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#include <iostream>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
int N, M, K;
vector<unordered_map<int, int>> C; // C[b][p] = bin b stakes with DSU parent p
unordered_set<int> S; // Set of currently uniform bin numbers
void update_parent(int i, int r_old, int r_new) {
if (r_old == r_new) {
return;
}
auto &bin = C[i / K];
if (--bin[r_old] == 0) {
bin.erase(r_old);
}
bin[r_new]++;
if (bin.size() == 1) {
S.insert(i / K);
} else {
S.erase(i / K);
}
}
struct disjoint_sets {
vector<vector<int>> values;
vector<int> parent, color_of_parent, parent_of_color;
public:
disjoint_sets(int N)
: values(N), parent(N), color_of_parent(N), parent_of_color(N) {
for (int i = 0; i < N; i++) {
values[i] = {i};
parent[i] = i;
color_of_parent[i] = i;
parent_of_color[i] = i;
}
}
// O(M + N log N) across M calls to unite().
void unite(int a, int b) {
a = parent[a];
b = parent[b];
if (a != b) {
if (values[a].size() < values[b].size()) {
swap(a, b);
}
while (!values[b].empty()) {
int v = values[b].back();
values[b].pop_back();
update_parent(v, parent[v], a);
parent[v] = a;
color_of_parent[v] = color_of_parent[a];
values[a].push_back(v);
}
}
}
void repaint(int c1, int c2) {
int pa = parent_of_color[c1];
if (pa == -1) {
return;
}
color_of_parent[pa] = c2;
parent_of_color[c1] = -1;
int pb = parent_of_color[c2];
if (pb == -1) {
parent_of_color[c2] = pa;
return;
}
unite(pa, pb);
color_of_parent[pb] = c2;
parent_of_color[c2] = parent[pb];
}
};
int solve() {
cin >> N >> M >> K;
int nbins = (N + K - 1) / K; // ceil(N / K)
// Initialize parent counts.
C.assign(nbins, {});
for (int i = 0; i < N; i++) {
C[i / K][i]++;
}
S.clear();
for (int b = 0; b < nbins; b++) {
if (C[b].size() == 1) {
S.insert(b);
}
}
int ans = (S.size() == nbins ? 0 : -1);
disjoint_sets DS(N);
for (int i = 0, a, b; i < M; i++) {
cin >> a >> b;
DS.repaint(--a, --b);
if (S.size() == nbins && ans < 0) {
ans = i + 1;
}
}
return ans;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int T;
cin >> T;
for (int t = 1; t <= T; t++) {
cout << "Case #" << t << ": " << solve() << endl;
}
return 0;
}
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