struct Solution;
struct UnionFind {
parent: Vec<usize>,
n: usize,
}
impl UnionFind {
fn new(n: usize) -> Self {
let parent = (0..n).collect();
UnionFind { parent, n }
}
fn find(&mut self, i: usize) -> usize {
let j = self.parent[i];
if i == j {
i
} else {
let k = self.find(j);
self.parent[i] = k;
k
}
}
fn union(&mut self, i: usize, j: usize) -> bool {
let i = self.find(i);
let j = self.find(j);
if i != j {
self.parent[i] = j;
self.n -= 1;
true
} else {
false
}
}
}
impl Solution {
fn find_critical_and_pseudo_critical_edges(n: i32, edges: Vec<Vec<i32>>) -> Vec<Vec<i32>> {
let m = edges.len();
let n = n as usize;
let mut sorted_index: Vec<usize> = (0..m).collect();
sorted_index.sort_unstable_by_key(|&i| edges[i][2]);
let min_cost = Self::mst(std::usize::MAX, std::usize::MAX, &sorted_index, &edges, n);
let mut critical = vec![];
let mut noncritical = vec![];
dbg!(min_cost);
for i in 0..m {
if Self::mst(i, std::usize::MAX, &sorted_index, &edges, n) > min_cost {
critical.push(i as i32);
} else {
if Self::mst(std::usize::MAX, i, &sorted_index, &edges, n) == min_cost {
noncritical.push(i as i32);
}
}
}
vec![critical, noncritical]
}
fn mst(skip: usize, pick: usize, sorted_index: &[usize], edges: &[Vec<i32>], n: usize) -> i32 {
let mut uf = UnionFind::new(n);
let mut res = 0;
if pick != std::usize::MAX {
if uf.union(edges[pick][0] as usize, edges[pick][1] as usize) {
res += edges[pick][2];
}
}
for &idx in sorted_index {
if idx != skip {
if uf.union(edges[idx][0] as usize, edges[idx][1] as usize) {
res += edges[idx][2];
}
}
}
if uf.n == 1 {
res
} else {
std::i32::MAX
}
}
}
#[test]
fn test() {
let n = 5;
let edges = vec_vec_i32![
[0, 1, 1],
[1, 2, 1],
[2, 3, 2],
[0, 3, 2],
[0, 4, 3],
[3, 4, 3],
[1, 4, 6]
];
let res = vec_vec_i32![[0, 1], [2, 3, 4, 5]];
assert_eq!(
Solution::find_critical_and_pseudo_critical_edges(n, edges),
res
);
let n = 4;
let edges = vec_vec_i32![[0, 1, 1], [1, 2, 1], [2, 3, 1], [0, 3, 1]];
let res = vec_vec_i32![[], [0, 1, 2, 3]];
assert_eq!(
Solution::find_critical_and_pseudo_critical_edges(n, edges),
res
);
}