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- #include <iostream>
- #include <algorithm>
- #include <vector>
- #include <map>
- #include <set>
- #include <array>
- #include <stack>
- #include <queue>
- #include <random>
- #include <numeric>
- #include <functional>
- #include <chrono>
- #include <utility>
- #include <iomanip>
- #include <assert.h>
- using namespace std;
- void dbg_out() { cerr << endl; }
- template<typename Head, typename... Tail>
- void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); }
- #define dbg(...) cerr << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
- #define rng_init mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
- #define rng_seed(x) mt19937 rng(x)
- #define all(x) (x).begin(), (x).end()
- #define sz(x) (int) (x).size()
- // #define int long long
- const int MXN = 2e5 + 5, INF = 1e9 + 5;
- int N, M, Q;
- pair<int, int> edges[MXN];
- int info[MXN], parity[MXN];
- int is_bipartite;
- stack<array<int, 4>> changes; // {node, size of component, did this make the graph non bipartite}
- int valid[MXN];
- pair<int, int> find_par(int x) {
- if (info[x] < 0) return make_pair(x, parity[x]);
- pair<int, int> p = find_par(info[x]);
- p.second ^= 1;
- return p;
- }
- void unite(int x, int y) {
- auto [px, parity_x] = find_par(x);
- auto [py, parity_y] = find_par(y);
- if (px == py) {
- if (parity_x == parity_y) {
- changes.emplace(array<int, 4>{py, -info[py], is_bipartite, parity[py]});
- is_bipartite = 0;
- } else {
- changes.emplace(array<int, 4>{py, -info[py], 0, parity[py]});
- }
- return;
- }
- if (info[px] > info[py]) {
- swap(px, py);
- swap(parity_x, parity_y);
- swap(x, y);
- }
- changes.emplace(array<int, 4>{py, -info[py], 0, parity[py]});
- parity[py] = parity_x ^ parity_y ^ 1;
- info[px] += info[py];
- info[py] = px;
- }
- void rollback() {
- assert(changes.empty() == false);
- auto [y, comp_sz, non_bipartite, parity_y] = changes.top();
- int x = info[y];
- if (x == y) return;
- parity[y] = parity_y;
- info[x] += comp_sz;
- info[y] = -comp_sz;
- if (non_bipartite)
- is_bipartite = 1;
- changes.pop();
- }
- void add_edge(int idx) { unite(edges[idx].first, edges[idx].second); }
- void dnc(int l, int r, int optl, int optr) {
- if (l > r) return;
- int mid = (l + r) / 2;
- dbg(l, r, mid);
- dbg(optl, optr);
- // Add prefix of edges
- for (int i = l; i < mid; i++)
- add_edge(i);
- dbg(sz(changes));
- int ufds_r = optr; // Edge list pointer
- // Calculate optimal right for mid, store in best
- int best = 0;
- while (ufds_r > mid + 1 && ufds_r >= optl && is_bipartite)
- add_edge(--ufds_r);
- dbg(ufds_r, sz(changes));
- if (!is_bipartite)
- best = ufds_r;
- valid[mid] = best;
- dbg(is_bipartite, best);
- // Right side will be dnc(mid + 1, r, best, optr)
- // For right side, already have prefix, need to work on removing suffix
- while (ufds_r < optr) {
- rollback();
- ufds_r++;
- }
- dbg(ufds_r, sz(changes));
- dbg(is_bipartite, best);
- dbg_out();
- dnc(mid + 1, r, best, optr);
- // Remove prefix
- for (int i = mid - 1; i >= l; i--)
- rollback();
- // Now add those edges again
- while (ufds_r > best + 1)
- add_edge(--ufds_r);
- unite(edges[mid].first, edges[mid].second);
- // Left side will be dnc(l, mid - 1, optl, best + 1)
- dnc(l, mid - 1, optl, best + 1);
- rollback();
- // Rollback suffix add
- while (ufds_r < optr) {
- rollback();
- ufds_r++;
- }
- }
- void solve() {
- cin >> N >> M >> Q;
- for (int i = 0; i < M; i++) {
- cin >> edges[i].first >> edges[i].second;
- edges[i].first--, edges[i].second--;
- }
- is_bipartite = 1;
- for (int i = 0; i < MXN; i++)
- info[i] = -1, parity[i] = 0;
- dnc(0, M - 1, 0, M);
- for (int i = 0; i < M; i++)
- dbg(i, valid[i]);
- while (Q--) {
- int l, r;
- cin >> l >> r;
- l--, r--;
- cout << (valid[l] > r ? "YES" : "NO") << "\n";
- }
- }
- signed main() {
- ios_base::sync_with_stdio(false);
- cin.tie(nullptr);
- int TC = 1;
- // cin >> TC;
- while (TC--) solve();
- }
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