remove par (#101)

* remove par

* fix

---------

Co-authored-by: Luke Videckis <lukevideckis@gmail.com>

Author: lrvideckis

examples/graphs/dijk_aizu.rs

@@ -16,9 +16,7 @@ fn main() {
         adj[u].push((v, w));
     }
 
-    let (dist, par) = dijk(&adj, s);
-
-    assert_eq!(par[s], None);
+    let dist = dijk(&adj, s);
 
     for d in dist {
         if d == u64::MAX {

examples/graphs/dijk_yosupo.rs

@@ -17,21 +17,35 @@ fn main() {
         adj[u].push((v, w));
     }
 
-    let (dist, par) = dijk(&adj, s);
-
-    assert_eq!(par[s], None);
+    let dist = dijk(&adj, s);
 
     if dist[t] == u64::MAX {
         println!("{}", -1);
         return;
     }
 
-    let mut path = vec![];
+    let mut par = vec![None; n];
+    {
+        let mut seen = vec![false; n];
+        seen[s] = true;
+        let mut q = std::collections::VecDeque::new();
+        q.push_back(s);
+        while let Some(u) = q.pop_front() {
+            for &(v, w) in &adj[u] {
+                if seen[v] || dist[u] + w != dist[v] {
+                    continue;
+                }
+                par[v] = Some(u);
+                seen[v] = true;
+                q.push_back(v);
+            }
+        }
+    }
+    let mut path = vec![t];
     let mut u = t;
-    path.push(u);
-    while let Some(prev_u) = par[u] {
-        path.push(prev_u);
-        u = prev_u;
+    while let Some(v) = par[u] {
+        u = v;
+        path.push(u);
     }
 
     path.reverse();

src/graphs/dijk.rs

@@ -9,36 +9,29 @@
 ///    adj[u].push((v, w));
 /// }
 ///
-/// let (dist, par) = dijk(&adj, 0);
+/// let dist = dijk(&adj, 0);
 /// assert_eq!(dist, [0, 10, 110, u64::MAX]);
-/// assert_eq!(par, [None, Some(0), Some(1), None]);
-///
-/// let mut u = 2; // loop over shortest path in reverse
-/// while let Some(prev) = par[u] {
-///    u = prev;
-/// }
 /// ```
 ///
 /// # Complexity
 /// - V: number of vertices
 /// - E: number of edges
 /// - Time: O(V + E log E)
 /// - Space: O(V + E)
-pub fn dijk(adj: &[Vec<(usize, u64)>], s: usize) -> (Vec<u64>, Vec<Option<usize>>) {
+pub fn dijk(adj: &[Vec<(usize, u64)>], s: usize) -> Vec<u64> {
     use std::cmp::Reverse;
     let n = adj.len();
     let mut dist = vec![u64::MAX; n];
-    let mut par = vec![None; n];
     let mut q = std::collections::BinaryHeap::new();
-    q.push(Reverse((0, s, None)));
-    while let Some(Reverse((d, u, p))) = q.pop() {
+    q.push(Reverse((0, s)));
+    while let Some(Reverse((d, u))) = q.pop() {
         if dist[u] <= d {
             continue;
         }
-        (dist[u], par[u]) = (d, p);
+        dist[u] = d;
         for &(v, w) in &adj[u] {
-            q.push(Reverse((dist[u] + w, v, Some(u))));
+            q.push(Reverse((dist[u] + w, v)));
         }
     }
-    (dist, par)
+    dist
 }