Submission #810486

#	Time	Username	Problem	Language	Result	Execution time	Memory
810486		hugo_pm	Reconstruction Project (JOI22_reconstruction)	C++17	0 / 100	5076 ms	66844 KiB

reconstruction

#include <bits/stdc++.h>
#define int long long
using namespace std;
	
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define rep(i, a, b) for(int i = (a); i < (b); i++)
#define sz(v) ((int)((v).size()))
	
template<typename T>
void chmax(T &x, const T &v) { if (x < v) x = v; }
template<typename T>
void chmin(T &x, const T &v) { if (x > v) x = v; }
	
using pii = pair<int, int>;
using vi = vector<int>;
	
string to_string(string s) { return s; }
template <typename T> string to_string(T v) {
	bool first = true;
	string res = "[";
	for (const auto &x : v) {
		if (!first)
			res += ", ";
		first = false;
		res += to_string(x);
	}
	res += "]";
	return res;
}
	
template <typename A, typename B>
string to_string(pair<A, B> p) {
	return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
	
void dbg_out() { cout << endl; }
template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) {
	cout << ' ' << to_string(H);
	dbg_out(T...);
}
	
#ifdef DEBUG
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif
	
struct uf {
	int N;
	vector<int> repr, taille;
	void rebuild() {
		iota(repr.begin(), repr.end(), 0);
		taille.assign(N, 1);
	}
	uf(int _N) : N(_N), repr(_N) {
		rebuild();
	}
	int find(int u) {
		if (repr[u] == u) return u;
		return repr[u] = find(repr[u]);
	}
	bool unite(int u, int v) {
		u = find(u), v = find(v);
		if (u == v) return false;
		if (taille[u] < taille[v]) swap(u, v);
		repr[v] = u;
		taille[u] += taille[v];
		return true;
	}
};
struct Edge {
	int u, v, p;
};
int nbNode, nbEdge, nbReq;
vector<Edge> edges;
vector<pii> reqs;
struct MST {
	int cntDown = 0, sumDown = 0, cntUp = 0, sumUp = 0, cntEgal = 0, sumEgal = 0;
	int egalDown(int X) {
		// up - X, X - down
		return sumUp - sumDown - sumEgal + (cntEgal+cntDown - cntUp)*X;
	}
	int egalUp(int X) {
		// up - X, X - down
		return sumUp - sumDown + sumEgal + (-cntEgal+cntDown - cntUp)*X;
	}
};
const int LG = 17;
static_assert((1<<LG) > (int)(1e5));

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >> nbNode >> nbEdge;
	edges.resize(nbEdge);
	for (auto &[u,v,p] : edges) {
		cin >> u >> v >> p;
		--u, --v;
		p *= 2;
	}
	sort(all(edges), [&] (Edge a, Edge b) { return a.p < b.p; });
	vector<int> times {0, (int)1e18};
	vector<vi> anc(LG, vi(nbEdge, -1));
	auto minPoids = anc;
	vector<bool> taken(nbEdge, false);
	uf firstMst(nbNode);
	vector<int> prof(nbNode);
	vector<vector<pii>> adjTree(nbNode);
	rep(iEdge, 0, nbEdge) {
		const auto [u,v,p] = edges[iEdge];
		if (firstMst.unite(u, v)) {
			taken[iEdge] = true;
			adjTree[u].emplace_back(v, p);
			adjTree[v].emplace_back(u, p);
		}
	}
	auto Dfs = [&] (auto dfs, int node, int parent, int parPoids) -> void {
		if (parent != -1) {
			anc[0][node] = parent;
			minPoids[0][node] = parPoids;
		}
		for (auto [child, w] : adjTree[node]) if (child != parent) {
			prof[child] = prof[node]+1;
			dfs(dfs, child, node, w);
		}
	};
	Dfs(Dfs, 0, -1, -1);
	rep(lvl, 0, LG-1) {
		rep(node, 0, nbNode) {
			int mid = anc[lvl][node];
			if (mid != -1) {
				anc[lvl+1][node] = anc[lvl][mid];
				minPoids[lvl+1][node] = min(minPoids[lvl][node], minPoids[lvl][mid]);
			}
		}
	}
	auto minChemin = [&] (int u, int v) {
		int ans = 3e18;
		auto jump = [&] (int lvl, int &node) {
			chmin(ans, minPoids[lvl][node]);
			node = anc[lvl][node];
		};
		if (prof[u] > prof[v]) swap(u, v);
		int firstJmp = prof[v] - prof[u];
		rep(i, 0, LG) if ((1<<i) & firstJmp) {
			jump(i, v);
		}
		assert(prof[u] == prof[v]);
		if (u == v) return ans;
		for (int i = LG-1; i >= 0; --i) {
			int pu = anc[i][u], pv = anc[i][v];
			if (pu != -1 && pv != -1 && pu != pv) {
				jump(i, u), jump(i, v);
			}
		}
		jump(0, u), jump(0, v);
		assert(u == v);
		return ans;
	};
	rep(i, 0, nbEdge) {
		times.push_back(edges[i].p);
		if (!taken[i]) {
			int minTime = minChemin(edges[i].u, edges[i].v);
			times.push_back((edges[i].p + minTime)/2);
		}
	}
	sort(all(times));
	times.resize(unique(all(times)) - begin(times));
	uf mst(nbNode);
	vector<int> order(nbEdge);
	iota(all(order), 0);
	auto getMst = [&] (int X) {
		int N = nbEdge;
		while (N >= 1) {
			int newN = 0;
			rep(i, 1, N) {
				if (abs(edges[order[i-1]].p - X) > abs(edges[order[i]].p - X)) {
					swap(order[i-1], order[i]);
					newN = i;
				}
			}
			N = newN;
		}
		// assert(is_sorted(all(order), [&] (int i, int j) {
		// 	const Edge &a = edges[i];
		// 	const Edge &b = edges[j];
		// 	return abs(a.p-X) < abs(b.p-X);
		// }));
		mst.rebuild();
		MST info;
		for (int iEdge : order) {
			auto [u, v, p] = edges[iEdge];
			if (mst.unite(u,v)) {
				if (p < X) info.cntDown++, info.sumDown += p;
				else if (p == X) info.cntEgal++, info.sumEgal += p;
				else info.cntUp++, info.sumUp += p;
			}
		}
		return info;
	};
	cin >> nbReq;
	reqs.resize(nbReq);
	rep(iReq, 0, nbReq) {
		cin >> reqs[iReq].first;
		reqs[iReq].first *= 2;
		reqs[iReq].second = iReq;
	}
	sort(all(reqs));
	vector<int> ans(nbReq);
	int ptr = 0;
	auto v1 = getMst(times[ptr]), v2 = getMst(times[ptr+1]);
	for (auto [X, iReq] : reqs) {
		while (X >= times[ptr+1]) {
			++ptr;
			swap(v1, v2);
			v2 = getMst(times[ptr+1]);
		}
		ans[iReq] = min(v1.egalDown(X), v2.egalUp(X));
		//ans[iReq] = getMst(X).calc(X);
		assert(ans[iReq] % 2 == 0);
	}
	rep(i, 0, nbReq) cout << ans[i]/2 << '\n';
}

• Subtask 1: 0 / 3
• Subtask 2: 0 / 4
• Subtask 3: 0 / 7
• Subtask 4: 0 / 28
• Subtask 5: 0 / 35
• Subtask 6: 0 / 23