From 250f0e163c470a4492c075f5342a329b2d4950e0 Mon Sep 17 00:00:00 2001
From: Lennard Brinkhaus <lennard.brinkhaus@dragse.de>
Date: Wed, 6 Dec 2023 16:51:30 +0100
Subject: [PATCH] refactor: day 6 is now more performant

---
 src/day05.rs |  3 ++-
 src/day06.rs | 35 +++++++++++++++++++----------------
 2 files changed, 21 insertions(+), 17 deletions(-)

diff --git a/src/day05.rs b/src/day05.rs
index b152943..e348812 100644
--- a/src/day05.rs
+++ b/src/day05.rs
@@ -1,4 +1,5 @@
-use std::collections::{HashMap};
+#![allow(dead_code)]
+
 use std::time::Instant;
 use itertools::Itertools;
 use rayon::prelude::*;
diff --git a/src/day06.rs b/src/day06.rs
index e1c3e7f..48f43cf 100644
--- a/src/day06.rs
+++ b/src/day06.rs
@@ -1,3 +1,4 @@
+use std::ops::Range;
 use std::time::Instant;
 
 pub fn execute_task01(content: &str) {
@@ -18,7 +19,7 @@ pub fn execute_task02(content: &str) {
     println!("Day06 - Task02 - Duration: {duration:?} - Correct Race: {}", product_correct_races)
 }
 
-fn solve_01(content: &str) -> anyhow::Result<usize> {
+fn solve_01(content: &str) -> anyhow::Result<i64> {
     let result = content
         .lines()
         .map(|line| line
@@ -42,11 +43,11 @@ fn solve_01(content: &str) -> anyhow::Result<usize> {
     Ok(races
         .iter()
         .map(|(time, distance)| calc_possible_options(*time, *distance))
-        .map(|options| options.len())
+        .map(|options| options.end - options.start)
         .product())
 }
 
-fn solve_02(content: &str) -> anyhow::Result<usize> {
+fn solve_02(content: &str) -> anyhow::Result<i64> {
     let result = content
         .lines()
         .map(|line| line
@@ -63,24 +64,26 @@ fn solve_02(content: &str) -> anyhow::Result<usize> {
     Ok(races
         .iter()
         .map(|(time, distance)| calc_possible_options(*time, *distance))
-        .map(|options| options.len())
+        .map(|options| options.end - options.start)
         .product())
 }
 
 
-fn calc_possible_options(time: i64, distance: i64) -> Vec<i64> {
-    let mut data = vec![];
-    // TODO Performance!!!
-    for i in 1..time {
-        let y = i * (time - i);
-        if y > distance {
-            data.push(i)
-        } else if data.len() > 0 {
-            break
-        }
-    }
+fn calc_possible_options(time: i64, distance: i64) -> Range<i64> {
+    // f(x) = x * (time - x)
+    // f(x) = time * x - x * x
+    // PQ Ready: 0 = x * x - time * x + distance
+    // =>
+    // p = - time
+    // q = distance
 
-    data
+    let time = time as f64;
+    let distance = distance as f64;
+
+    let x1 = time / 2.0 - ((time * time / 4.0) - distance).sqrt();
+    let x2 = time / 2.0 + ((time * time / 4.0) - distance).sqrt();
+
+    (x1.floor() as i64 + 1)..(x2.ceil() as i64)
 }
 
 #[test]