Update row data with dynamic lag

I have a table of items and restaurants. We assume that if the restaurant entry is missing, it has to be completed with the last non-null restaurant value in the previous rows (as defined by ascending id values). CREATE TABLE food_items ( id SERIAL PRIMARY KEY, item VARCHAR(255) NOT NULL, restaurant VARCHAR(255) ); INSERT INTO food_items(item, restaurant) VALUES ('Salad','McDonalds'), ('Burger',''),('Fries',''),('Salad','Taco Bell'),('Quesadilla',''); The tricky part is that the number of rows for each restaurant is variable, so it cannot be captured with a fixed lag.