1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
//! `UnionFind<K>` is a disjoint-set data structure.

use super::graph::IndexType;

/// `UnionFind<K>` is a disjoint-set data structure. It tracks set membership of *n* elements
/// indexed from *0* to *n - 1*. The scalar type is `K` which must be an unsigned integer type.
///
/// http://en.wikipedia.org/wiki/Disjoint-set_data_structure
///
/// Too awesome not to quote:
///
/// “The amortized time per operation is **O(α(n))** where **α(n)** is the
/// inverse of **f(x) = A(x, x)** with **A** being the extremely fast-growing Ackermann function.”
#[derive(Debug, Clone)]
pub struct UnionFind<K>
{
    // For element at index *i*, store the index of its parent; the representative itself
    // stores its own index. This forms equivalence classes which are the disjoint sets, each
    // with a unique representative.
    parent: Vec<K>,
    // It is a balancing tree structure,
    // so the ranks are logarithmic in the size of the container -- a byte is more than enough.
    //
    // Rank is separated out both to save space and to save cache in when searching in the parent
    // vector.
    rank: Vec<u8>,
}

#[inline]
unsafe fn get_unchecked<K>(xs: &[K], index: usize) -> &K
{
    debug_assert!(index < xs.len());
    xs.get_unchecked(index)
}

impl<K> UnionFind<K>
    where K: IndexType
{
    /// Create a new `UnionFind` of `n` disjoint sets.
    pub fn new(n: usize) -> Self
    {
        let rank = vec![0; n];
        let parent = (0..n).map(K::new).collect::<Vec<K>>();

        UnionFind{parent: parent, rank: rank}
    }

    /// Return the representative for `x`.
    ///
    /// **Panics** if `x` is out of bounds.
    pub fn find(&self, x: K) -> K
    {
        assert!(x.index() < self.parent.len());
        unsafe {
            let mut x = x;
            loop {
                // Use unchecked indexing because we can trust the internal set ids.
                let xparent = *get_unchecked(&self.parent, x.index());
                if xparent == x {
                    break
                }
                x = xparent;
            }
            x
        }
    }

    /// Return the representative for `x`.
    ///
    /// Write back the found representative, flattening the internal
    /// datastructure in the process and quicken future lookups.
    ///
    /// **Panics** if `x` is out of bounds.
    pub fn find_mut(&mut self, x: K) -> K
    {
        assert!(x.index() < self.parent.len());
        unsafe {
            self.find_mut_recursive(x)
        }
    }

    unsafe fn find_mut_recursive(&mut self, x: K) -> K
    {
        let xparent = *get_unchecked(&self.parent, x.index());
        if xparent != x {
            let xrep = self.find_mut_recursive(xparent);
            let xparent = self.parent.get_unchecked_mut(x.index());
            *xparent = xrep;
            *xparent
        } else {
            xparent
        }
    }


    /// Unify the two sets containing `x` and `y`.
    ///
    /// Return `false` if the sets were already the same, `true` if they were unified.
    /// 
    /// **Panics** if `x` or `y` is out of bounds.
    pub fn union(&mut self, x: K, y: K) -> bool
    {
        if x == y {
            return false
        }
        let xrep = self.find_mut(x);
        let yrep = self.find_mut(y);

        if xrep == yrep {
            return false
        }

        let xrepu = xrep.index();
        let yrepu = yrep.index();
        let xrank = self.rank[xrepu];
        let yrank = self.rank[yrepu];

        // The rank corresponds roughly to the depth of the treeset, so put the 
        // smaller set below the larger
        if xrank < yrank {
            self.parent[xrepu] = yrep;
        } else if xrank > yrank {
            self.parent[yrepu] = xrep;
        } else {
            // put y below x when equal.
            self.parent[yrepu] = xrep;
            self.rank[xrepu] += 1;
        }
        true
    }

    /// Return a vector mapping each element to its representative.
    pub fn into_labeling(mut self) -> Vec<K>
    {
        // write in the labeling of each element
        unsafe {
            for ix in 0..self.parent.len() {
                let k = *get_unchecked(&self.parent, ix);
                let xrep = self.find_mut_recursive(k);
                *self.parent.get_unchecked_mut(ix) = xrep;
            }
        }
        self.parent
    }
}