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
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165

//! A simple sparse set based on an indexed sorted vector.

use crate::{
    persist::{load_usize, load_vec_u64, save_vec, Persistent, load_vec_usize},
    rank::Rank,
    select::Select,
    set::ImpliedSet,
};

/// A simple index sparse set representation.
/// 
/// This representation is not succinct - it stores the elements of the set
/// in a sorted vector, and computes a table-of-contents to accelerate the
/// binary search based implementation of `rank`.
/// 
/// It uses a 1024 entry table of contents.
/// 
pub struct NaiveSparse {
    b: usize,
    elements: Vec<u64>,
    toc: Vec<usize>,
}

static B: usize = 10;

impl NaiveSparse {
    /// Create a naive sparse set for values with `b` bits.
    pub fn new(b: usize, elements: &[u64]) -> NaiveSparse {
        assert!(b > B);
        let m = 1 << B;
        let s = if b > B { b - B } else { 0 };
        let mut toc = Vec::new();
        toc.resize(m + 1, 0);
        for i in 0..elements.len() {
            let x = elements[i];
            let v = (x >> s) as usize;
            toc[v] += 1;
        }
        let mut count = 0;
        for i in 0..toc.len() {
            let c = toc[i];
            toc[i] = count;
            count += c;
        }
        NaiveSparse {
            b,
            elements: Vec::from(elements),
            toc,
        }
    }
}

impl ImpliedSet for NaiveSparse {
    fn count(&self) -> usize {
        self.elements.len()
    }

    fn size(&self) -> u64 {
        1 << self.b
    }
}

impl Rank for NaiveSparse {
    fn rank(&self, value: u64) -> usize {
        if value >= (1 << self.b) {
            return self.count();
        }
        let s = self.b - B;
        let i = (value >> s) as usize;
        let mut first = self.toc[i];
        let last = self.toc[i + 1];
        let mut count = last - first;
        while count > 0 {
            let step = count / 2;
            let i = first + step;
            if self.elements[i] < value {
                first = i + 1;
                count -= step + 1;
            } else {
                count = step;
            }
        }
        first
    }
}

impl Select for NaiveSparse {
    fn select(&self, index: usize) -> u64 {
        self.elements[index]
    }
}

impl Persistent for NaiveSparse {
    fn save<Sink>(&self, sink: &mut Sink) -> std::io::Result<()>
    where
        Sink: std::io::Write,
    {
        sink.write_all(&self.b.to_ne_bytes())?;
        save_vec(sink, &self.elements)?;
        save_vec(sink, &self.toc)?;
        Ok(())
    }

    fn load<Source>(source: &mut Source) -> std::io::Result<Box<Self>>
    where
        Source: std::io::Read,
    {
        let b: usize = load_usize(source)?;
        let elements = load_vec_u64(source)?;
        let toc = load_vec_usize(source)?;
        Ok(Box::new(NaiveSparse { b, elements, toc }))
    }
}

#[cfg(test)]
mod tests {
    #[allow(unused_imports)]
    use num_traits::WrappingAdd;
    #[allow(unused_imports)]
    use num_traits::WrappingMul;

    use super::*;

    struct MiniRng {
        x: u64,
    }

    impl MiniRng {
        fn new(seed: u64) -> MiniRng {
            MiniRng { x: seed }
        }

        fn rnd(&mut self) -> u64 {
            self.x = self.x.wrapping_mul(2862933555777941757u64);
            self.x = self.x.wrapping_add(3037000493u64);
            self.x
        }
    }

    #[test]
    fn test_rank_1() {
        let b: usize = 20;
        let m: u64 = (1 << b) - 1;
        let k: usize = 1024;
        let mut xs: Vec<u64> = Vec::new();
        let mut rng = MiniRng::new(0xfbdb8b2bcc6674b9u64);
        for _i in 0..k {
            let x: u64 = (rng.rnd() ^ (rng.rnd() << 32) ^ (rng.rnd() >> 32)) & m;
            xs.push(x);
        }
        xs.sort();
        xs.dedup();
        println!("xs={:?}", xs);

        let r = NaiveSparse::new(b, &xs);
        for i in 0..xs.len() {
            let x = xs[i];
            println!("xs[i]={}", x);
            let j = r.rank(x);
            assert_eq!(j, i);
            assert!(r.contains(x));
            assert_eq!(r.access_and_rank(x), (i, true));
        }
    }
}