Prepare day 20

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2024/Day_20/README.md

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+Link: <https://adventofcode.com/2024/day/20> <br>
+Author: Eric Wastl ([@ericwastl](https://twitter.com/ericwastl)) (2024)
+
+---
+
+## --- Day 20: Race Condition ---
+
+The Historians are quite pixelated again. This time, a massive, black building looms over you - you're [right outside](/2017/day/24) the CPU!
+
+While The Historians get to work, a nearby program sees that you're idle and challenges you to a **race**. Apparently, you've arrived just in time for the frequently-held **race condition** festival!
+
+The race takes place on a particularly long and twisting code path; programs compete to see who can finish in the **fewest picoseconds**. The winner even gets their very own [mutex](https://en.wikipedia.org/wiki/Lock_(computer_science))!
+
+They hand you a **map of the racetrack** (your puzzle input). For example:
+
+```
+###############
+#...#...#.....#
+#.#.#.#.#.###.#
+#S#...#.#.#...#
+#######.#.#.###
+#######.#.#...#
+#######.#.###.#
+###..E#...#...#
+###.#######.###
+#...###...#...#
+#.#####.#.###.#
+#.#...#.#.#...#
+#.#.#.#.#.#.###
+#...#...#...###
+###############
+```
+
+The map consists of track (`.`) - including the **start** (`S`) and **end** (`E`) positions (both of which also count as track) - and **walls** (`#`).
+
+When a program runs through the racetrack, it starts at the start position. Then, it is allowed to move up, down, left, or right; each such move takes **1 picosecond**. The goal is to reach the end position as quickly as possible. In this example racetrack, the fastest time is `84` picoseconds.
+
+Because there is only a single path from the start to the end and the programs all go the same speed, the races used to be pretty boring. To make things more interesting, they introduced a new rule to the races: programs are allowed to **cheat**.
+
+The rules for cheating are very strict. **Exactly once** during a race, a program may **disable collision** for up to **2 picoseconds**. This allows the program to **pass through walls** as if they were regular track. At the end of the cheat, the program must be back on normal track again; otherwise, it will receive a [segmentation fault](https://en.wikipedia.org/wiki/Segmentation_fault) and get disqualified.
+
+So, a program could complete the course in 72 picoseconds (saving **12 picoseconds**) by cheating for the two moves marked `1` and `2`:
+
+```
+###############
+#...#...12....#
+#.#.#.#.#.###.#
+#S#...#.#.#...#
+#######.#.#.###
+#######.#.#...#
+#######.#.###.#
+###..E#...#...#
+###.#######.###
+#...###...#...#
+#.#####.#.###.#
+#.#...#.#.#...#
+#.#.#.#.#.#.###
+#...#...#...###
+###############
+```
+
+Or, a program could complete the course in 64 picoseconds (saving **20 picoseconds**) by cheating for the two moves marked `1` and `2`:
+
+```
+###############
+#...#...#.....#
+#.#.#.#.#.###.#
+#S#...#.#.#...#
+#######.#.#.###
+#######.#.#...#
+#######.#.###.#
+###..E#...12..#
+###.#######.###
+#...###...#...#
+#.#####.#.###.#
+#.#...#.#.#...#
+#.#.#.#.#.#.###
+#...#...#...###
+###############
+```
+
+This cheat saves **38 picoseconds**:
+
+```
+###############
+#...#...#.....#
+#.#.#.#.#.###.#
+#S#...#.#.#...#
+#######.#.#.###
+#######.#.#...#
+#######.#.###.#
+###..E#...#...#
+###.####1##.###
+#...###.2.#...#
+#.#####.#.###.#
+#.#...#.#.#...#
+#.#.#.#.#.#.###
+#...#...#...###
+###############
+```
+
+This cheat saves **64 picoseconds** and takes the program directly to the end:
+
+```
+###############
+#...#...#.....#
+#.#.#.#.#.###.#
+#S#...#.#.#...#
+#######.#.#.###
+#######.#.#...#
+#######.#.###.#
+###..21...#...#
+###.#######.###
+#...###...#...#
+#.#####.#.###.#
+#.#...#.#.#...#
+#.#.#.#.#.#.###
+#...#...#...###
+###############
+```
+
+Each cheat has a distinct **start position** (the position where the cheat is activated, just before the first move that is allowed to go through walls) and **end position**; cheats are uniquely identified by their start position and end position.
+
+In this example, the total number of cheats (grouped by the amount of time they save) are as follows:
+
+- There are 14 cheats that save 2 picoseconds.
+- There are 14 cheats that save 4 picoseconds.
+- There are 2 cheats that save 6 picoseconds.
+- There are 4 cheats that save 8 picoseconds.
+- There are 2 cheats that save 10 picoseconds.
+- There are 3 cheats that save 12 picoseconds.
+- There is one cheat that saves 20 picoseconds.
+- There is one cheat that saves 36 picoseconds.
+- There is one cheat that saves 38 picoseconds.
+- There is one cheat that saves 40 picoseconds.
+- There is one cheat that saves 64 picoseconds.
+
+You aren't sure what the conditions of the racetrack will be like, so to give yourself as many options as possible, you'll need a list of the best cheats. **How many cheats would save you at least 100 picoseconds?**