view 2017/day13/problem @ 35:1d99d733cf13defaulttip@

day08: replace static foreach with workaround
author Jordi Gutiérrez Hermoso Tue, 16 Jan 2018 11:28:55 -0500 049fb8e56025
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--- Day 13: Packet Scanners ---

You need to cross a vast firewall. The firewall consists of several
layers, each with a security scanner that moves back and forth across
the layer. To succeed, you must not be detected by a scanner.

By studying the firewall briefly, you are able to record (in your
puzzle input) the depth of each layer and the range of the scanning
area for the scanner within it, written as depth: range. Each layer
has a thickness of exactly 1. A layer at depth 0 begins immediately
inside the firewall; a layer at depth 1 would start immediately after
that.

For example, suppose you've recorded the following:

0: 3
1: 2
4: 4
6: 4

This means that there is a layer immediately inside the firewall (with
range 3), a second layer immediately after that (with range 2), a
third layer which begins at depth 4 (with range 4), and a fourth layer
which begins at depth 6 (also with range 4). Visually, it might look
like this:

0   1   2   3   4   5   6
[ ] [ ] ... ... [ ] ... [ ]
[ ] [ ]         [ ]     [ ]
[ ]             [ ]     [ ]
[ ]     [ ]

Within each layer, a security scanner moves back and forth within its
range. Each security scanner starts at the top and moves down until it
reaches the bottom, then moves up until it reaches the top, and
repeats. A security scanner takes one picosecond to move one step.
Drawing scanners as S, the first few picoseconds look like this:

Picosecond 0:
0   1   2   3   4   5   6
[S] [S] ... ... [S] ... [S]
[ ] [ ]         [ ]     [ ]
[ ]             [ ]     [ ]
[ ]     [ ]

Picosecond 1:
0   1   2   3   4   5   6
[ ] [ ] ... ... [ ] ... [ ]
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

Picosecond 2:
0   1   2   3   4   5   6
[ ] [S] ... ... [ ] ... [ ]
[ ] [ ]         [ ]     [ ]
[S]             [S]     [S]
[ ]     [ ]

Picosecond 3:
0   1   2   3   4   5   6
[ ] [ ] ... ... [ ] ... [ ]
[S] [S]         [ ]     [ ]
[ ]             [ ]     [ ]
[S]     [S]

Your plan is to hitch a ride on a packet about to move through the
firewall. The packet will travel along the top of each layer, and it
moves at one layer per picosecond. Each picosecond, the packet moves
one layer forward (its first move takes it into layer 0), and then the
scanners move one step. If there is a scanner at the top of the layer
as your packet enters it, you are caught. (If a scanner moves into the
top of its layer while you are there, you are not caught: it doesn't
have time to notice you before you leave.) If you were to do this in
the configuration above, marking your current position with
parentheses, your passage through the firewall would look like this:

Initial state:
0   1   2   3   4   5   6
[S] [S] ... ... [S] ... [S]
[ ] [ ]         [ ]     [ ]
[ ]             [ ]     [ ]
[ ]     [ ]

Picosecond 0:
0   1   2   3   4   5   6
(S) [S] ... ... [S] ... [S]
[ ] [ ]         [ ]     [ ]
[ ]             [ ]     [ ]
[ ]     [ ]

0   1   2   3   4   5   6
( ) [ ] ... ... [ ] ... [ ]
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

Picosecond 1:
0   1   2   3   4   5   6
[ ] ( ) ... ... [ ] ... [ ]
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

0   1   2   3   4   5   6
[ ] (S) ... ... [ ] ... [ ]
[ ] [ ]         [ ]     [ ]
[S]             [S]     [S]
[ ]     [ ]

Picosecond 2:
0   1   2   3   4   5   6
[ ] [S] (.) ... [ ] ... [ ]
[ ] [ ]         [ ]     [ ]
[S]             [S]     [S]
[ ]     [ ]

0   1   2   3   4   5   6
[ ] [ ] (.) ... [ ] ... [ ]
[S] [S]         [ ]     [ ]
[ ]             [ ]     [ ]
[S]     [S]

Picosecond 3:
0   1   2   3   4   5   6
[ ] [ ] ... (.) [ ] ... [ ]
[S] [S]         [ ]     [ ]
[ ]             [ ]     [ ]
[S]     [S]

0   1   2   3   4   5   6
[S] [S] ... (.) [ ] ... [ ]
[ ] [ ]         [ ]     [ ]
[ ]             [S]     [S]
[ ]     [ ]

Picosecond 4:
0   1   2   3   4   5   6
[S] [S] ... ... ( ) ... [ ]
[ ] [ ]         [ ]     [ ]
[ ]             [S]     [S]
[ ]     [ ]

0   1   2   3   4   5   6
[ ] [ ] ... ... ( ) ... [ ]
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

Picosecond 5:
0   1   2   3   4   5   6
[ ] [ ] ... ... [ ] (.) [ ]
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

0   1   2   3   4   5   6
[ ] [S] ... ... [S] (.) [S]
[ ] [ ]         [ ]     [ ]
[S]             [ ]     [ ]
[ ]     [ ]

Picosecond 6:
0   1   2   3   4   5   6
[ ] [S] ... ... [S] ... (S)
[ ] [ ]         [ ]     [ ]
[S]             [ ]     [ ]
[ ]     [ ]

0   1   2   3   4   5   6
[ ] [ ] ... ... [ ] ... ( )
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

In this situation, you are caught in layers 0 and 6, because your
packet entered the layer when its scanner was at the top when you
entered it. You are not caught in layer 1, since the scanner moved
into the top of the layer once you were already there.

The severity of getting caught on a layer is equal to its depth
multiplied by its range. (Ignore layers in which you do not get
caught.) The severity of the whole trip is the sum of these values. In
the example above, the trip severity is 0*3 + 6*4 = 24.

Given the details of the firewall you've recorded, if you leave
immediately, what is the severity of your whole trip?

--- Part Two ---

Now, you need to pass through the firewall without being caught -
easier said than done.

You can't control the speed of the packet, but you can delay it any
number of picoseconds. For each picosecond you delay the packet before
beginning your trip, all security scanners move one step. You're not
in the firewall during this time; you don't enter layer 0 until you
stop delaying the packet.

In the example above, if you delay 10 picoseconds (picoseconds 0 - 9),
you won't get caught:

State after delaying:
0   1   2   3   4   5   6
[ ] [S] ... ... [ ] ... [ ]
[ ] [ ]         [ ]     [ ]
[S]             [S]     [S]
[ ]     [ ]

Picosecond 10:
0   1   2   3   4   5   6
( ) [S] ... ... [ ] ... [ ]
[ ] [ ]         [ ]     [ ]
[S]             [S]     [S]
[ ]     [ ]

0   1   2   3   4   5   6
( ) [ ] ... ... [ ] ... [ ]
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

Picosecond 11:
0   1   2   3   4   5   6
[ ] ( ) ... ... [ ] ... [ ]
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

0   1   2   3   4   5   6
[S] (S) ... ... [S] ... [S]
[ ] [ ]         [ ]     [ ]
[ ]             [ ]     [ ]
[ ]     [ ]

Picosecond 12:
0   1   2   3   4   5   6
[S] [S] (.) ... [S] ... [S]
[ ] [ ]         [ ]     [ ]
[ ]             [ ]     [ ]
[ ]     [ ]

0   1   2   3   4   5   6
[ ] [ ] (.) ... [ ] ... [ ]
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

Picosecond 13:
0   1   2   3   4   5   6
[ ] [ ] ... (.) [ ] ... [ ]
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

0   1   2   3   4   5   6
[ ] [S] ... (.) [ ] ... [ ]
[ ] [ ]         [ ]     [ ]
[S]             [S]     [S]
[ ]     [ ]

Picosecond 14:
0   1   2   3   4   5   6
[ ] [S] ... ... ( ) ... [ ]
[ ] [ ]         [ ]     [ ]
[S]             [S]     [S]
[ ]     [ ]

0   1   2   3   4   5   6
[ ] [ ] ... ... ( ) ... [ ]
[S] [S]         [ ]     [ ]
[ ]             [ ]     [ ]
[S]     [S]

Picosecond 15:
0   1   2   3   4   5   6
[ ] [ ] ... ... [ ] (.) [ ]
[S] [S]         [ ]     [ ]
[ ]             [ ]     [ ]
[S]     [S]

0   1   2   3   4   5   6
[S] [S] ... ... [ ] (.) [ ]
[ ] [ ]         [ ]     [ ]
[ ]             [S]     [S]
[ ]     [ ]

Picosecond 16:
0   1   2   3   4   5   6
[S] [S] ... ... [ ] ... ( )
[ ] [ ]         [ ]     [ ]
[ ]             [S]     [S]
[ ]     [ ]

0   1   2   3   4   5   6
[ ] [ ] ... ... [ ] ... ( )
[S] [S]         [S]     [S]
[ ]             [ ]     [ ]
[ ]     [ ]

Because all smaller delays would get you caught, the fewest number of
picoseconds you would need to delay to get through safely is 10.

What is the fewest number of picoseconds that you need to delay the
packet to pass through the firewall without being caught?