2022 day 13 init

2022/day13/README.org

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+** --- Day 13: Distress Signal ---
+You climb the hill and again try contacting the Elves. However, you
+instead receive a signal you weren't expecting: a /distress signal/.
+
+Your handheld device must still not be working properly; the packets
+from the distress signal got decoded /out of order/. You'll need to
+re-order the list of received packets (your puzzle input) to decode the
+message.
+
+Your list consists of pairs of packets; pairs are separated by a blank
+line. You need to identify /how many pairs of packets are in the right
+order/.
+
+For example:
+
+#+begin_example
+[1,1,3,1,1]
+[1,1,5,1,1]
+
+[[1],[2,3,4]]
+[[1],4]
+
+[9]
+[[8,7,6]]
+
+[[4,4],4,4]
+[[4,4],4,4,4]
+
+[7,7,7,7]
+[7,7,7]
+
+[]
+[3]
+
+[[[]]]
+[[]]
+
+[1,[2,[3,[4,[5,6,7]]]],8,9]
+[1,[2,[3,[4,[5,6,0]]]],8,9]
+#+end_example
+
+Packet data consists of lists and integers. Each list starts with =[=,
+ends with =]=, and contains zero or more comma-separated values (either
+integers or other lists). Each packet is always a list and appears on
+its own line.
+
+When comparing two values, the first value is called /left/ and the
+second value is called /right/. Then:
+
+- If /both values are integers/, the /lower integer/ should come first.
+  If the left integer is lower than the right integer, the inputs are in
+  the right order. If the left integer is higher than the right integer,
+  the inputs are not in the right order. Otherwise, the inputs are the
+  same integer; continue checking the next part of the input.
+- If /both values are lists/, compare the first value of each list, then
+  the second value, and so on. If the left list runs out of items first,
+  the inputs are in the right order. If the right list runs out of items
+  first, the inputs are not in the right order. If the lists are the
+  same length and no comparison makes a decision about the order,
+  continue checking the next part of the input.
+- If /exactly one value is an integer/, convert the integer to a list
+  which contains that integer as its only value, then retry the
+  comparison. For example, if comparing =[0,0,0]= and =2=, convert the
+  right value to =[2]= (a list containing =2=); the result is then found
+  by instead comparing =[0,0,0]= and =[2]=.
+
+Using these rules, you can determine which of the pairs in the example
+are in the right order:
+
+#+begin_example
+== Pair 1 ==
+- Compare [1,1,3,1,1] vs [1,1,5,1,1]
+  - Compare 1 vs 1
+  - Compare 1 vs 1
+  - Compare 3 vs 5
+    - Left side is smaller, so inputs are in the right order
+
+== Pair 2 ==
+- Compare [[1],[2,3,4]] vs [[1],4]
+  - Compare [1] vs [1]
+    - Compare 1 vs 1
+  - Compare [2,3,4] vs 4
+    - Mixed types; convert right to [4] and retry comparison
+    - Compare [2,3,4] vs [4]
+      - Compare 2 vs 4
+        - Left side is smaller, so inputs are in the right order
+
+== Pair 3 ==
+- Compare [9] vs [[8,7,6]]
+  - Compare 9 vs [8,7,6]
+    - Mixed types; convert left to [9] and retry comparison
+    - Compare [9] vs [8,7,6]
+      - Compare 9 vs 8
+        - Right side is smaller, so inputs are not in the right order
+
+== Pair 4 ==
+- Compare [[4,4],4,4] vs [[4,4],4,4,4]
+  - Compare [4,4] vs [4,4]
+    - Compare 4 vs 4
+    - Compare 4 vs 4
+  - Compare 4 vs 4
+  - Compare 4 vs 4
+  - Left side ran out of items, so inputs are in the right order
+
+== Pair 5 ==
+- Compare [7,7,7,7] vs [7,7,7]
+  - Compare 7 vs 7
+  - Compare 7 vs 7
+  - Compare 7 vs 7
+  - Right side ran out of items, so inputs are not in the right order
+
+== Pair 6 ==
+- Compare [] vs [3]
+  - Left side ran out of items, so inputs are in the right order
+
+== Pair 7 ==
+- Compare [[[]]] vs [[]]
+  - Compare [[]] vs []
+    - Right side ran out of items, so inputs are not in the right order
+
+== Pair 8 ==
+- Compare [1,[2,[3,[4,[5,6,7]]]],8,9] vs [1,[2,[3,[4,[5,6,0]]]],8,9]
+  - Compare 1 vs 1
+  - Compare [2,[3,[4,[5,6,7]]]] vs [2,[3,[4,[5,6,0]]]]
+    - Compare 2 vs 2
+    - Compare [3,[4,[5,6,7]]] vs [3,[4,[5,6,0]]]
+      - Compare 3 vs 3
+      - Compare [4,[5,6,7]] vs [4,[5,6,0]]
+        - Compare 4 vs 4
+        - Compare [5,6,7] vs [5,6,0]
+          - Compare 5 vs 5
+          - Compare 6 vs 6
+          - Compare 7 vs 0
+            - Right side is smaller, so inputs are not in the right order
+#+end_example
+
+What are the indices of the pairs that are already /in the right order/?
+(The first pair has index 1, the second pair has index 2, and so on.) In
+the above example, the pairs in the right order are 1, 2, 4, and 6; the
+sum of these indices is =13=.
+
+Determine which pairs of packets are already in the right order. /What
+is the sum of the indices of those pairs?/