use std::ops::*;
pub fn pascal_triangle<T>(size: usize) -> Vec<Vec<T>>
where
T: Add<Output = T> + From<i32> + Clone,
{
let mut p: Vec<Vec<T>> = vec![vec![0.into(); size]; size];
for i in 0..size {
p[i][0] = 1.into();
}
for i in 1..size {
for j in 1..=i {
p[i][j] = p[i - 1][j - 1].clone() + p[i - 1][j].clone();
}
}
p
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test() {
use crate::{
define_const_modulus_macro::Mod1_000_000_007I64,
modular_int_with_static_modulus::Modint,
};
type Mint = Modint<Mod1_000_000_007I64>;
let p = pascal_triangle::<Mint>(6);
let mut inner = vec![vec![0; 6]; 6];
for i in 0..6 {
for j in 0..6 {
inner[i][j] = p[i][j].0;
}
}
assert_eq!(
inner,
vec![
vec![1, 0, 0, 0, 0, 0],
vec![1, 1, 0, 0, 0, 0],
vec![1, 2, 1, 0, 0, 0],
vec![1, 3, 3, 1, 0, 0],
vec![1, 4, 6, 4, 1, 0],
vec![1, 5, 10, 10, 5, 1],
]
);
}
}