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/// edges are directed.
/// similar to bellman ford.
/// but epochs must be specified by user.
pub fn bellman_ford_strict<F>(
edges: &[(usize, usize)],
mut f: F,
epochs: usize,
) where
F: FnMut(usize, usize),
{
for _ in 0..epochs {
for &(u, v) in edges.iter() {
f(u, v);
}
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_atcoder_abc244_e() {
let cases = vec![
((4, 4, 4, 1, 3, 2, vec![(1, 2), (2, 3), (3, 4), (1, 4)]), 4),
(
(
6,
5,
10,
1,
2,
3,
vec![(2, 3), (2, 4), (4, 6), (3, 6), (1, 5)],
),
0,
),
(
(
10,
15,
20,
4,
4,
6,
vec![
(2, 6),
(2, 7),
(5, 7),
(4, 5),
(2, 4),
(3, 7),
(1, 7),
(1, 4),
(2, 9),
(5, 10),
(1, 3),
(7, 8),
(7, 9),
(1, 6),
(1, 2),
],
),
952504739,
),
];
for ((n, m, k, s, t, x, edges_origin), ans) in cases {
let s = s - 1;
let t = t - 1;
let x = x - 1;
let encode = |u: usize, p: usize| -> usize { p * n + u };
let mut edges = Vec::with_capacity(m * 2 * 4);
for (u, v) in edges_origin {
let u = u - 1;
let v = v - 1;
let p = if v == x { 1 } else { 0 };
let q = if u == x { 1 } else { 0 };
for j in 0..2 {
edges.push((encode(u, j), encode(v, j ^ p)));
edges.push((encode(v, j), encode(u, j ^ q)));
}
}
let mut dp = vec![0; n * 2];
let mut ndp = vec![0; n * 2];
let s = encode(s, 0);
let t = encode(t, 0);
dp[s] = 1;
let mut epochs = 0;
const MOD: usize = 998_244_353;
let m = edges.len();
let mut f = |u: usize, v: usize| {
ndp[v] += dp[u];
ndp[v] %= MOD;
epochs += 1;
if epochs % m == 0 {
std::mem::swap(&mut dp, &mut ndp);
for x in ndp.iter_mut() {
*x = 0;
}
}
};
bellman_ford_strict(&edges, &mut f, k);
assert_eq!(dp[t], ans);
}
}
}