big changes

lab5/zad1/src/main.rs

@@ -1,84 +1,173 @@
 #![feature(exitcode_exit_method)]
 
-use std::{fmt::Display, fs::OpenOptions, io::{self, Write}, process::ExitCode, sync::Arc, time::Instant};
+use std::{cmp::{Ordering, Reverse}, collections::{BinaryHeap, HashSet}, fmt::Display, fs::OpenOptions, hash::Hash, io::{self, Write}, process::ExitCode, sync::Arc, time::Instant};
 
 use dashmap::DashMap;
 use rand::{thread_rng, Rng};
 use rayon::iter::{IndexedParallelIterator, IntoParallelIterator, ParallelIterator};
 
-#[derive(Clone, Copy)]
+#[derive(Clone, Copy, Debug)]
 pub struct Edge {
-    pub u: usize,
-    pub v: usize,
-    pub w: f64,
+    pub src: usize,
+    pub dst: usize,
+    pub weight: f64,
+}
+
+impl Hash for Edge {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        self.src.hash(state);
+        self.dst.hash(state);
+    }
+}
+
+impl PartialOrd for Edge {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        self.weight.partial_cmp(&other.weight)
+    }
+}
+
+impl PartialEq for Edge {
+    fn eq(&self, other: &Self) -> bool {
+        self.weight == other.weight
+    }
+}
+
+impl Eq for Edge {}
+
+impl Ord for Edge {
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+        self.weight.total_cmp(&other.weight)
+    }
 }
 
 pub struct Graph {
     pub size: usize,
-    pub edges: Vec<Vec<f64>>,
+    pub edges: Vec<Edge>,
 }
 
 impl Graph {
     pub fn new(size: usize) -> Self {
         Self {
             size,
-            edges: (0..size)
-                .map(|i|
-                    (0..size)
-                        .map(|j|
-                            if i == j { 0.0 }
-                            else { thread_rng().gen::<f64>() }
-                        )
-                        .collect::<Vec<_>>()
-                )
-                .collect::<Vec<_>>(),
+            edges: (0..size).map(|u|
+                (0..size).map(|v|
+                    Edge { src: u, dst: v, weight: 0.0 }
+                ).collect::<Vec<_>>()
+                ).flatten()
+                    .collect::<Vec<_>>(),
         }
     }
 
-    fn min(&self, key: &Vec<f64>, mst: &Vec<bool>) -> usize {
-        let mut min = f64::INFINITY;
-        let mut min_index = usize::MAX;
+    pub fn new_rand(size: usize) -> Self {
+        Self {
+            size,
+            edges: (0..size).map(|u|
+                (0..size).map(|v|
+                    Edge {
+                        src: u,
+                        dst: v,
+                        weight: if u == v { 0.0 }
+                            else { thread_rng().gen::<f64>() }
+                    }
+                ).collect::<Vec<_>>()
+                ).flatten()
+                    .collect::<Vec<_>>(),
+        }
+    }
 
-        for i in 0..self.size {
-            if mst[i] == false && key[i] < min {
-                min = key[i];
-                min_index = i;
-            }
+    pub fn vertex(&self, u: usize, v: usize) -> Option<f64> {
+        if u >= self.size || v >= self.size {
+            return None;
         }
 
-        min_index
+        Some(self.edges.iter().find(|e| e.src == u && e.dst == v).unwrap().weight)
     }
 
     pub fn prim(&self) -> Vec<Edge> {
-        let mut parent = vec![0; self.size];
+        // Associate with each vertex v of the graph a number C[v] (the cheapest cost of a connection to v) and an edge E[v] (the edge providing that cheapest connection). To initialize these values, set all values of C[v] to +∞ (or to any number larger than the maximum edge weight) and set each E[v] to a special flag value indicating that there is no edge connecting v to earlier vertices.
+        let mut min_edges = (0..self.size)
+            .map(|i|
+                *self.edges.iter()
+                    .filter(|e| (e.src == i || e.dst == i) && e.src != e.dst)
+                    .min()
+                    .unwrap()
+            ).collect::<Vec<_>>();
+        // dbg!(&min_edges);
 
-        let mut key = vec![f64::INFINITY; self.size];
+        // helper struct for the queue
+        #[derive(Clone, Debug)]
+        struct Vertex {
+            index: usize,
+            min_weight: f64,
+        }
 
-        let mut mst = vec![false; self.size];
+        impl Hash for Vertex {
+            fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+                self.index.hash(state);
+            }
+        }
 
-        key[0] = 0.0;
-        parent[0] = usize::MAX;
+        impl PartialEq for Vertex {
+            fn eq(&self, other: &Self) -> bool {
+                self.min_weight == other.min_weight
+            }
+        }
 
-        for _ in 0..(self.size - 1) {
-            let u = self.min(&key, &mst);
-            mst[u] = true;
+        impl Eq for Vertex {}
 
-            for j in 0..self.size {
-                if self.edges[u][j] != 0.0 && mst[j] == false && self.edges[u][j] < key[j] {
-                    parent[j] = u;
-                    key[j] = self.edges[u][j];
+        impl PartialOrd for Vertex {
+            fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+                self.min_weight.partial_cmp(&other.min_weight)
+            }
+        }
+
+        impl Ord for Vertex {
+            fn cmp(&self, other: &Self) -> Ordering {
+                self.min_weight.total_cmp(&other.min_weight)
+            }
+        }
+
+        // Initialize an empty forest F
+        let mut forest = vec![];
+        // and a set Q of vertices 
+        let mut queue = BinaryHeap::<Reverse<Vertex>>::new();
+
+        // that have not yet been included in F (initially, all vertices).
+        (0..self.size)
+            .map(|i| Vertex { index: i, min_weight: min_edges[i].weight })
+            .for_each(|v| queue.push(Reverse(v)));
+
+        // Repeat the following steps until Q is empty: 
+        // Find and remove a vertex v from Q having the minimum possible value of C[v]
+        while let Some(Reverse(v)) = queue.pop() {
+            // Add v to F
+            forest.push(v.clone());
+
+            // Loop over the edges vw connecting v to other vertices w.
+            for vw in self.edges.iter()
+                .filter(|e| (e.src == v.index || e.dst == v.index) && e.src != e.dst) {
+
+                // the vertex in the current edge that isn't v.src
+                let w = if vw.src == v.index { vw.dst } else { vw.src };
+
+                // For each such edge, if w still belongs to Q and vw has smaller weight than C[w], perform the following steps:
+                if queue.clone().iter().any(|Reverse(e)| e.index == w || e.index == w) && vw.weight < min_edges[w].weight {
+                    dbg!(&w);
+                    // Set C[w] to the cost of edge vw
+                    // Set E[w] to point to edge vw.
+                    min_edges[w] = *vw;
                 }
             }
         }
 
-        (0..self.size)
-            .filter(|i| parent[*i] != usize::MAX)
-            .map(|i| Edge {
-                u: parent[i],
-                v: i,
-                w: self.edges[i][parent[i]],
-            })
-            .collect()
+        // dbg!(&min_edges);
+        // Return F, which specifically includes the corresponding edges in E
+        forest.iter()
+            .map(|i| min_edges[i.index])
+            .collect::<HashSet<_>>()
+            .iter()
+            .map(|e| *e)
+            .collect::<Vec<_>>()
     }
 
     fn find_id(belongs: &mut Vec<usize>, i: usize) -> usize {
@@ -104,21 +193,11 @@ impl Graph {
     }
 
     pub fn kruskal(&self) -> Vec<Edge> {
-        let mut edges = vec![];
+        let mut edges = self.edges.iter()
+            .filter(|e| e.weight != 0.0)
+            .collect::<Vec<_>>();
 
-        for i in 0..self.size {
-            for j in 0..i {
-                if self.edges[i][j] != 0.0 {
-                    edges.push(Edge {
-                        u: i,
-                        v: j,
-                        w: self.edges[i][j],
-                    });
-                }
-            }
-        }
-
-        edges.sort_by(|e1, e2| e1.w.total_cmp(&e2.w));
+        edges.sort();
 
         let mut belongs = (0..self.size).collect::<Vec<_>>();
         let mut rank = vec![0; self.size];
@@ -126,11 +205,11 @@ impl Graph {
         let mut mst = Vec::with_capacity(self.size);
 
         for i in 0..edges.len() {
-            let a = Self::find_id(&mut belongs, edges[i].u);
-            let b = Self::find_id(&mut belongs, edges[i].v);
+            let a = Self::find_id(&mut belongs, edges[i].src);
+            let b = Self::find_id(&mut belongs, edges[i].dst);
 
             if a != b {
-                mst.push(edges[i]);
+                mst.push(*edges[i]);
 
                 Self::union(&mut belongs, &mut rank, a, b);
             }
@@ -144,7 +223,7 @@ impl Display for Graph {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         for i in 0..self.size {
             for j in 0..self.size {
-                write!(f, "{weight:.6} ", weight = self.edges[i][j])?;
+                write!(f, "{weight:.6} ", weight = self.vertex(i, j).unwrap())?;
             }
             write!(f, "\n")?;
         }
@@ -157,7 +236,7 @@ fn print_mst(mst: &Vec<Edge>) {
     println!("vertex\t\tweight");
 
     for edge in mst {
-        println!("{} - {}\t\t{:.6}", edge.u, edge.v, edge.w);
+        println!("{} - {}\t\t{:.6}", edge.src, edge.dst, edge.weight);
     }
 }
 
@@ -190,7 +269,7 @@ fn test() {
         println!("{n}: starting");
         (0..rep).into_par_iter().for_each(|k| {
             println!("\t{n}: iteration {k}");
-            let graph = Graph::new(n);
+            let graph = Graph::new_rand(n);
 
             let prim_timer = Instant::now();
             graph.prim();
@@ -239,7 +318,7 @@ fn show() {
         .parse::<usize>()
         .expect("graph size should be usize");
 
-    let graph = Graph::new(size);
+    let graph = Graph::new_rand(size);
 
     println!();
     println!("graph:");