From e69ad47143866a08571a760af3c809a34c3fa10b Mon Sep 17 00:00:00 2001
From: kageru <kageru@encode.moe>
Date: Mon, 16 Dec 2019 13:04:23 +0100
Subject: [PATCH] Add D16P2

---
 2019/16/src/main.rs | 54 +++++++++++++++++++++++++++++++++++++++------
 1 file changed, 47 insertions(+), 7 deletions(-)

diff --git a/2019/16/src/main.rs b/2019/16/src/main.rs
index 16d6d99..9bf933e 100644
--- a/2019/16/src/main.rs
+++ b/2019/16/src/main.rs
@@ -2,19 +2,59 @@ use std::io::{stdin, BufRead};
 use std::iter::*;
 
 #[rustfmt::skip]
-fn read_input() -> Vec<i16> {
+fn read_input() -> Vec<i32> {
     stdin().lock().lines().next().unwrap().unwrap().chars().map(|c| c.to_string().parse().unwrap()).collect()
 }
 
 #[rustfmt::skip]
-fn main() {
-    let mut last_phase = read_input();
-    //let mut last_phase: Vec<i16> = "80871224585914546619083218645595".chars().map(|c| c.to_string().parse().unwrap()).collect();
+fn part1(mut last_phase: Vec<i32>) -> String {
     for _ in 0..100 {
         last_phase = (1..=last_phase.len()).map(|i| {
-            let mut pattern = [0i16, 1, 0, -1].iter().flat_map(|x| repeat(x).take(i)).cycle().skip(1);
-            last_phase.iter().map(|x| x*pattern.next().unwrap()).sum::<i16>().abs() % 10
+            let mut pattern = [0i32, 1, 0, -1].iter().flat_map(|x| repeat(x).take(i)).cycle().skip(1);
+            last_phase.iter().map(|x| x*pattern.next().unwrap()).sum::<i32>().abs() % 10
         }).collect();
     }
-    println!("Part 1: {}", last_phase.iter().take(8).map(|n| n.to_string()).collect::<String>());
+    last_phase.iter().take(8).map(|n| n.to_string()).collect::<String>()
+}
+
+/**
+ * The outputs after each phase are related in a way that I can’t really explain.
+ * They are essentially a summed-area table, but built starting with the last element.
+ * However, this only works for the second half of the output. The rest seem to be random?
+ * 
+ * The examples show this quite clearly:
+ * Input signal:  12345678 (let’s call this `input`)
+ * After 1 phase: 48226158 (`output`)
+ * We can build the state after 1 phase right to left.
+ * ```
+ * output[7] = input[7..8].iter().sum() % 10; // 8
+ * output[6] = input[6..8].iter().sum() % 10; // 15 % 10 == 5
+ * output[5] = input[5..8].iter().sum() % 10; // 21 % 10 == 1
+ * output[4] = input[4..8].iter().sum() % 10; // 26 % 10 == 6
+ * ```
+ * Which is exactly the output sequence.
+ * This pattern only holds true for the second half of the array,
+ * but the offset always seems to be high enough for that.
+ *
+ * Because all input elements only affect outputs with lower indices,
+ * we can also drop all elements before the output starts.
+ */
+#[rustfmt::skip]
+fn part2(input: Vec<i32>) -> String {
+    let offset: usize = input.iter().take(7).map(|n| n.to_string()).collect::<String>().parse().unwrap();
+    let mut p2 = input.repeat(10_000).split_off(offset);
+    for _ in 0..100 {
+        let mut s = 0;
+        for i in (0..p2.len()).rev() {
+            s += p2[i];
+            p2[i] = s % 10;
+        }
+    }
+    p2.iter().take(8).map(|n| n.to_string()).collect::<String>()
+}
+
+fn main() {
+    let input = read_input();
+    println!("Part 1: {}", part1(input.clone()));
+    println!("Part 2: {}", part2(input));
 }