competitive-hpp 0.10.23

Competitive Programming Library for AtCoder with Rust
Documentation 
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

use num::traits::PrimInt;
use std::collections::HashMap;
#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Eratosthenes {
    primes: Vec<usize>,
    flags: Vec<usize>,
}

/// # Eratosthenes
///
/// Example:
/// ```
/// use competitive_hpp::prelude::*;
/// let eratosthenes = Eratosthenes::new(100);
///
/// assert!(!eratosthenes.is_prime(-1));
/// assert!(!eratosthenes.is_prime(0));
/// assert!(eratosthenes.is_prime(2));
/// assert!(!eratosthenes.is_prime(10));
/// assert!(eratosthenes.is_prime(11));
///
/// let mut map = HashMap::new();
/// map.insert(2, 1);
/// map.insert(5, 2);
/// assert_eq!(map, eratosthenes.factorization(50));
/// ```
#[allow(clippy::many_single_char_names)]
impl Eratosthenes {
    pub fn new<T>(n: T) -> Self
    where
        T: PrimInt,
    {
        let n = n.to_usize().unwrap();
        let bits = 32;
        let flags_num = n / bits + 1;

        let defaults: Vec<usize> = vec![0x5D75D75D, 0xD75D75D7, 0x75D75D75];

        let (mut i, mut f, mut j);
        let max = ((n as f64).sqrt() as usize) + 1;

        let mut flags: Vec<usize> = (0..flags_num).map(|i| defaults[i % 3]).collect();
        flags[flags_num - 1] &= (1 << (n % bits + 1)) - 1;

        i = 5;
        f = 4;
        while i <= max {
            let t = (flags[i / bits] >> (i % bits)) & 1 == 1;
            if !t {
                j = i * (i | 1);
                while j <= n {
                    flags[j / bits] |= 1 << (j % bits);
                    j += i * 2;
                }
            }
            f = 6 - f;
            i += f;
        }

        flags[0] &= !0b1100;
        flags[0] |= 0b11;

        let mut primes = vec![];
        for p in 2..n + 1 {
            if (flags[p / bits] >> (p % bits)) & 1 == 0 {
                primes.push(p);
            }
        }

        Eratosthenes { primes, flags }
    }

    pub fn is_prime<T>(&self, m: T) -> bool
    where
        T: PrimInt,
    {
        match m.to_usize() {
            Some(um) => self.flags[um / 32] >> (um % 32) & 1 == 0,
            None => false,
        }
    }

    pub fn factorization<T>(&self, n: T) -> HashMap<usize, usize>
    where
        T: PrimInt,
    {
        let mut n = n.to_usize().unwrap();
        let mut factors: HashMap<usize, usize> = HashMap::new();
        for &p in &self.primes {
            while n % p == 0 {
                n /= p;
                factors
                    .entry(p)
                    .and_modify(|entry| *entry += 1)
                    .or_insert(1);
            }
            if p > n {
                break;
            }
        }
        factors
    }
}

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

    #[test]
    fn test_eratosthenes() {
        let eratosthenes = Eratosthenes::new(100);

        assert!(!eratosthenes.is_prime(-1));
        assert!(!eratosthenes.is_prime(0));
        assert!(!eratosthenes.is_prime(1));
        assert!(eratosthenes.is_prime(2));
        assert!(eratosthenes.is_prime(3));
        assert!(!eratosthenes.is_prime(4));
        assert!(eratosthenes.is_prime(5));
        assert!(!eratosthenes.is_prime(6));
        assert!(eratosthenes.is_prime(7));
        assert!(!eratosthenes.is_prime(8));
        assert!(!eratosthenes.is_prime(9));
        assert!(!eratosthenes.is_prime(10));
        assert!(eratosthenes.is_prime(11));

        let mut map = HashMap::new();
        map.insert(2, 1);
        map.insert(5, 2);

        assert_eq!(map, eratosthenes.factorization(50));
        assert_ne!(map, eratosthenes.factorization(100));
    }
}