add 85 and 86

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
+

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
+}