Which diet is characterized by high fat, adequate protein, and low carbohydrate intake?

The ketogenic diet is distinguished by its specific macronutrient composition, which is high in fat, adequate in protein, and low in carbohydrates. This dietary pattern is designed to shift the body's metabolism away from relying on carbohydrates for energy and towards utilizing fats in the form of ketones, which is a primary energy source in a state of ketosis. On a ketogenic diet, the usual macronutrient ratio is typically around 70-80% fats, 15-25% protein, and about 5-10% carbohydrates.

This contrasts with other diets mentioned. The paleo diet focuses more on whole, unprocessed foods and emphasizes lean meats, fish, fruits, and vegetables, generally including more carbohydrates than the ketogenic diet. The Mediterranean diet emphasizes healthy fats from olive oil and fish, along with whole grains, vegetables, and modest amounts of dairy, but does not restrict carbohydrates to the extent that the ketogenic diet does. The vegetarian diet excludes meat and fish and varies widely in macronutrient ratios depending upon food choices, but it does not typically focus on high fat and low carbohydrates as a primary goal.

Therefore, the ketogenic diet is uniquely characterized by its high fat and low carbohydrate intake, making it the correct answer.