Holiday Challenge Time :)

Question

I have a daily puzzle calendar on my desk and I found a puzzle that I thought may be fun to solve using SQL.
Sample Data
WITH    matrix AS
        SELECT  'A' AS ID, 1 AS A,1 AS B,1 AS C,0 AS D,0 AS E,0 AS F,1 AS G,0 AS H,1 AS I,0 AS J FROM DUAL UNION ALL
        SELECT  'B' AS ID, 0,0,0,0,1,1,1,0,1,0 FROM DUAL UNION ALL
        SELECT  'C' AS ID, 0,1,1,1,1,0,0,0,0,1 FROM DUAL UNION ALL
        SELECT  'D' AS ID, 1,0,0,0,1,0,1,0,0,0 FROM DUAL UNION ALL
        SELECT  'E' AS ID, 1,1,0,0,0,0,0,0,0,1 FROM DUAL UNION ALL
        SELECT  'F' AS ID, 0,1,1,0,1,1,0,0,0,0 FROM DUAL UNION ALL
        SELECT  'G' AS ID, 0,1,0,1,1,1,0,1,0,1 FROM DUAL UNION ALL
        SELECT  'H' AS ID, 1,1,0,1,0,0,0,1,0,0 FROM DUAL UNION ALL
        SELECT  'I' AS ID, 0,1,1,1,0,1,1,1,0,1 FROM DUAL UNION ALL
        SELECT  'J' AS ID, 1,0,0,0,0,0,0,1,0,1 FROM DUAL UNION ALL
        SELECT  'K' AS ID, 1,0,0,1,1,1,0,1,1,0 FROM DUAL UNION ALL
        SELECT  'L' AS ID, 0,0,1,0,1,1,0,0,1,0 FROM DUAL UNION ALL
        SELECT  'M' AS ID, 0,0,1,0,0,0,0,1,1,1 FROM DUAL UNION ALL
        SELECT  'N' AS ID, 1,0,1,0,0,0,1,1,1,0 FROM DUAL UNION ALL
        SELECT  'O' AS ID, 1,0,0,1,1,0,1,0,0,0 FROM DUAL
SELECT  *
FROM    MATRIX
ORDER BY 1
Problem Statement
Suppose we have a matrix of one's and zero's like the following:
ID  A  B  C  D  E  F  G  H  I  J
A   1  1  1  0  0  0  1  0  1  0
B   0  0  0  0  1  1  1  0  1  0
C   0  1  1  1  1  0  0  0  0  1
D   1  0  0  0  1  0  1  0  0  0
E   1  1  0  0  0  0  0  0  0  1
F   0  1  1  0  1  1  0  0  0  0
G   0  1  0  1  1  1  0  1  0  1
H   1  1  0  1  0  0  0  1  0  0
I   0  1  1  1  0  1  1  1  0  1
J   1  0  0  0  0  0  0  1  0  1
K   1  0  0  1  1  1  0  1  1  0
L   0  0  1  0  1  1  0  0  1  0
M   0  0  1  0  0  0  0  1  1  1
N   1  0  1  0  0  0  1  1  1  0
O   1  0  0  1  1  0  1  0  0  0Positions in this matrix are defined using (ROW,COLUMN) throughout the problem statement.
Challenge
Our goal is from a start position identified as (A,E), First Row, Fifth column, traverse DOWN the matrix to reach a valid point on row "O."
Restrictions
1. You can only move UP, DOWN, LEFT, or RIGHT (not diagonally) by one unit.
2. The path must be a repeating pattern of 0 1 0 1 0 1 ... etc For example a move from (A,E) to (B,E) is valid while a move from (A,E) to (A,F) is not.
Correct Solution
The correct solution has the following requirements:
1. Identifies the path from start to finish using an identifiable way to determine the ROW,COLUMN for each entry point in the path while abiding by the restrictions above.
2. PL/SQL and SQL are acceptable.
3. Solution must be perform well and be elegant as judged (loosely, since we don't have any voting functionality) by your peers. This solution will be marked as "Correct." Helpful points will be given to runner ups as determined by your peers.
Enjoy :D

Answer 1

Building on Frank's solution, the following generates maps showing the valid paths. If I had 11g handy I could use pivot and unpivot to great advantage, but someone else will have to make that attempt.
Interesting to note that if you generate a random matrix it most often produces no solutions at all, but when it does it usually produces a large number of valid paths.
Regards,
Bob
Random matrix:
create global temporary table  matrix on commit preserve rows AS
select chr(64+level) as ID
, ROUND(DBMS_RANDOM.VALUE(),0) as A
, ROUND(DBMS_RANDOM.VALUE(),0) as B
, ROUND(DBMS_RANDOM.VALUE(),0) as C
, ROUND(DBMS_RANDOM.VALUE(),0) as D
, ROUND(DBMS_RANDOM.VALUE(),0) as E
, ROUND(DBMS_RANDOM.VALUE(),0) as F
, ROUND(DBMS_RANDOM.VALUE(),0) as G
, ROUND(DBMS_RANDOM.VALUE(),0) as H
, ROUND(DBMS_RANDOM.VALUE(),0) as I
, ROUND(DBMS_RANDOM.VALUE(),0) as J
from dual
connect by level <= 15Map generator:
select pnum, chr(64+rw) as id, a, b, c, d, e, f, g, h, i, j from (
select * from (
WITH   matrix AS
        SELECT  'A' AS ID, 1 AS A,1 AS B,1 AS C,0 AS D,0 AS E,0 AS F,1 AS G,0 AS H,1 AS I,0 AS J FROM DUAL UNION ALL
        SELECT  'B' AS ID, 0,0,0,0,1,1,1,0,1,0 FROM DUAL UNION ALL
        SELECT  'C' AS ID, 0,1,1,1,1,0,0,0,0,1 FROM DUAL UNION ALL
        SELECT  'D' AS ID, 1,0,0,0,1,0,1,0,0,0 FROM DUAL UNION ALL
        SELECT  'E' AS ID, 1,1,0,0,0,0,0,0,0,1 FROM DUAL UNION ALL
        SELECT  'F' AS ID, 0,1,1,0,1,1,0,0,0,0 FROM DUAL UNION ALL
        SELECT  'G' AS ID, 0,1,0,1,1,1,0,1,0,1 FROM DUAL UNION ALL
        SELECT  'H' AS ID, 1,1,0,1,0,0,0,1,0,0 FROM DUAL UNION ALL
        SELECT  'I' AS ID, 0,1,1,1,0,1,1,1,0,1 FROM DUAL UNION ALL
        SELECT  'J' AS ID, 1,0,0,0,0,0,0,1,0,1 FROM DUAL UNION ALL
        SELECT  'K' AS ID, 1,0,0,1,1,1,0,1,1,0 FROM DUAL UNION ALL
        SELECT  'L' AS ID, 0,0,1,0,1,1,0,0,1,0 FROM DUAL UNION ALL
        SELECT  'M' AS ID, 0,0,1,0,0,0,0,1,1,1 FROM DUAL UNION ALL
        SELECT  'N' AS ID, 1,0,1,0,0,0,1,1,1,0 FROM DUAL UNION ALL
        SELECT  'O' AS ID, 1,0,0,1,1,0,1,0,0,0 FROM DUAL
, unpivoted     AS
     SELECT     r.id || c.id     AS coordinates
     ,     r.id          AS row_l
     ,     c.id          AS col_l
     ,     ASCII (r.id)     AS row_n
     ,     ASCII (c.id)     AS col_n
     ,     CASE     c.id
               WHEN  'A'     THEN  r.a
               WHEN  'B'     THEN  r.b
               WHEN  'C'     THEN  r.c
               WHEN  'D'     THEN  r.d
               WHEN  'E'     THEN  r.e
               WHEN  'F'     THEN  r.f
               WHEN  'G'     THEN  r.g
               WHEN  'H'     THEN  r.h
               WHEN  'I'     THEN  r.i
               WHEN  'J'     THEN  r.j
          END     AS val
     FROM          matrix     r
     CROSS JOIN     matrix     c
     WHERE          c.id     <= 'J'
SELECT     rownum as pnum , SYS_CONNECT_BY_PATH (coordinates, '>')     AS path
       , translate(sys_connect_by_path(case when prior row_n is null then coordinates
                                  when row_n=15 then 'v'||coordinates
                                  when row_n>prior row_n then 'v'
                                  when row_n<prior row_n then '^'
                                  when col_n<prior col_n then '<'
                                  else                  '>'
                                  end,';'),'~;','~') as route
FROM     unpivoted
WHERE     coordinates     LIKE 'O_'
START WITH     coordinates     = 'AE'
CONNECT BY NOCYCLE  (     (     row_n                    = PRIOR     row_n
               AND     ABS (col_n - PRIOR col_n)     = 1
              OR  (     ABS (row_n - PRIOR row_n)     = 1
               AND     col_n                    = PRIOR col_n
     AND         val     != PRIOR val
  and prior row_l != 'O'
model
partition by (pnum, path)
dimension by (1 rw) measures (0 Z,'  ' X,'  ' Y,' ' L, ' ' A, ' ' B, ' ' C, ' ' D, ' ' E, ' ' F, ' ' G, ' ' H, ' ' I, ' ' J)
rules upsert all sequential order
  Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'A')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then '*'
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, A[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
, Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'B')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then L[cv()]
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, B[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
, Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'C')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then L[cv()]
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, C[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
, Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'D')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then '*'
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, D[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
, Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'E')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then '*'
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, E[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
, Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'F')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then '*'
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, F[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
, Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'G')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then '*'
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, G[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
, Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'H')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then '*'
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, H[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
, Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'I')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then '*'
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, I[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
, Z[for rw from 1 to 15 increment 1]=instr(cv(path),chr(64+cv(rw))||'J')
, X[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then substr(cv(path),Z[cv()],2) else '  ' end
, Y[for rw from 1 to 15 increment 1]=case when cv(rw)<15 then substr(cv(path),Z[cv()]+3,2) else '  ' end
, L[for rw from 1 to 15 increment 1]=case when cv(rw)=15 then '*'
                                          when substr(Y[cv()],1,1)< substr(X[cv()],1,1) then '^'
                                          when substr(Y[cv()],1,1)> substr(X[cv()],1,1) then 'v'
                                          when substr(Y[cv()],2,1)> substr(X[cv()],2,1) then '>'
                                          else  '<' end
, J[for rw from 1 to 15 increment 1]=case when Z[cv()]>0 then L[cv()] else ' ' end
order by 1,2