Claire Xen  🏳️‍⚧️ 🏳️‍🌈 🧙🏻‍♀️ BLM  🏴 🚩

Given a set of unsigned integers. How can I find the bit-permutation so that the maximum number is minimal?

find a bit position with a zero in one of the numbers and take it as the MSB; if they are all 1's chose any. Repeat for the remaining bits, working your way to the LSB. ?

I mean a bit position where they're all zero.

That method would suggest that for the set 001, 100, 110 the order does not matter, because there are zeros and ones in each position. But obviously the order does matter, because swapping the middle and LSB bit will reduce the max from 110 to 101.

Trying to understand your unstated assumptions/rules: So you are allowed to only swap 2 bits? And you have to use the same permutation for each integer?

You are allowed to swap any bits. So for N bit numbers we are looking at N! possible permutations. We'd like to find one permutation so that, when applied to all numbers, the maximum number after permutation is smaller or equal than what you'd get for any other permutation.