Placing a new order means adding a new Order to the tail of the PriceLevel. This is O(1) time complexity for a doubly-linked list.

Matching an order means deleting an Order from the head of the PriceLevel. This is O(1) time complexity for a doubly-linked list.

Canceling an order means deleting an Order from the OrderBook. We leverage the helper data structure Map orderMap in the OrderBook to find the Order to cancel in O(1) time. Once the order is found, if the “orders“ list was a singly-linked list, the code would have to traverse the entire list to locate the previous pointer in order to delete the order. That would have taken O(n) time. Since the list is now doubly-linked, the order itself has a pointer to the previous order, which allows the code to delete the order without traversing the entire order list.