Update the documentation for dsu

Author: qryxip

src/dsu.rs

@@ -1,7 +1,49 @@
-/// Implement (union by size) + (path compression)
-/// Reference:
-/// Zvi Galil and Giuseppe F. Italiano,
-/// Data structures and algorithms for disjoint set union problems
+//! A Disjoint set union (DSU) with union by size and path compression.
+
+/// A Disjoint set union (DSU) with union by size and path compressione.
+///
+/// See: [Zvi Galil and Giuseppe F. Italiano, Data structures and algorithms for disjoint set union problems](https://core.ac.uk/download/pdf/161439519.pdf)
+///
+/// In the following documentation, let $n$ be size of the DSU.
+///
+/// # Example
+///
+/// ```
+/// use ac_library_rs::Dsu;
+/// use proconio::{input, source::once::OnceSource};
+///
+/// input! {
+///     from OnceSource::from(
+///         "5\n\
+///          3\n\
+///          0 1\n\
+///          2 3\n\
+///          3 4\n",
+///     ),
+///     n: usize,
+///     abs: [(usize, usize)],
+/// }
+///
+/// let mut dsu = Dsu::new(n);
+/// for (a, b) in abs {
+///     dsu.merge(a, b);
+/// }
+///
+/// assert!(dsu.same(0, 1));
+/// assert!(!dsu.same(1, 2));
+/// assert!(dsu.same(2, 4));
+///
+/// assert_eq!(
+///     dsu.groups()
+///         .into_iter()
+///         .map(|mut group| {
+///             group.sort_unstable();
+///             group
+///         })
+///         .collect::<Vec<_>>(),
+///     [&[0, 1][..], &[2, 3, 4][..]],
+/// );
+/// ```
 pub struct Dsu {
     n: usize,
     // root node: -1 * component size
@@ -10,13 +52,37 @@ pub struct Dsu {
 }
 
 impl Dsu {
-    // 0 <= size <= 10^8 is constrained.
+    /// Creates a new `Dsu`.
+    ///
+    /// # Constraints
+    ///
+    /// - $0 \leq n \leq 10^8$
+    ///
+    /// # Complexity
+    ///
+    /// - $O(n)$
     pub fn new(size: usize) -> Self {
         Self {
             n: size,
             parent_or_size: vec![-1; size],
         }
     }
+
+    // `\textsc` does not work in KaTeX
+    /// Performs the `UNION` operation.
+    ///
+    /// # Constraints
+    ///
+    /// - $0 \leq a < n$
+    /// - $0 \leq b < n$
+    ///
+    /// # Panics
+    ///
+    /// Panics if the above constraints are not satisfied.
+    ///
+    /// # Complexity
+    ///
+    /// - $O(\alpha(n))$ amortized
     pub fn merge(&mut self, a: usize, b: usize) -> usize {
         assert!(a < self.n);
         assert!(b < self.n);
@@ -32,11 +98,39 @@ impl Dsu {
         x
     }
 
+    /// Returns whether the vertices $a$ and $b$ are in the same connected component.
+    ///
+    /// # Constraints
+    ///
+    /// - $0 \leq a < n$
+    /// - $0 \leq b < n$
+    ///
+    /// # Panics
+    ///
+    /// Panics if the above constraint is not satisfied.
+    ///
+    /// # Complexity
+    ///
+    /// - $O(\alpha(n))$ amortized
     pub fn same(&mut self, a: usize, b: usize) -> bool {
         assert!(a < self.n);
         assert!(b < self.n);
         self.leader(a) == self.leader(b)
     }
+
+    /// Performs the `FIND` operation.
+    ///
+    /// # Constraints
+    ///
+    /// - $0 \leq a < n$
+    ///
+    /// # Panics
+    ///
+    /// Panics if the above constraint is not satisfied.
+    ///
+    /// # Complexity
+    ///
+    /// - $O(\alpha(n))$ amortized
     pub fn leader(&mut self, a: usize) -> usize {
         assert!(a < self.n);
         if self.parent_or_size[a] < 0 {
@@ -45,11 +139,33 @@ impl Dsu {
         self.parent_or_size[a] = self.leader(self.parent_or_size[a] as usize) as i32;
         self.parent_or_size[a] as usize
     }
+
+    /// Returns the size of the connected component that contains the vertex $a$.
+    ///
+    /// # Constraints
+    ///
+    /// - $0 \leq a < n$
+    ///
+    /// # Panics
+    ///
+    /// Panics if the above constraint is not satisfied.
+    ///
+    /// # Complexity
+    ///
+    /// - $O(\alpha(n))$ amortized
     pub fn size(&mut self, a: usize) -> usize {
         assert!(a < self.n);
         let x = self.leader(a);
         -self.parent_or_size[x] as usize
     }
+
+    /// Divides the graph into connected components.
+    ///
+    /// The result may not be ordered.
+    ///
+    /// # Complexity
+    ///
+    /// - $O(\alpha(n))$ amortized
     pub fn groups(&mut self) -> Vec<Vec<usize>> {
         let mut leader_buf = vec![0; self.n];
         let mut group_size = vec![0; self.n];