Question

Oftentimes, you have a problem where property A can be either true or false, property B also either true or false, and so on. We want to test every combination of A being true while B being false, and so on. So for example we might need the following list:

[true,true,true]
[true,true,false]
[true,false,true]
[true,false,false]
[false,true,true]
[false,true,false]
[false,false,true]
[false,false,false]

In Haskell or Python, this can be done by a list product function.

My question is, what’s the simplest and/or quickest way to generate this? I have always done this by converting a number to binary, then converting the binary into an array. But this seems cumbersome because decimal to binary conversion isn’t completely trivial, and also we need to worry about padding the binary with leading zeroes to fill up the array properly.

I have implemented and re-implemented this kind of function in different contexts enough times to wonder, is there a way simple enough that you can implement it from scratch when necessary — without really having to think?

Answer 1

I’m not exactly sure of the code but something along these lines should work.

for( int i = 0; i < 8; i++ ){
  printf( "[%s, %s, %s]\n", (i & 0x1)?"True":"False", ((i & 0x2) >> 1)?"True":"False" , ((i & 0x4) >> 2)?"True":"False" );
}

I’m iterating through the numbers 0 to 7 (000 to 111 respectively) and isolating each bit to identify the boolean value.