From 1a34dfda82d43d411d3fc7af58a63836e8e9a8e9 Mon Sep 17 00:00:00 2001
From: "Dr. Matthias Ratajczak" <m.ratajczak@hzdr.de>
Date: Tue, 20 Jun 2023 14:25:54 +0200
Subject: [PATCH] add 85 and 86

---
 src/euler85/Cargo.toml  |  8 +++++
 src/euler85/src/main.rs | 66 +++++++++++++++++++++++++++++++++++++++++
 src/euler86/Cargo.toml  | 11 +++++++
 src/euler86/src/main.rs | 60 +++++++++++++++++++++++++++++++++++++
 4 files changed, 145 insertions(+)
 create mode 100644 src/euler85/Cargo.toml
 create mode 100644 src/euler85/src/main.rs
 create mode 100644 src/euler86/Cargo.toml
 create mode 100644 src/euler86/src/main.rs

diff --git a/src/euler85/Cargo.toml b/src/euler85/Cargo.toml
new file mode 100644
index 0000000..d5b1234
--- /dev/null
+++ b/src/euler85/Cargo.toml
@@ -0,0 +1,8 @@
+[package]
+name = "euler85"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
diff --git a/src/euler85/src/main.rs b/src/euler85/src/main.rs
new file mode 100644
index 0000000..b26c2ab
--- /dev/null
+++ b/src/euler85/src/main.rs
@@ -0,0 +1,66 @@
+const TARGET: usize = 2_000_000;
+
+fn main() {
+    let mut x = 1_000;
+    let mut y = 2;
+
+    let mut grid = Grid::new(x, y);
+    let mut number;
+    let mut best_grid = grid.clone();
+    let mut best_diff = 5_000_000;
+    loop {
+        number = grid.number_rectangles();
+        let diff = number.abs_diff(TARGET);
+        if diff < best_diff {
+            best_diff = diff;
+            best_grid = grid.clone();
+        }
+        if number < TARGET {
+            y += 1;
+        } else {
+            x -= 1;
+        }
+        if x == 1 {
+            break;
+        }
+
+        grid = Grid::new(x, y);
+    }
+
+    let area = best_grid.area();
+    println!("{area}");
+}
+
+#[derive(Debug, Clone)]
+struct Grid {
+    x: usize,
+    y: usize,
+}
+
+impl Grid {
+    fn new(x: usize, y: usize) -> Self {
+        Self { x, y }
+    }
+
+    fn number_rectangles(&self) -> usize {
+        let mut result = 0;
+
+        for x in 1..=self.x {
+            for y in 1..=self.y {
+                result += self.fits(x, y);
+            }
+        }
+
+        result
+    }
+
+    fn fits(&self, x: usize, y: usize) -> usize {
+        let fits_in_x = self.x - (x - 1);
+        let fits_in_y = self.y - (y - 1);
+        fits_in_x * fits_in_y
+    }
+
+    fn area(&self) -> usize {
+        self.x * self.y
+    }
+}
diff --git a/src/euler86/Cargo.toml b/src/euler86/Cargo.toml
new file mode 100644
index 0000000..4e96566
--- /dev/null
+++ b/src/euler86/Cargo.toml
@@ -0,0 +1,11 @@
+[package]
+name = "euler86"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[profile.release]
+lto = "fat"
+debug = true
+
diff --git a/src/euler86/src/main.rs b/src/euler86/src/main.rs
new file mode 100644
index 0000000..9334990
--- /dev/null
+++ b/src/euler86/src/main.rs
@@ -0,0 +1,60 @@
+use std::f64::EPSILON;
+
+const TARGET: u32 = 1_000_000;
+
+fn main() {
+    let mut m = 1;
+    let mut distinct = 0;
+
+    loop {
+        println!("trying: {m}");
+
+        for x in 1..m + 1 {
+            for y in x..m + 1 {
+                let z = m;
+                let c = Cuboid::new(x, y, z);
+                if c.shortest_path_is_integer() {
+                    distinct += 1;
+                };
+            }
+        }
+
+        if distinct > TARGET {
+            break;
+        }
+
+        m += 1;
+    }
+
+    println!("\n{m}");
+}
+
+struct Cuboid {
+    x: u32,
+    y: u32,
+    z: u32,
+}
+
+impl Cuboid {
+    fn new(x: u32, y: u32, z: u32) -> Self {
+        Self { x, y, z }
+    }
+
+    fn shortest_path_is_integer(&self) -> bool {
+        // because of the way we iterator over x, y and z, these are guaranteed to be in order
+        // and therefore produces the shortest path
+        let shortest_path = pythagorean(self.x + self.y, self.z);
+
+        is_integer(shortest_path)
+    }
+}
+
+fn pythagorean(x: u32, y: u32) -> f64 {
+    ((x.pow(2) + y.pow(2)) as f64).sqrt()
+}
+
+fn is_integer(result: f64) -> bool {
+    let rounded = result.round();
+
+    (result - rounded).abs() <= EPSILON
+}