#include "split.h"
#include <bits/stdc++.h>
using namespace std;
struct disj { //disjoint set union find data structure
vector<int> p, sz;
disj(int n) { p.resize(n); iota(p.begin(), p.end(), 0); sz.assign(n, 1); }
int par(int n) { return (p[n] == n)? n : p[n] = par(p[n]); }
};
void centroid(int n, int p, vector<vector<int>> &G, int ¢, vector<int> &sz_dfs) { //find centroid of tree
bool is_centroid = true;
for (auto i : G[n]) {
if (i == p) continue;
centroid(i, n, G, cent, sz_dfs);
if (sz_dfs[i] > G.size() / 2) is_centroid = false;
sz_dfs[n] += sz_dfs[i];
}
if (G.size() - sz_dfs[n] > G.size() / 2) is_centroid = false;
if (is_centroid) cent = n;
}
int find_size(int n, int p, int id, vector<vector<int>> &G, disj &a, vector<int> &sz_dfs) { //find size of subtree
a.p[n] = id;
int res = 1;
for (auto i : G[n]) {
if (i == p) continue;
sz_dfs[n] += find_size(i, n, id, G, a, sz_dfs);
}
return sz_dfs[n];
}
void dfs_color(int n, int p, int &cnt, int color, vector<vector<int>> &G, vector<int> &res, int except) { //coloring by dfs
if (n == except) return;
if (cnt > 0) {
cnt--;
res[n] = color;
}
for (auto i : G[n]) {
if (i == p) continue;
if (res[i] != 0) continue;
if (cnt <= 0) break;
dfs_color(i, n, cnt, color, G, res, except);
}
}
vector<int> find_split(int n, int a, int b, int c, vector<int> p, vector<int> q) {
vector<int> res(n, 0);
vector<pair<int, int>> tmp = {{a, 1}, {b, 2}, {c, 3}}; sort(tmp.begin(), tmp.end()); //assume a <= b <= c
disj ds(n);
vector<pair<int, int>> edge;
vector<vector<int>> G(n);
vector<int> sz_dfs(n, 1);
for (int i = 0; i < p.size(); i++) edge.push_back({p[i], q[i]});
for (auto i : edge) { //create (random) spanning tree
int p1 = ds.par(i.first), p2 = ds.par(i.second);
if (p1 != p2) {
ds.p[p1] = p2;
G[i.first].push_back(i.second); G[i.second].push_back(i.first);
}
}
int center; centroid(0, 0, G, center, sz_dfs); //find centroid of spanning tree
int max_subtree = 0;
vector<int> subtrees;
disj anc(n);
sz_dfs.assign(n, 1);
bool done = false; //check if a is already found
int lim = tmp[0].first;
//finding and coloring
for (auto i : G[center]) {
if (done) break;
max_subtree = max(max_subtree, sz_dfs[i] = find_size(i, center, i, G, anc, sz_dfs));
anc.sz[i] = sz_dfs[i];
if (max_subtree >= tmp[0].first) { //pick if subtree of centroid has size >= a; b is guaranteed (centroid to all nodes in other subtrees), c is leftover
dfs_color(i, center, tmp[0].first, tmp[0].second, G, res, -1);
done = true;
}
}
for (auto i : edge) if (!done) { //a <= n / 3
if (i.first == center || i.second == center) continue;
int p1 = anc.par(i.first), p2 = anc.par(i.second); //worst case coloring scenario: dfs coloring of a through all child of centroid -> centroid trapped
if (p1 == p2) continue; //for worst case scenario, all subtrees < a (since a cannot be chosen from a single subtree)
G[i.first].push_back(i.second); G[i.second].push_back(i.first); //a+b+c -(2a-2) - 1(centroid) = b + c - a + 1 = sizeof connected subtrees left from centroid
max_subtree = max(max_subtree, anc.sz[p1] + anc.sz[p2]); //assume b (needed size of subtree) > b + c - a + 2 (centroid-connected subtree left)
anc.sz[p1] += anc.sz[p2]; anc.sz[p2] = 0; anc.p[p2] = p1; //then a - 2 > c, however a <= c. Contradiction. Thus coloring always works
if (max_subtree >= tmp[0].first) { //connect subtrees of spanning tree -> if component has size >= a, then found a
dfs_color(p1, center, tmp[0].first, tmp[0].second, G, res, center);
done = true;
}
}
dfs_color(center, -1, tmp[1].first, tmp[1].second, G, res, -1); //since centroid isn't used and it is connected to all nodes, it can be used to get b
for (int i = 0; i < n; i++) res[i] = (res[i] == 0)? tmp[2].second : res[i]; //leftover for c
if (max_subtree < lim) res.assign(n, 0); //if max connected subtree has size < a, then there is no solution
return res;
}
