Depending on how confident your are in your foraging skills, food designed for travel is good to have plenty of. Given the time of year, you'll also want both a warm enough sleep bag or tent for sleeping, and likely a heat source or a means to create one as well.

That said, it takes most people at least a week or so to make the trip to Violet city on foot, so you don't want to pack so much that it will slow you down, either.