From a2d966926b185befcf24c804cdd5243a79cda160 Mon Sep 17 00:00:00 2001
From: Bruno BELANYI <bruno@belanyi.fr>
Date: Wed, 16 Dec 2020 10:11:06 +0100
Subject: [PATCH] 2020: d16: ex2: add solution

---
 2020/d16/ex2/ex2.py | 106 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 106 insertions(+)
 create mode 100755 2020/d16/ex2/ex2.py

diff --git a/2020/d16/ex2/ex2.py b/2020/d16/ex2/ex2.py
new file mode 100755
index 0000000..61423f4
--- /dev/null
+++ b/2020/d16/ex2/ex2.py
@@ -0,0 +1,106 @@
+#!/usr/bin/env python
+import math
+import sys
+from typing import Dict, List, Set, Tuple
+
+Ranges = Dict[str, Set[int]]
+Ticket = List[int]
+
+
+def parse(raw: List[str]) -> Tuple[Ranges, List[Ticket]]:
+    def extract_field_info(line: str) -> Tuple[str, Set[int]]:
+        field, rest = line.split(":")
+        ranges: Set[int] = set()
+        for r in rest.strip().split(" or "):
+            lhs, rhs = r.split("-")
+            ranges |= set(range(int(lhs), int(rhs) + 1))
+        return field, ranges
+
+    def parse_tickets(line: str) -> Ticket:
+        return [int(i) for i in line.split(",")]
+
+    ranges: Ranges = {}
+    tickets: List[Ticket] = []
+
+    should_parse_tickets = False
+    for line in raw:
+        if line == "":
+            should_parse_tickets = True
+            continue
+        if "ticket" in line:
+            continue
+        if should_parse_tickets:
+            tickets.append(parse_tickets(line))
+        else:
+            field, field_ranges = extract_field_info(line)
+            ranges[field] = field_ranges
+
+    return ranges, tickets
+
+
+def verify_mapping(possibilites: Dict[int, Set[str]]) -> None:
+    for pos in possibilites.values():
+        assert len(pos) == 1
+
+
+def cross_eliminate(possibilites: Dict[int, Set[str]]) -> None:
+    while True:
+        eliminated = False
+        for pos in possibilites:
+            if len(possibilites[pos]) != 1:
+                continue
+            for other_pos in possibilites:
+                if other_pos == pos:
+                    continue
+                if len(possibilites[other_pos] & possibilites[pos]) == 0:
+                    continue
+                eliminated = True
+                possibilites[other_pos] = possibilites[other_pos] - (possibilites[pos])
+        if not eliminated:
+            break
+
+
+def match_ranges(ranges: Ranges, tickets: List[Ticket]) -> Dict[int, str]:
+    possibilites: Dict[int, Set[str]] = {
+        i: set(ranges.keys()) for i in range(len(ranges))
+    }
+
+    def whittle_down() -> None:
+        for t in tickets[1:]:
+            for i, val in enumerate(t):
+                for field, valid in ranges.items():
+                    if val in valid:
+                        continue
+                    possibilites[i].remove(field)
+
+    whittle_down()
+    cross_eliminate(possibilites)
+    verify_mapping(possibilites)
+
+    return {i: pos.pop() for i, pos in possibilites.items()}
+
+
+def solve(raw: List[str]) -> int:
+    ranges, tickets = parse(raw)
+
+    def valid(t: Ticket) -> bool:
+        for val in t:
+            if not any(val in r for r in ranges.values()):
+                return False
+        return True
+
+    tickets = [t for i, t in enumerate(tickets) if i == 0 or valid(t)]
+
+    mapping = match_ranges(ranges, tickets)
+    return math.prod(
+        tickets[0][i] for i, field in mapping.items() if "departure" in field
+    )
+
+
+def main() -> None:
+    input = [line.strip() for line in sys.stdin.readlines()]
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()