I was looking at the implementation of push_pop_min and replace_min and was expected to see more or less the same thing.

However, when the min-max-head is empty, push_pop_min will not push the element. It look like it's a bug.

Also, I don't understand why two functions are needed. I would have thought that one would be an alias to the other. The documentation doesn't explain why two of them are needed.