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pub struct Combination {
fact: Vec<usize>,
inv_fact: Vec<usize>,
modulo: usize,
}
impl Combination {
pub fn new(max: usize, modulo: usize) -> Combination {
let mut inv = vec![0; max + 1];
let mut fact = vec![0; max + 1];
let mut inv_fact = vec![0; max + 1];
inv[1] = 1;
for i in 2..(max + 1) {
inv[i] = inv[modulo % i] * (modulo - modulo / i) % modulo;
}
fact[0] = 1;
inv_fact[0] = 1;
for i in 0..max { fact[i + 1] = fact[i] * (i + 1) % modulo; }
for i in 0..max {
inv_fact[i + 1] = inv_fact[i] * inv[i + 1] % modulo;
}
Combination { fact: fact, inv_fact: inv_fact, modulo: modulo }
}
pub fn get(&self, x: usize, y: usize) -> usize {
assert!(x >= y);
self.fact[x] * self.inv_fact[y] % self.modulo * self.inv_fact[x - y] % self.modulo
}
}
#[cfg(test)]
mod test {
extern crate rand;
use super::*;
fn gcd(a: usize, b: usize) -> usize { if b == 0 { a } else { gcd(b, a % b) } }
#[test]
fn random_combination() {
let modulo = 1_000_000_007;
for n in 100..200 {
let comb = Combination::new(n, modulo);
for m in 0..(n + 1) {
let mut upper = (0..m).map(|i| n - i).collect::<Vec<_>>();
for i in 0..m {
let mut divisor = i + 1;
for j in 0..(i + 1) {
if divisor == 1 { break; }
let g = gcd(divisor, upper[j]);
upper[j] /= g;
divisor /= g;
}
}
let mut check = 1;
for u in &upper { check = (check * u) % modulo; }
assert_eq!(comb.get(n, m), check);
}
}
}
}