Struct nekolib::math::Interpolation

source ·
pub struct Interpolation { /* private fields */ }
Expand description

Lagrange 補間。

与えられた $\langle f(0), f(1), \dots, f(n-1)\rangle$ に対して $\hat{f}(i)=f(i)$ ($i=0,1,\dots,n-1$) なる $n$ 次多項式 $\hat{f}$ を考える。 この $\hat{f}$ に対して $\hat{f}(x)\bmod p$ を返す。

Idea

todo!()

Complexity

前処理に $O(n)$ 時間、$\hat{f}(x)$ を求めるのに $O(n)$ 時間。

Examples

use nekolib::math::Interpolation;

let f = Interpolation::with(vec![0, 1, 3], 998244353);
assert_eq!(f.interpolate(0), 0);
assert_eq!(f.interpolate(3), 6);
assert_eq!(f.interpolate(4), 10);
assert_eq!(f.interpolate(100000000), 722404071);

See also

Implementations§

source§

impl Interpolation

source

pub fn with(first: Vec<u64>, modulo: u64) -> Self

source

pub fn interpolate(&self, x: u64) -> u64

Auto Trait Implementations§

Blanket Implementations§

source§

impl<T> Any for Twhere T: 'static + ?Sized,

source§

fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
source§

impl<T> Borrow<T> for Twhere T: ?Sized,

source§

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
source§

impl<T> BorrowMut<T> for Twhere T: ?Sized,

source§

fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
source§

impl<T> From<T> for T

source§

fn from(t: T) -> T

Returns the argument unchanged.

source§

impl<T, U> Into<U> for Twhere U: From<T>,

source§

fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

source§

impl<T, U> TryFrom<U> for Twhere U: Into<T>,

§

type Error = Infallible

The type returned in the event of a conversion error.
source§

fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
source§

impl<T, U> TryInto<U> for Twhere U: TryFrom<T>,

§

type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
source§

fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
§

impl<V, T> VZip<V> for Twhere V: MultiLane<T>,

§

fn vzip(self) -> V