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

//!Generate a random shuffle of the numbers between start (inclusive) and end (exclusive)
//!
//! No repeats will be generated. No number in the range won't be generated.
//!

use rand::Rng;
use primes::is_prime;
use num::Integer;

fn first_prime_above(mut value: u64) -> u64 {
    while !is_prime(value) {
        value += 1;
    }
    value
}

pub struct RandomSequence {
    curr: u64,
    modulus: u64,
    offset: u64,
    range_size: u64,
    a: u64,
    c: u64,
    num_generated: u64,
}

impl RandomSequence {

    /// Generate a random shuffle of the numbers between start (inclusive) and end (exclusive)
    ///
    /// No repeats will be generated. No number in the range won't be generated.
    ///
    /// The space complexity of this system is O(1), and time complexity O(n) (obviously)
    fn new(start: u64, end: u64) -> Self {
        assert!(end >= start);
        let length = end - start;

        // first value (seed)
        let seed: u64 = rand::thread_rng().gen();

        // modulus
        let m = first_prime_above(length);

        // multiplier (2m + 1) to make sure (a-1) % m == 0
        let a: u64 = (m * 2) + 1;

        // offset
        let c: u64 = rand::thread_rng().gen();

        let mut c = c % m;
        // Make sure c is never 0
        if c == 0 {
            c += 1;
        }

        // m prime
        assert!(is_prime(m));
        // c not 0
        assert_ne!(c, 0);
        // c and m relatively prime
        assert!(m.gcd(&c) == 1 && c.gcd(&m) == 1);
        // a - 1 divisible by m (which is the only prime factor of m, m is prime)
        assert_eq!((a - 1) % m, 0);

        // if m is divisible by 4, then a-1 is
        if m % 4 == 0 {
            assert_eq!((a - 1) % 4, 0);
        }

        Self {
            curr: seed % m,
            modulus: m,
            offset: start,
            range_size: length,
            a,
            c,
            num_generated: 0,
        }
    }
}

impl Iterator for RandomSequence {
    type Item = u64;

    fn next(&mut self) -> Option<Self::Item> {
        if self.num_generated > self.range_size {
            return None
        }

        loop {
            self.curr = ((self.a as u128 * self.curr as u128 + self.c as u128) % self.modulus as u128) as u64;

            if self.curr > self.range_size {
                continue;
            }

            self.num_generated += 1;
            break;
        }


        Some(self.curr + self.offset)
    }
}


#[cfg(test)]
mod tests {
    extern crate std;

    use std::collections::HashMap;
    use crate::RandomSequence;

    #[test]
    fn test() {

        let start = 1000;
        let end = 100000;
        let mut seen = HashMap::new();

        for i in RandomSequence::new(start, end) {
            *seen.entry(i).or_insert(0) += 1;
        }


        for i in start..end {
            assert_eq!(seen.get(&i), Some(&1));
        }
    }

}