feat: add Kernighan–Lin algorithm

Cargo.toml

@@ -4,4 +4,5 @@ version = "0.1.0"
 edition = "2021"
 
 [dependencies]
-rocket = "0.5.0"
+rand = "0.9.0"
+rocket = "0.5.1"

src/main.rs

@@ -1,9 +1,66 @@
+use rand::rng;
+use rand::seq::SliceRandom;
+
 #[macro_use]
 extern crate rocket;
 
+fn calculate_distance(city1: &(f64, f64), city2: &(f64, f64)) -> f64 {
+    let dx = city1.0 - city2.0;
+    let dy = city1.1 - city2.1;
+    (dx * dx + dy * dy).sqrt()
+}
+
+fn calculate_tour_length(tour: &[usize], cities: &[(f64, f64)]) -> f64 {
+    let mut length = 0.0;
+    for i in 0..tour.len() {
+        let city1 = &cities[tour[i]];
+        let city2 = &cities[tour[(i + 1) % tour.len()]];
+        length += calculate_distance(city1, city2);
+    }
+    length
+}
+
+fn lin_kernighan(mut tour: Vec<usize>, cities: &[(f64, f64)]) -> Vec<usize> {
+    // let rng = rng();
+    let n = cities.len();
+    let mut improved = true;
+
+    while improved {
+        improved = false;
+        for i in 0..n {
+            for j in (i + 2)..n {
+                if i == 0 && j == n - 1 {
+                    continue;
+                }
+                let mut new_tour = tour.clone();
+                new_tour[i + 1..=j].reverse();
+                if calculate_tour_length(&new_tour, cities) < calculate_tour_length(&tour, cities) {
+                    tour = new_tour;
+                    improved = true;
+                }
+            }
+        }
+    }
+    tour
+}
+
 #[get("/")]
-fn index() -> &'static str {
-    "Hello, world!"
+fn index() -> String {
+    let cities = vec![(0.0, 0.0), (1.0, 5.0), (5.0, 2.0), (6.0, 7.0), (3.0, 4.0)];
+
+    let mut tour: Vec<usize> = (0..cities.len()).collect();
+    tour.shuffle(&mut rng());
+
+    let best_tour = lin_kernighan(tour, &cities);
+
+    // println!("Beste Tour: {:?}", best_tour);
+    println!(
+        "Länge der besten Tour: {}",
+        calculate_tour_length(&best_tour, &cities)
+    );
+
+    let tour_str = format!("Beste Tour: {:?}", best_tour);
+    return tour_str;
 }
 
 #[launch]