Submission #570485

#	Time	Username	Problem	Language	Result	Execution time	Memory
570485		grt	Road Closures (APIO21_roads)	C++17	100 / 100	345 ms	51172 KiB

roads

#include <bits/stdc++.h>
#define PB push_back
#define ST first
#define ND second

//#pragma GCC optimize ("O3")
//#pragma GCC target("tune=native")

//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

using namespace std;
using ll = long long;
using pi = pair<int, int>;
using vi = vector<int>;

mt19937 rng(1190310);

const int nax = 100 * 1000 + 10, INF = 1e9;
int n, k;
set<pi>G[nax];
ll dp[nax][2];
vi ord[nax];
bool vis[nax];
int cnt[nax];
ll h[nax];
int nxt;

struct Node {
	int pri = rng() % INF, val, sz = 1;
	ll sum;
	Node *c[2];
};

using pt = Node*;

Node T[2 * nax];
pt roots[nax];

int getsz(pt x) {
	return (x == NULL ? 0 : x->sz);
}

ll getsum(pt x) {
	return (x == NULL ? 0 : x->sum);
}

pt recalc(pt x) {
	x->sz = getsz(x->c[0]) + getsz(x->c[1]) + 1;
	x->sum = getsum(x->c[0]) + getsum(x->c[1]) + x->val;
	return x;
}

pair<pt, pt>split(pt t, int kk) {
	if(!t) return {t, t};
	if(getsz(t->c[0]) >= kk) {
		auto p = split(t->c[0], kk);
		t->c[0] = p.ND;
		return {p.ST, recalc(t)};
	} else {
		auto p = split(t->c[1], kk - getsz(t->c[0]) - 1);
		t->c[1] = p.ST;
		return {recalc(t), p.ND};
	}
}

pair<pt, pt>split_val(pt t, int vs) {
	if(!t) return {t, t};
	if(t->val >= vs) {
		auto p = split_val(t->c[1], vs);
		t->c[1] = p.ST;
		return {recalc(t), p.ND};
	} else {
		auto p = split_val(t->c[0], vs);
		t->c[0] = p.ND;
		return {p.ST, recalc(t)};
	}
}

pt merge(pt a, pt b) {
	if(!a || !b) return a ? a : b;
	if(a->pri > b->pri) {
		auto t = merge(a->c[1], b);
		a->c[1] = t;
		return recalc(a);
	} else {
		auto t = merge(a, b->c[0]);
		b->c[0] = t;
		return recalc(b);
	}
}

void traverse(pt t) {
	if(!t) return;
	traverse(t->c[0]);
	cout << t->val << " ";
	traverse(t->c[1]);
}

void dfs(int x) {
	ll sum = 0;
	vis[x] = true;
	vector<ll>dx = {};
	for(auto [nbh, w] : G[x]) if(!vis[nbh]) {
		dfs(nbh);
		sum += dp[nbh][0];
		if(-dp[nbh][0] + dp[nbh][1] + w > 0) dx.PB(-dp[nbh][0] + dp[nbh][1] + w);
	}
	sum -= h[x];
	sort(dx.rbegin(), dx.rend());
	dp[x][0] = dp[x][1] = sum;
	int total = 0, i;
	pt lft = NULL;
	for(i = 0; i < (int)dx.size() && total < k - 1; ++i) {
		auto p = split_val(roots[x], dx[i]);
		int rem = (k - 1) - total;
		if(getsz(p.ST) >= rem) {
			auto p2 = split(p.ST, rem);
			dp[x][1] += getsum(p2.ST);
			dp[x][0] += getsum(p2.ST);
			total += getsz(p2.ST);
			lft = merge(lft, p2.ST);
			roots[x] = merge(p2.ND, p.ND);
			break;
		}
		dp[x][1] += getsum(p.ST);
		dp[x][0] += getsum(p.ST);
		total += getsz(p.ST);
		lft = merge(lft, p.ST);
		roots[x] = p.ND;
		//cerr << "PRZED: " << getsum(p.ST) << " " << getsz(p.ST) << " " << dx[i] << "\n";
		dp[x][1] += dx[i];
		dp[x][0] += dx[i];
		total++;
	}
	
	if(total < (k-1)) {
		int rem = (k-1) - total;
		//cerr << "REM: " << rem << "\n";
		auto p = split(roots[x], rem);
		total += getsz(p.ST);
		dp[x][1] += getsum(p.ST);
		dp[x][0] += getsum(p.ST);
		lft = merge(lft, p.ST);
		roots[x] = p.ND;
	}
	
	auto p = split(roots[x], 1);
	
	if(i < (int)dx.size()) {
		dp[x][0] += max(dx[i], getsum(p.ST));
	} else {
		dp[x][0] += getsum(p.ST);
	}
	
	roots[x] = merge(p.ST, p.ND);
	roots[x] = merge(lft, roots[x]);
	
	//cerr << "DP: " << x << " -> " << dp[x][0] << " " << dp[x][1] << "\n";
	//cout << "VALS: ";
	//traverse(roots[x]);
	//cout << "\n";
}


vector<ll> minimum_closure_costs(int N, vi U, vi V, vi W) {
	n = N;
	ll sum = 0;
	for(int i = 0; i < n - 1; ++i) {
		G[U[i]].insert({V[i], W[i]});
		G[V[i]].insert({U[i], W[i]});
		sum += W[i];
	}
	set<int>act = {};
	for(int i = 0; i < n; ++i) {
		act.insert(i);
	}
	for(int i = 0; i < n; ++i) {
		ord[(int)G[i].size()].PB(i);
		T[i].val = 0;
		roots[i] = &T[i];
	}
	nxt = n;
	vector<ll>res(n);
	res[0] = sum;
	ll delta = 0;
	for(k = 1; k < n; ++k) {
		//cerr << "K->" << k << "\n";
		for(auto v : ord[k]) {
			act.erase(v);
			for(auto [nbh, w] : G[v]) {
				if(act.count(nbh)) {
					delta += w;
					G[nbh].erase({v, w});
					cnt[nbh]++;
					h[nbh] += w;
					T[nxt].val = T[nxt].sum = w;
					auto p = split_val(roots[nbh], w);
					roots[nbh] = merge(p.ST, &T[nxt]);
					roots[nbh] = merge(roots[nbh], p.ND);
					nxt++;
				}
			}	
		}
		ll s = 0;
		for(auto v : act) {
			if(!vis[v]) {
				dfs(v);
				s += dp[v][0];
			}
		}
		for(auto v : act)
			vis[v] = false;
		res[k] = (sum - (s + delta));
	}
	return res;
}


//int main() {
	//ios_base::sync_with_stdio(0);
	//cin.tie(0);
	//auto vec = minimum_closure_costs(4, {0, 2, 0}, {1, 0, 3}, {5, 10, 5});
	//auto vec = minimum_closure_costs(5, {0, 0, 0, 2}, {1, 2, 3, 4}, {1, 4, 3, 2});
	//cin >> n;
	//vi u(n-1), v(n-1), w(n-1);
	//for(int i = 0; i < n-1; ++i) cin >> u[i] >> v[i] >> w[i];
	//auto vec = minimum_closure_costs(n, u, v, w);
	//for(auto x : vec) cout << x << " ";
//}

• Subtask 1: 5 / 5
• Subtask 2: 7 / 7
• Subtask 3: 14 / 14
• Subtask 4: 10 / 10
• Subtask 5: 17 / 17
• Subtask 6: 25 / 25
• Subtask 7: 22 / 22