55 lines
3.3 KiB
Plaintext
55 lines
3.3 KiB
Plaintext
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--- Day 8: Memory Maneuver ---
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The sleigh is much easier to pull than you'd expect for something its weight. Unfortunately, neither you nor the Elves know which way the North Pole is from here.
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You check your wrist device for anything that might help. It seems to have some kind of navigation system! Activating the navigation system produces more bad news: "Failed to start navigation system. Could not read software license file."
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The navigation system's license file consists of a list of numbers (your puzzle input). The numbers define a data structure which, when processed, produces some kind of tree that can be used to calculate the license number.
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The tree is made up of nodes; a single, outermost node forms the tree's root, and it contains all other nodes in the tree (or contains nodes that contain nodes, and so on).
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Specifically, a node consists of:
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A header, which is always exactly two numbers:
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The quantity of child nodes.
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The quantity of metadata entries.
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Zero or more child nodes (as specified in the header).
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One or more metadata entries (as specified in the header).
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Each child node is itself a node that has its own header, child nodes, and metadata. For example:
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2 3 0 3 10 11 12 1 1 0 1 99 2 1 1 2
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A----------------------------------
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B----------- C-----------
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D-----
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In this example, each node of the tree is also marked with an underline starting with a letter for easier identification. In it, there are four nodes:
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A, which has 2 child nodes (B, C) and 3 metadata entries (1, 1, 2).
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B, which has 0 child nodes and 3 metadata entries (10, 11, 12).
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C, which has 1 child node (D) and 1 metadata entry (2).
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D, which has 0 child nodes and 1 metadata entry (99).
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The first check done on the license file is to simply add up all of the metadata entries. In this example, that sum is 1+1+2+10+11+12+2+99=138.
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What is the sum of all metadata entries?
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--- Part Two ---
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The second check is slightly more complicated: you need to find the value of the root node (A in the example above).
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The value of a node depends on whether it has child nodes.
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If a node has no child nodes, its value is the sum of its metadata entries. So, the value of node B is 10+11+12=33, and the value of node D is 99.
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However, if a node does have child nodes, the metadata entries become indexes which refer to those child nodes. A metadata entry of 1 refers to the first child node, 2 to the second, 3 to the third, and so on. The value of this node is the sum of the values of the child nodes referenced by the metadata entries. If a referenced child node does not exist, that reference is skipped. A child node can be referenced multiple time and counts each time it is referenced. A metadata entry of 0 does not refer to any child node.
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For example, again using the above nodes:
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Node C has one metadata entry, 2. Because node C has only one child node, 2 references a child node which does not exist, and so the value of node C is 0.
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Node A has three metadata entries: 1, 1, and 2. The 1 references node A's first child node, B, and the 2 references node A's second child node, C. Because node B has a value of 33 and node C has a value of 0, the value of node A is 33+33+0=66.
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So, in this example, the value of the root node is 66.
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What is the value of the root node?
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