Query to find previous Activity in STM

Question

I have a database to reflect a State Transition Machine (STM). It contains 3 tables: Activity, Node and Transition.
The Node and Transition tables are the configuration of the STM. They define the different possible states and the possible transitions between states.
The path I take through the STM is recorded in the Activity Table. A record is created for every Node visited.
I need a query that uses the id of my current Activity to find my previous activity, i.e. the activity that directly preceded me. The following rules apply:
- My Id is meaningless
- It has to work for different configurations of the transition and node tables, but:
- The Start Node is always Node 'A'.
- There are no recursive transitions, e.g. ('B','B');
- There are no circular transitions, e.g. ('B','C') and ('C','B')
- The transition and node tables will never change between the creation of the first activity and the execution of the query.
- The path reflected by the Activity table is always a valid path.
- My current activity is always the last activity.
For the dataset below, find the previous activity of activity with id=4. The correct answer is 'C'.
DROP TABLE Transition;
DROP TABLE Activity;
DROP TABLE Node;
CREATE TABLE Node
     Id VARCHAR2(1) PRIMARY KEY
CREATE TABLE Activity
     Id Number(8,0) PRIMARY KEY,
     Node_Id VARCHAR2(1)
CREATE TABLE Transition
     FromNode_Id VARCHAR2(1),
     ToNode_Id VARCHAR2(1)
ALTER TABLE Activity
ADD FOREIGN KEY
(Node_Id) REFERENCES Node(Id);
ALTER TABLE Transition
ADD FOREIGN KEY
(FromNode_Id) REFERENCES Node(Id);
ALTER TABLE Transition
ADD FOREIGN KEY
(ToNode_Id) REFERENCES Node(Id);
INSERT INTO Node VALUES ('A');
INSERT INTO Node VALUES ('B');
INSERT INTO Node VALUES ('C');
INSERT INTO Node VALUES ('D');
INSERT INTO Transition VALUES ('A','B');
INSERT INTO Transition VALUES ('B','C');
INSERT INTO Transition VALUES ('B','D');
INSERT INTO Transition VALUES ('C','D');
INSERT INTO Activity VALUES (1,'A');
INSERT INTO Activity VALUES (2,'B');
INSERT INTO Activity VALUES (3,'C');
INSERT INTO Activity VALUES (4,'D');Desired output:
ID
C

Answer 1

Hi,
Assuming Activity_id tells us nothing about the path, but that all the rows in Activity together form a single, complete path, we can get the desired results this way:
WITH     all_paths    AS
     SELECT     'A' || SYS_CONNECT_BY_PATH (a.Node_id, '/')
              || '/'     AS node_id_path
     FROM     Transition  t
     JOIN     Activity    a  ON  a.Node_Id  = t.ToNode_Id
     WHERE     LEVEL             = (
                            SELECT  COUNT (*)
                         FROM     activity
                         ) - 1
     START WITH  t.FromNode_Id  = 'A'
     CONNECT BY  t.FromNode_Id  = PRIOR t.ToNode_Id
SELECT       REGEXP_SUBSTR ( node_id_path
                 , '([^/]+)/' || (
                                    SELECT  Node_Id
                             FROM    activity
                             WHERE   Id     = 4  -- target_id
                         || '/'
               , 1
               , 1
               , NULL
               , 1
               )     AS prev_id
FROM       all_paths
;This assumes there is some character (I used '/' above) that we know never appears in Activity.Node_Id.
Since there are no loops in Transition, there can not be more than 1 path that involves all the rows in Activity. If there are N rows in Activity, that complete path will be the one that extends to LEVEL = N-1. (That's N-1, not N, because the join between Activity and Transition will always leave out the 1 row in Activity that has Node_Id = 'A'.) Once we have the complete path (which is node_id_path in the 1 row produced by all_paths), we just need to figure out what was the Node_Id that corresponds to the target id (4 in this example), and find the previous node_id from the delimited node_id_path.