Minimum Spanning Tree [Union Find]

We are asked to construct a minimum spanning tree, so we use a union find.

- Every OFF bulbs have 2 edges connecting the 2 closest bulbs.
- Every ON bulbs is connected with the supernode BRIGHT which is denoted as node
`N`

.

```
private static int solve(int[] bulbs, int[] dist){ // Java
int N = bulbs.length;
UF uf = new UF(N+1);
List<int[]> edges = new ArrayList<>();
for (int i = 0; i < N; i++){
if (bulbs[i] == 1){
uf.union(i, N);
}else{
if (i > 0){
edges.add(new int[]{dist[i]-dist[i-1], i, i-1});
}else if (i < N-1){
edges.add(new int[]{dist[i+1]-dist[i], i, i+1});
}
}
}
if (uf.size() == N+1){
return -1; // IMPOSSIBLE
}
int ans = 0;
edges.sort(Comparator.comparingInt(o -> o[0]));
for (int[] e : edges){
int cost = e[0], v = e[1], u = e[2];
if (uf.union(v, u)){
ans += cost;
}
}
return ans;
}
```