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pub struct PascalRule<T> {
cache: std::collections::HashMap<u64, T>,
}
impl<T> PascalRule<T> {
pub fn new() -> Self {
Self { cache: std::collections::HashMap::new() }
}
/// interface is not u64 but u32
/// to avoid key's overflow but memory overflow or infinite run time.
/// memory overflow should not be handled here (low level API).
pub fn calc(
&mut self,
n: u32,
k: u32,
) -> T
where
T: std::ops::Add<Output = T> + From<usize> + Copy,
{
assert!(k <= n);
// unlike combination, (n, k) is undefined if k > n
// on pascal's triangle.
if k == 0 {
return 1.into();
}
let key = (n as u64) << 32 | k as u64;
if !self.cache.contains_key(&key) {
let mut v = self.calc(n - 1, k - 1);
if k < n {
v = v + self.calc(n - 1, k);
}
self.cache.insert(key, v);
}
*self.cache.get(&key).unwrap()
}
}