=1 to 5. In each iteration, there will be a main loop, and inside the main loop, there will be a nested loop. The number of the nested loop will be [dimension]. For example, in dimension=1, there is a For loop. In dimension=2, there is a For loop inside a For loop. And so on.

Is there any possible way to simplify the algorithm? currently I'm manually write totally different code for each value of [dimension]. Imagine if dimension=1 to 100? I'll be dead.

Here's my piece of program (written in VB.NET)

for dimension=2

Dim result(2) As Integer For i = 0 To 1 For j = 0 To 1 result(0)=i result(1)=j Next Next 

For dimension=3

 Dim result(3) As Integer For i = 0 To 1 For j = 0 To 1 For k = 0 To 1 result(0)=i result(1)=j result(2)=k Next Next Next 

For dimension=4

Dim result(4) As Integer For i = 0 To 1 For j = 0 To 1 For k = 0 To 1 For l = 0 To 1 result(0)=i result(1)=j result(2)=k result(3)=l Next Next Next Next 

And so on..

Any suggestion? Thanks!

Answer 1

There are plenty of solutions:

Recursion

Idk, if vb.net supports methods, but if it does, this would probably be the simplest:

void nestedLoop(int lower , int upper , int remaining_loops , int[] values) if(remaining_loops == 0) //process values list else for int i in [lower , upper) values[remaining_loops] = i nestedLoop(lower , upper , remaining_loops - 1) 

Integer Transformation

In theory, a number can be represented by any radix:

d_i * radix ^ i + d_i-1 * radix ^ (i - 1) ... + d_0 * radix ^ 0 

Consider each digit the value of one of the nested loops:

for int i in [0 , max) for int j in [0 , max) for int k in [0 , max) ... 

Could be represented by a 3-digit number with radix max, where d_0 = i, d_1 = j, etc.. Basically how each digit is mapped to one of the values can be arbitrary and will only affect the order of the output.

void nestedLoops(int upper , int dimension) for int i in [0 , pow(upper , dimension)) int[] values int digit_sub = 1 int tmp = i for int j in [0 , dimension) values[j] = tmp % dimension tmp /= dimension //all values of the loops are now in values //process them here 

There would be a few other options aswell, but these are the most common.

Answer 2

Please do note that when you do

Dim result(2) As Integer 

You are actually declaring an array of 3 elements see this question for why. It's a subtle difference in VB.NET

That being said, I'll assume that you meant to declare an array of only 2 elements. If this is the case then you could build and call a recursive function like this

LoopOver(result) Sub LoopOver(ByRef array() As Integer, ByVal Optional level As Integer = 0) If array.Length = level Then Return Else array(level) = 1 LoopOver(array, level + 1) End If End Sub 

This recursive function will call itself (i.e., it will loop) for as many times as the array's size.