WITH MUTUALLY RECURSIVE
lines(line TEXT, row_no INT) AS (
SELECT regexp_split_to_array(input, '\n')[i], i
FROM input, generate_series(1, array_length(regexp_split_to_array(input, '\n'), 1)) i
),
symbols(symb TEXT, row_no INT, col_no INT) as (
SELECT substring(line, j, 1), row_no, j
FROM lines, generate_series(1, length(line)) j
),
-- Each location that is pipe has two neighbors
edge1(r1 INT, c1 INT, r2 INT, c2 INT) AS (
SELECT
row_no,
col_no,
CASE WHEN symb = '-' THEN row_no
WHEN symb = '|' THEN row_no - 1
WHEN symb = 'F' THEN row_no + 1
WHEN symb = 'L' THEN row_no - 1
WHEN symb = 'J' THEN row_no
WHEN symb = '7' THEN row_no
ELSE NULL
END,
CASE WHEN symb = '-' THEN col_no - 1
WHEN symb = '|' THEN col_no
WHEN symb = 'F' THEN col_no
WHEN symb = 'L' THEN col_no
WHEN symb = 'J' THEN col_no - 1
WHEN symb = '7' THEN col_no - 1
ELSE NULL
END
FROM symbols
WHERE symb != '.' AND symb != 'S'
),
edge2(r1 INT, c1 INT, r2 INT, c2 INT) AS (
SELECT
row_no,
col_no,
CASE WHEN symb = '-' THEN row_no
WHEN symb = '|' THEN row_no + 1
WHEN symb = 'F' THEN row_no
WHEN symb = 'L' THEN row_no
WHEN symb = 'J' THEN row_no - 1
WHEN symb = '7' THEN row_no + 1
ELSE NULL
END,
CASE WHEN symb = '-' THEN col_no + 1
WHEN symb = '|' THEN col_no
WHEN symb = 'F' THEN col_no + 1
WHEN symb = 'L' THEN col_no + 1
WHEN symb = 'J' THEN col_no
WHEN symb = '7' THEN col_no
ELSE NULL
END
FROM symbols
WHERE symb != '.' AND symb != 'S'
),
-- Symmetrized graph
symm(r1 INT, c1 INT, r2 INT, c2 INT) AS (
SELECT r1, c1, r2, c2
FROM (
SELECT * FROM edge1
UNION ALL
SELECT * FROM edge2
UNION ALL
SELECT r2, c2, r1, c1 FROM edge1
UNION ALL
SELECT r2, c2, r1, c1 FROM edge2
UNION ALL
SELECT row_no, col_no, row_no + 1, col_no FROM symbols WHERE symb = 'S'
UNION ALL
SELECT row_no, col_no, row_no, col_no + 1 FROM symbols WHERE symb = 'S'
UNION ALL
SELECT row_no, col_no, row_no - 1, col_no FROM symbols WHERE symb = 'S'
UNION ALL
SELECT row_no, col_no, row_no, col_no - 1 FROM symbols WHERE symb = 'S'
)
GROUP BY r1, c1, r2, c2
HAVING COUNT(*) = 2
),
reach(r INT, c INT) AS (
SELECT row_no, col_no
FROM symbols
WHERE symb = 'S'
UNION
SELECT r2, c2
FROM reach, symm
WHERE r = r1 AND c = c1
),
part1(part1 BIGINT) AS (
SELECT COUNT(*)/2 FROM reach
),
-- Part 2: how many cells are *inside* the loop?
-- All (1, *) and (*, 1) cells have their upper left outside the loop (outer edge of the diagram).
-- Each cell inherits from its UL neighbor, toggled by any pipe except '7' and 'L' pipe.
-- Rewrite the pipe to have symbols, and resolve 'S' to actual oriented pipe.
pipe(r INT, c INT, symb TEXT) AS (
SELECT r, c, symb
FROM reach, symbols
WHERE r = row_no AND c = col_no AND symb != 'S'
UNION
SELECT
row_no,
col_no,
CASE WHEN row_no = s1.r1 AND col_no = s1.c1 + 1 AND row_no = s2.r2 + 1 AND col_no = s2.c2 THEN 'J' -- toggle
WHEN row_no = s1.r1 AND col_no = s1.c1 + 1 AND row_no = s2.r2 AND col_no = s2.c2 - 1 THEN '-' -- toggle
WHEN row_no = s1.r1 AND col_no = s1.c1 + 1 AND row_no = s2.r2 - 1 AND col_no = s2.c2 THEN '7' -- no toggle
WHEN row_no = s1.r1 + 1 AND col_no = s1.c1 AND row_no = s2.r2 AND col_no = s2.c2 - 1 THEN 'L' -- no toggle
WHEN row_no = s1.r1 + 1 AND col_no = s1.c1 AND row_no = s2.r2 - 1 AND col_no = s2.c2 THEN '|' -- toggle
WHEN row_no = s1.r1 AND col_no = s1.c1 - 1 AND row_no = s2.r2 AND col_no = s2.c2 - 1 THEN 'F' -- toggle
ELSE '???'
END
FROM symbols, symm s1, symm s2
WHERE symb = 'S'
AND row_no = s1.r1
AND col_no = s1.c1
AND row_no = s2.r1
AND col_no = s2.c1
),
-- Enclosed(1,*) and Enclosed(*,1) are all false.
-- Enclosed(x+1,y+1) = Enclosed(x,y) perhaps toggled by pipe(x,y)
status(r INT, c INT, encl BOOL) AS (
SELECT row_no, col_no, false
FROM symbols
WHERE row_no = 1 OR col_no = 1
UNION
SELECT
row_no + 1,
col_no + 1,
CASE WHEN pipe.symb IN (VALUES ('J'),('-'),('|'),('F')) THEN NOT encl
ELSE encl
END
FROM status LEFT JOIN pipe ON (status.r = pipe.r AND status.c = pipe.c)
JOIN symbols ON (status.r = symbols.row_no AND status.c = symbols.col_no)
),
part2(part2 BIGINT) AS (
SELECT COUNT(*)
FROM status
WHERE encl = true AND (r, c) NOT IN (SELECT r, c FROM pipe)
)
SELECT * FROM part1, part2;Day 10 was brought to you by: @frankmcsherry