Is there a way to randomly shuffle an array using only a source of random boolean values? SO to clarify, shuffle using true /false only, and not integers or decimals.
For this question, I'm specifically excluding an approach whereby the booleans are just arranged into an integer and then it's used in a Fisher-Yates shuffle. I'd be repeatedly shuffling approximately 30,000 items and have a ready source of random booleans. I'd need to build up a very large integer for Fischer-Yates to avoid any form of bias in the shuffle. Can this step be avoided and true /false used directly somehow? I have the sense that some soft of bubble sort might do it, with the comparison determined randomly, but I can't quite flesh it out.
I'd be interested in any algorithm than wasn't ridiculous i.e. with a stupid time complexity of something like 2^O(n). This question builds upon some of the concepts of Best random permutation employing only one random number but isn't identical.