union_find.rs

/// Disjoint-set data structure
///
/// This provides operations for disjoint sets.
/// They runs in nearly constatant time.
/// (the actual time is `O(A(n))` where `A(n)` is the inverse of ackermann function.)
///
/// 1. unite(x, y) - unite a set including x and another set including y into one.
/// 2. same(x, y) - determine if x and y are in the same set.
/// 3. size(x) - calculate the number of elements of the set including x.
///
/// [`UnionFind::new(n)`](#method.new) creates n disjoint sets. `i`-th set contains single element `i` (0-indexed).
///
/// # Examples
/// ```
/// use algorithms::data_structure::UnionFind;
///
/// let mut uf = UnionFind::new(4);
/// assert!(!uf.same(0, 1));
///
/// uf.unite(0, 1);
/// assert!(uf.same(0, 1));
/// assert_eq!(uf.size(0), 2);
///
/// uf.unite(1, 2);
/// assert!(uf.same(0, 2));
/// assert_eq!(uf.size(0), 3);
/// ```
///
/// # Panics
/// panics if `x` or `y` is not less than number of elements given in the initialization method.
///
pub struct UnionFind {
    data: Vec<i32>,
}

impl UnionFind {
    /// Creates a object with n disjoint sets. `i`-th set is `{ i }`.
    pub fn new(n: usize) -> UnionFind {
        UnionFind { data: vec![-1; n] }
    }

    /// Unite a set including `x` and another set including y into one.
    /// Returns `true` only if they were in different set.
    pub fn unite(&mut self, x: usize, y: usize) -> bool {
        let x = self.root(x);
        let y = self.root(y);
        if x != y {
            let (x, y) = if self.data[x] <= self.data[y] {
                (x, y)
            } else {
                (y, x)
            };
            self.data[x] += self.data[y];
            self.data[y] = x as i32;
        }
        x != y
    }

    /// Returns `true` only if `x` and `y` are in a same set.
    pub fn same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }

    /// Returns the number of elements of a set including `x`.
    pub fn size(&mut self, x: usize) -> u32 {
        let r = self.root(x);
        (-self.data[r]) as u32
    }

    /// internal method to return representative element of a set including `x`.
    pub fn root(&mut self, x: usize) -> usize {
        if self.data[x] < 0 {
            x
        } else {
            let nx = self.data[x] as usize;
            let r = self.root(nx);
            self.data[x] = r as i32;
            r
        }
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_simple() {
        let mut uf = UnionFind::new(3);
        assert_eq!(1, uf.size(0));
        assert_eq!(1, uf.size(1));
        assert_eq!(1, uf.size(2));
        assert_eq!(0, uf.root(0));
        assert_eq!(1, uf.root(1));
        assert_eq!(2, uf.root(2));
        assert!(!uf.same(1, 2));
        uf.unite(1, 2);
        assert_ne!(uf.root(0), uf.root(2));
        assert_eq!(uf.root(1), uf.root(2));
        assert_eq!(1, uf.size(0));
        assert_eq!(2, uf.size(1));
        assert_eq!(2, uf.size(2));
        assert!(uf.same(1, 2));
        uf.unite(0, 1);
        assert_eq!(uf.root(0), uf.root(2));
        assert_eq!(uf.root(1), uf.root(2));
        assert_eq!(3, uf.size(0));
        assert_eq!(3, uf.size(1));
        assert_eq!(3, uf.size(2));
        assert!(uf.same(1, 2));
        assert!(uf.same(0, 2));
    }
}