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+## 19. Calculating Fares**
+
+In order to calculate a fare for a trip in GTFS, you must use data from
+`fare_attributes.txt` and `fare_rules.txt`. It is relatively
+straightforward to calculate the cost of a single trip (that is,
+boarding a vehicle, traveling for a number of stops, then disembarking),
+but it becomes much more complicated when you need to take into account
+multiple trip segments (that is, one or more transfers).
+
+***Note:** As it stands, many feed providers do not include fare
+information. This is because many systems have a unique set of rules
+that cannot be modelled with the current structure of fares in GTFS.
+Additionally, it is not possible to determine different classes of
+pricing (such as having a separate price for adults and children). For
+the purposes of this chapter, these limitations are ignored.*
+
+For more discussion on how fares work in GTFS, refer to *Fare
+Definitions (`fare_attributes.txt` & `fare_rules.txt`)*.
+
+This chapter first shows you how to calculate fares for a single trip,
+then how to account for transfers and for multiple trips.
+
+### Calculating a Single Trip Fare
+
+Much of the logic used when calculating fares requires knowledge of the
+zones used in a trip.
+
+***Note:** A zone is a physical area within a transit system that
+contains a series of stops. They are used to group trip pricing into key
+areas in a system. Some transit systems do not work like this (for
+instance, they may measure the physical distance travelled rather than
+specific stops), which is one reason why the GTFS fares model does not
+work in all cases.*
+
+A zone is defined in GTFS by the `zone_id` column in `stops.txt`. A
+single stop can only belong to one zone.
+
+Fares are matched to a trip using a combination of any of the following:
+
+* The route of the trip
+* The zone of the stop the passenger boards from
+* The zone of the stop the passenger disembarks
+* The zone(s) of any stops on the trip that are passed while the
+  passenger is on board.
+
+Consider the following simplified data set that may appear in
+`stops.txt` and `stop_times.txt`. Assume for this example that the
+trip `T1` belongs to a route with an ID of `R1`.
+
+```
+stop_id,zone_id
+S1,Z1
+S2,Z1
+S3,Z2
+S4,Z3
+
+trip_id,stop_id,stop_sequence
+T1,S1,1
+T1,S2,2
+T1,S3,3
+T1,S4,4
+```
+
+If a passenger travels from stop S1 to stop S4, then their starting zone
+is Z1, their finishing zone is Z3, and the zones they pass through are
+Z1, Z2 and Z3.
+
+***Note:** When calculating fares, the start and finish zones are also
+included in the zones passed through, so in this example you Z3 is also
+considered as a zone that the trip passes through.*
+
+Using this data, you can now calculate matching fares. To do so, you
+need to find all fares that match either of the following:
+
+* Fares that have no associated rules.
+* Fares that have rules that match the specified trip. If a fare
+  defines multiple zones that must be passed through (using
+  `contains_id`), then all zones must be matched.
+
+If multiple fares qualify for a trip, then the cheapest fare is the one
+to use.
+
+### Finding Fares With No Rules
+
+This is the simplest use-case for fares. You can find all matching fares
+with the following SQL.
+
+```sql
+SELECT * FROM fare_attributes WHERE fare_id NOT IN (
+  SELECT DISTINCT fare_id FROM fare_rules
+);
+```
+
+If a feed only has `fare_attributes.txt` records with no rules, then
+the difference between the fares is in the transfer rules. This section
+only covers calculating fares for a single trip with no transfers, so
+for now you can just select the cheapest fare using the following SQL.
+
+```sql
+SELECT * FROM fare_attributes WHERE fare_id NOT IN (
+    SELECT DISTINCT fare_id FROM fare_rules
+  )
+  ORDER BY price + 0 LIMIT 1;
+```
+
+***Note:** You still need to check for fares with one or more rules in
+order to find the cheapest price. Also, `0` is added in this query in
+order to cast a string to a number. When you roll your own importer you
+should instead import this as a numerical value.*
+
+### Finding Fares With Matched Rules
+
+Next you must check against specific rules for a fare. In order to do
+this, you need the starting zone, finishing zone, and all zones passed
+through (including the start and finish zones).
+
+Referring back to the previous example, if a trip starts at `Z1`,
+passes through `Z2` and finishes at `Z3`, you can find fare
+candidates (that is, trips that *may* match), using the following SQL
+query.
+
+```sql
+SELECT * FROM fare_attributes WHERE fare_id IN (
+    SELECT fare_id FROM fare_rules
+      WHERE (LENGTH(route_id) = 0 OR route_id = 'R1')
+      AND (LENGTH(origin_id) = 0 OR origin_id = 'Z1')
+      AND (LENGTH(destination_id) = 0 OR destination_id = 'Z3')
+      AND (LENGTH(contains_id) = 0 OR contains_id IN ('Z1', 'Z2', 'Z3')
+    )
+  );
+```
+
+This returns a list of fares that may qualify for the given trip. As
+some fares have multiple rules, all must be checked. The algorithm to
+represent this is as follows.
+
+```
+fares = [ result from above query ]
+
+qualifyingFares = [ ]
+
+for (fare in fares) {
+  if (qualifies(fare))
+    qualifyingFares.add(fare)
+}
+
+allFares = qualifyFares + faresWithNoRules
+
+passengerFare = cheapest(allFares)
+```
+
+As shown on the final two lines, once you have the list of qualifying
+fares, you can combine these with fares that have no rules (from the
+previous section) and then determine the cheapest fare.
+
+First though, you must determine if a fare with rules qualifies for the
+given trip. If a fare specifies zones that must be passed through, then
+all rules must be matched.
+
+***Note:** If a particular rule specifies a different route, start, or
+finish than the one you are checking, you do not need to ensure the
+`contains_id` matches, since this rule no longer applies. You still need
+to check the other rules for this fare.*
+
+The algorithm needs to build up a list of zone IDs from the fare rules
+in order to check against the trip. Once this has been done, you need to
+check that every zone ID collected from the rules is contained in the
+trip's list of zones.
+
+```
+qualifies(fare, routeId, originId, destinationId, containsIds) {
+
+  fareContains = [ ]
+  
+  for (rule in fare.rules) {
+    if (rule.contains.length == 0)
+      continue
+      
+    if (rule.route.length > 0 AND rule.route != routeId)
+      continue
+      
+    if (rule.origin.length > 0 AND rule.origin != originId)
+      continue
+      
+    if (rule.desination.length > 0 AND rule.destination != destinationId)
+      continue
+      
+    fareContains.add(rule.containsId);
+ }
+ 
+ if (fareContains.size == 0)
+   return YES
+   
+ if (containIds HAS EVERY ELEMENT IN fareContains)
+   return YES
+ else 
+   return NO
+}
+```
+
+This algorithm achieves the following:
+
+* Only rules that have a value for `contains_id` are relevant. Rules
+  that do not have this value fall through and should be considered as
+  qualified.
+* If the route is specified but not equal to the one being checked, it
+  is safe to ignore the rule's `contains_id`. If the route is empty
+  or equal, the loop iteration can continue.
+* Check for the `origin_id` and `destination_id` in the same
+  manner as `route_id`.
+* If the route, origin and destination all qualify then store the
+  `contains_id` so it can be checked after the loop.
+
+The algorithm returns *yes* if the fare qualifies, meaning you can save
+it as a qualifying fare. You can then return the cheapest qualifying
+fare to the user.
+
+### Calculating Trips With Transfers
+
+Once you introduce transfers, fare calculation becomes more complicated.
+A "trip with a transfer" is considered to be a trip where the passenger
+boards a vehicle, disembarks, and then gets on another vehicle. For
+example:
+
+* Travel on trip T1 from Stop S1 to Stop S2
+* Walk from Stop S2 to Stop S3
+* Travel on trip T2 from Stop S3 to Stop S4.
+
+In order to calculate the total fare for a trip with transfers, the
+following algorithm is used:
+
+1. Retrieve list of qualifying fares for each trip individually
+2. Create a list of every fare combination possible
+3. Loop over all combinations and find the total cost
+4. Return the lowest cost from Step 3.
+
+Step 1 was covered in *Calculating a Single Trip Fare*, but
+you must skip the final step of finding the cheapest fare. This is
+because the cheapest fare may change depending on subsequent transfers.
+Instead, this step is performed once the cheapest *combination* is
+determined.
+
+To demonstrate Step 2, consider the following example:
+
+* The trip on T1 from S1 to S2 yields the following qualifying fares:
+  F1, F2.
+* The subsequent trip on T2 from S3 to S4 yields the following
+  qualifying fares: F3, F4.
+
+Generating every combination of these fares yields the following
+possibilities:
+
+* F1 + F3
+* F1 + F4
+* F2 + F3
+* F2 + F4.
+
+Step 3 can now be performed, which involves finding the total cost for
+each combinations. As you need to take into account the possibility of
+timed transfers (according to the data stored in
+`fare_attributes.txt`), you also need to know about the times of these
+trips.
+
+The following algorithm can be used to calculate the total cost using
+transfer rules. In this example, you would call this function once for
+each fare combination.
+
+```
+function totalCost(fares) {
+  total = 0
+ 
+  for (fare in fares) {
+    freeTransfer = NO
+ 
+    if (previousFare ALLOWS TRANSFERS) {
+      if (HAS ENOUGH TRANSFERS REMAINING) {
+        if (TRANSFER NOT EXPIRED) {
+          freeTransfer = YES
+        }
+      }
+    }
+ 
+    if (!freeTransfer)
+      total = total + fare.price;
+     
+    previousFare = fare;
+  }
+ 
+  return total;
+}
+```
+
+Once all combinations have called the `totalCost` algorithm, you will
+have a price for each trip. You can then return the lowest price as the
+final price for the trip.
+