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pub fn homogeneous_products(
n: usize,
k: usize,
) -> Vec<Vec<usize>> {
assert!(n > 0);
let mut res = vec![];
fn dfs(
n: usize,
k: usize,
res: &mut Vec<Vec<usize>>,
a: &mut Vec<usize>,
) {
let m = a.len();
if m == k {
res.push(a.to_vec());
return;
}
let lo = if m == 0 { 0 } else { a[m - 1] };
for x in lo..n {
a.push(x);
dfs(n, k, res, a);
a.pop();
}
}
dfs(n, k, &mut res, &mut vec![]);
res
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test() {
let res = homogeneous_products(5, 3);
assert_eq!(
res,
[
[0, 0, 0],
[0, 0, 1],
[0, 0, 2],
[0, 0, 3],
[0, 0, 4],
[0, 1, 1],
[0, 1, 2],
[0, 1, 3],
[0, 1, 4],
[0, 2, 2],
[0, 2, 3],
[0, 2, 4],
[0, 3, 3],
[0, 3, 4],
[0, 4, 4],
[1, 1, 1],
[1, 1, 2],
[1, 1, 3],
[1, 1, 4],
[1, 2, 2],
[1, 2, 3],
[1, 2, 4],
[1, 3, 3],
[1, 3, 4],
[1, 4, 4],
[2, 2, 2],
[2, 2, 3],
[2, 2, 4],
[2, 3, 3],
[2, 3, 4],
[2, 4, 4],
[3, 3, 3],
[3, 3, 4],
[3, 4, 4],
[4, 4, 4]
]
);
}
}