Submission #885756

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
885756	2023-12-10T16:02:27 Z	qthang2k11	Designated Cities (JOI19_designated_cities)	C++17	100 / 100	380 ms	78420 KB

designated_cities

// [+]
#include <bits/stdc++.h>
using namespace std;

using ll = long long;

struct Edge { // w: out, rw: in
	int y, w, rw;
	Edge() = default;
	Edge(int y, int w, int rw):
		y(y), w(w), rw(rw) {}
};

const int N = 2e5 + 5;

vector<Edge> adj[N];
int n;

ll tot = 0, ans1 = 0;

ll sum_out[N];

ll dfs(int x, int p) {
	for (const auto &elem: adj[x]) {
		int y = elem.y;
		if (y == p) continue;
		sum_out[x] += dfs(y, x) + elem.w;
	}
	return sum_out[x];
}

ll dfs1(int x, int p, ll up) {
	ll down = 0;
	for (const auto &elem: adj[x]) {
		int y = elem.y;
		if (y == p) continue;
		down += dfs1(y, x, up + sum_out[x] - sum_out[y] - elem.w + elem.rw) + elem.w;
	}
	ans1 = max(ans1, up + down);
	return down;
}

bool chosen[N];
ll ans[N];

int tin[N], tout[N], node[N], tcur = 0;
int par[N], rt;

int xtopar[N];

namespace e2 {
	const ll INF = 1e18;
	
	array<ll, 3> res = {0, 0, 0};
	
	pair<ll, int> mx_up[N];
	
	pair<ll, int> dfs1(int x, int p, ll up) {
		pair<ll, int> &fst = mx_up[x], scd, tmp, now;

		scd = tmp = {-INF, 0};
		fst = {0, x};
		
		for (const auto &elem: adj[x]) {
			int y = elem.y, w = elem.w, rw = elem.rw;
			if (y == p) continue;
			now = dfs1(y, x, up + sum_out[x] - sum_out[y] - w + rw);
			tmp = max(tmp, {now.first + sum_out[x] - sum_out[y] + w + rw, now.second});
			scd = max(scd, {mx_up[y].first + rw, mx_up[y].second});
			if (scd > fst) swap(scd, fst);
		}
		
		res = max(res, {up + fst.first + scd.first + sum_out[x], fst.second, scd.second});
		
		return tmp;
	}
	
	void dfs2(int x, int p) {
		tin[x] = ++tcur;
		node[tcur] = x;
		par[x] = p;
		for (const auto &elem: adj[x]) {
			int y = elem.y;
			if (y == p) continue;
			dfs2(y, x);
			xtopar[y] = elem.rw;
		}
		tout[x] = tcur;
	}
		
	void solve() {
		auto now = dfs1(1, 0, 0);
		res = max(res, {now.first, 1, now.second});
		
		ans[2] = tot - res[0];
		rt = res[1];
		
		dfs2(rt, 0);
				
		int cur = res[2];
		while (cur) {
			chosen[cur] = 1;
			cur = par[cur];
		}
	}
}

ll dis[N];

void dfs2(int x, int p, ll d) {
	if (chosen[x]) d = 0;
	dis[x] = d;
	
	for (const auto &elem: adj[x]) {
		int y = elem.y;
		if (y == p) continue;
		dfs2(y, x, d + elem.rw);
	}
}

struct Node {
	ll val; int x; ll lz;
	Node() { val = x = lz = 0; }
	Node(ll val, int x, ll lz = 0):
		val(val), x(x), lz(lz) {}
};

Node merge(const Node &x, const Node &y) {
	if (x.val > y.val) return Node(x.val, x.x);
	return Node(y.val, y.x);
}

struct SegmentTree {
	Node IT[N << 2];
	SegmentTree() = default;
	
	void build(int id, int l, int r) {
		if (l == r) return IT[id] = Node(dis[node[l]], node[l]), void();
		int mid = (l + r) / 2;
		build(id << 1, l, mid);
		build(id << 1 | 1, mid + 1, r);
		IT[id] = merge(IT[id << 1], IT[id << 1 | 1]);
	}
	
	inline void apply(int id, ll w) {
		IT[id].val += w;
		IT[id].lz += w;
	}
	
	inline void down(int id) {
		ll &lz = IT[id].lz;
		if (lz) {
			apply(id << 1, lz);
			apply(id << 1 | 1, lz);
			lz = 0;
		}
	}
	
	void update(int x, int y, ll w, int id, int l, int r) {
		if (l > y || r < x) return;
		if (x <= l && r <= y) 
			return apply(id, w);
		down(id);
		int mid = (l + r) / 2;
		update(x, y, w, id << 1, l, mid);
		update(x, y, w, id << 1 | 1, mid + 1, r);
		IT[id] = merge(IT[id << 1], IT[id << 1 | 1]);
	}
	
	inline void update(int x, int y, ll w) {
		update(x, y, w, 1, 1, n);
	}
	
	void update_val(int x, int id, int l, int r) {
		if (l == r) return IT[id] = Node(0, x), void();
		down(id);
		int mid = (l + r) / 2;
		if (x <= mid) update_val(x, id << 1, l, mid);
		else update_val(x, id << 1 | 1, mid + 1, r);
		IT[id] = merge(IT[id << 1], IT[id << 1 | 1]);
	}
	
	inline void update_val(int x) {
		update_val(x, 1, 1, n);
	}
	
	pair<ll, int> get() {
		return {IT[1].val, IT[1].x};
	}
	
	ll debug(int x, int id, int l, int r) {
		if (l == r) return IT[id].val;
		down(id);
		int mid = (l + r) / 2;
		if (x <= mid) return debug(x, id << 1, l, mid);
		else return debug(x, id << 1 | 1, mid + 1, r);
	}
	
} seg;

void del(int x) {
	assert(!chosen[x]);
	
	vector<int> arr;
	while (!chosen[x]) {
		chosen[x] = 1;
		arr.emplace_back(x);
		x = par[x];
	}
	
	reverse(arr.begin(), arr.end());
	
	ll pref = 0;
	for (int x: arr) {
		pref += xtopar[x];
		for (const auto &elem: adj[x]) {
			int y = elem.y;
			if (chosen[y]) continue;
			seg.update(tin[y], tout[y], -pref);
		}
		seg.update_val(tin[x]);
	}
}

int32_t main() {
	cin.tie(0)->sync_with_stdio(0);
	
	cin >> n; 
	for (int i = 1; i < n; i++) {
		int x, y, w, rw;
		cin >> x >> y >> rw >> w;
		adj[x].emplace_back(y, w, rw);
		adj[y].emplace_back(x, rw, w);
		tot += w + rw;
	}
	
	ignore = dfs(1, 0);
	
	ignore = dfs1(1, 0, 0);
	ans[1] = tot - ans1;
		
	e2::solve(); // case E = 2
	
	dfs2(rt, 0, 0);
	seg.build(1, 1, n);
	
	ll val; int node;
	for (int i = 3; i <= n; i++) {
		ans[i] = ans[i - 1];		
		tie(val, node) = seg.get();
		if (val <= 0) {
			for (int j = i + 1; j <= n; j++)
				ans[j] = ans[j - 1];
			break;
		}
		ans[i] -= val;
		del(node);
	}

	int q; 	
	cin >> q;
	while (q--) {
		int x; cin >> x;
		cout << ans[x] << '\n';
	}
	
	return 0;
}

Subtask #1

6.0 / 6.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	5 ms	29528 KB	Output is correct
2	Correct	5 ms	29532 KB	Output is correct
3	Correct	5 ms	29660 KB	Output is correct
4	Correct	5 ms	29752 KB	Output is correct
5	Correct	5 ms	29532 KB	Output is correct
6	Correct	5 ms	29620 KB	Output is correct
7	Correct	5 ms	29532 KB	Output is correct
8	Correct	5 ms	29532 KB	Output is correct
9	Correct	5 ms	29532 KB	Output is correct
10	Correct	5 ms	29532 KB	Output is correct
11	Correct	5 ms	29532 KB	Output is correct

Subtask #2

7.0 / 7.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	6 ms	29532 KB	Output is correct
2	Correct	321 ms	44132 KB	Output is correct
3	Correct	238 ms	67396 KB	Output is correct
4	Correct	253 ms	44112 KB	Output is correct
5	Correct	259 ms	43956 KB	Output is correct
6	Correct	366 ms	47700 KB	Output is correct
7	Correct	230 ms	43904 KB	Output is correct
8	Correct	290 ms	68436 KB	Output is correct
9	Correct	190 ms	44280 KB	Output is correct

Subtask #3

9.0 / 9.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	5 ms	29532 KB	Output is correct
2	Correct	359 ms	44092 KB	Output is correct
3	Correct	242 ms	71708 KB	Output is correct
4	Correct	291 ms	44112 KB	Output is correct
5	Correct	285 ms	43788 KB	Output is correct
6	Correct	318 ms	47928 KB	Output is correct
7	Correct	226 ms	44720 KB	Output is correct
8	Correct	278 ms	59780 KB	Output is correct
9	Correct	203 ms	44256 KB	Output is correct

Subtask #4

17.0 / 17.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	5 ms	29528 KB	Output is correct
2	Correct	5 ms	29532 KB	Output is correct
3	Correct	5 ms	29660 KB	Output is correct
4	Correct	5 ms	29752 KB	Output is correct
5	Correct	5 ms	29532 KB	Output is correct
6	Correct	5 ms	29620 KB	Output is correct
7	Correct	5 ms	29532 KB	Output is correct
8	Correct	5 ms	29532 KB	Output is correct
9	Correct	5 ms	29532 KB	Output is correct
10	Correct	5 ms	29532 KB	Output is correct
11	Correct	5 ms	29532 KB	Output is correct
12	Correct	5 ms	29528 KB	Output is correct
13	Correct	6 ms	29784 KB	Output is correct
14	Correct	6 ms	30044 KB	Output is correct
15	Correct	8 ms	29788 KB	Output is correct
16	Correct	6 ms	29784 KB	Output is correct
17	Correct	6 ms	29788 KB	Output is correct
18	Correct	6 ms	29788 KB	Output is correct
19	Correct	6 ms	29788 KB	Output is correct
20	Correct	6 ms	29732 KB	Output is correct
21	Correct	7 ms	29784 KB	Output is correct
22	Correct	6 ms	29928 KB	Output is correct
23	Correct	7 ms	29928 KB	Output is correct
24	Correct	6 ms	29968 KB	Output is correct
25	Correct	6 ms	30044 KB	Output is correct
26	Correct	6 ms	29788 KB	Output is correct

Subtask #5

17.0 / 17.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	6 ms	29532 KB	Output is correct
2	Correct	321 ms	44132 KB	Output is correct
3	Correct	238 ms	67396 KB	Output is correct
4	Correct	253 ms	44112 KB	Output is correct
5	Correct	259 ms	43956 KB	Output is correct
6	Correct	366 ms	47700 KB	Output is correct
7	Correct	230 ms	43904 KB	Output is correct
8	Correct	290 ms	68436 KB	Output is correct
9	Correct	190 ms	44280 KB	Output is correct
10	Correct	5 ms	29532 KB	Output is correct
11	Correct	359 ms	44092 KB	Output is correct
12	Correct	242 ms	71708 KB	Output is correct
13	Correct	291 ms	44112 KB	Output is correct
14	Correct	285 ms	43788 KB	Output is correct
15	Correct	318 ms	47928 KB	Output is correct
16	Correct	226 ms	44720 KB	Output is correct
17	Correct	278 ms	59780 KB	Output is correct
18	Correct	203 ms	44256 KB	Output is correct
19	Correct	5 ms	29532 KB	Output is correct
20	Correct	302 ms	44248 KB	Output is correct
21	Correct	264 ms	78420 KB	Output is correct
22	Correct	310 ms	49144 KB	Output is correct
23	Correct	262 ms	50580 KB	Output is correct
24	Correct	268 ms	49388 KB	Output is correct
25	Correct	346 ms	50600 KB	Output is correct
26	Correct	291 ms	49260 KB	Output is correct
27	Correct	249 ms	50320 KB	Output is correct
28	Correct	316 ms	53760 KB	Output is correct
29	Correct	253 ms	50608 KB	Output is correct
30	Correct	315 ms	49664 KB	Output is correct
31	Correct	229 ms	50356 KB	Output is correct
32	Correct	293 ms	67152 KB	Output is correct
33	Correct	209 ms	50952 KB	Output is correct

Subtask #6

44.0 / 44.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	5 ms	29528 KB	Output is correct
2	Correct	5 ms	29532 KB	Output is correct
3	Correct	5 ms	29660 KB	Output is correct
4	Correct	5 ms	29752 KB	Output is correct
5	Correct	5 ms	29532 KB	Output is correct
6	Correct	5 ms	29620 KB	Output is correct
7	Correct	5 ms	29532 KB	Output is correct
8	Correct	5 ms	29532 KB	Output is correct
9	Correct	5 ms	29532 KB	Output is correct
10	Correct	5 ms	29532 KB	Output is correct
11	Correct	5 ms	29532 KB	Output is correct
12	Correct	6 ms	29532 KB	Output is correct
13	Correct	321 ms	44132 KB	Output is correct
14	Correct	238 ms	67396 KB	Output is correct
15	Correct	253 ms	44112 KB	Output is correct
16	Correct	259 ms	43956 KB	Output is correct
17	Correct	366 ms	47700 KB	Output is correct
18	Correct	230 ms	43904 KB	Output is correct
19	Correct	290 ms	68436 KB	Output is correct
20	Correct	190 ms	44280 KB	Output is correct
21	Correct	5 ms	29532 KB	Output is correct
22	Correct	359 ms	44092 KB	Output is correct
23	Correct	242 ms	71708 KB	Output is correct
24	Correct	291 ms	44112 KB	Output is correct
25	Correct	285 ms	43788 KB	Output is correct
26	Correct	318 ms	47928 KB	Output is correct
27	Correct	226 ms	44720 KB	Output is correct
28	Correct	278 ms	59780 KB	Output is correct
29	Correct	203 ms	44256 KB	Output is correct
30	Correct	5 ms	29528 KB	Output is correct
31	Correct	6 ms	29784 KB	Output is correct
32	Correct	6 ms	30044 KB	Output is correct
33	Correct	8 ms	29788 KB	Output is correct
34	Correct	6 ms	29784 KB	Output is correct
35	Correct	6 ms	29788 KB	Output is correct
36	Correct	6 ms	29788 KB	Output is correct
37	Correct	6 ms	29788 KB	Output is correct
38	Correct	6 ms	29732 KB	Output is correct
39	Correct	7 ms	29784 KB	Output is correct
40	Correct	6 ms	29928 KB	Output is correct
41	Correct	7 ms	29928 KB	Output is correct
42	Correct	6 ms	29968 KB	Output is correct
43	Correct	6 ms	30044 KB	Output is correct
44	Correct	6 ms	29788 KB	Output is correct
45	Correct	5 ms	29532 KB	Output is correct
46	Correct	302 ms	44248 KB	Output is correct
47	Correct	264 ms	78420 KB	Output is correct
48	Correct	310 ms	49144 KB	Output is correct
49	Correct	262 ms	50580 KB	Output is correct
50	Correct	268 ms	49388 KB	Output is correct
51	Correct	346 ms	50600 KB	Output is correct
52	Correct	291 ms	49260 KB	Output is correct
53	Correct	249 ms	50320 KB	Output is correct
54	Correct	316 ms	53760 KB	Output is correct
55	Correct	253 ms	50608 KB	Output is correct
56	Correct	315 ms	49664 KB	Output is correct
57	Correct	229 ms	50356 KB	Output is correct
58	Correct	293 ms	67152 KB	Output is correct
59	Correct	209 ms	50952 KB	Output is correct
60	Correct	5 ms	29744 KB	Output is correct
61	Correct	380 ms	52948 KB	Output is correct
62	Correct	338 ms	75604 KB	Output is correct
63	Correct	315 ms	51796 KB	Output is correct
64	Correct	325 ms	53076 KB	Output is correct
65	Correct	282 ms	51820 KB	Output is correct
66	Correct	295 ms	52968 KB	Output is correct
67	Correct	376 ms	52020 KB	Output is correct
68	Correct	280 ms	53124 KB	Output is correct
69	Correct	355 ms	56012 KB	Output is correct
70	Correct	355 ms	53028 KB	Output is correct
71	Correct	296 ms	52384 KB	Output is correct
72	Correct	303 ms	53472 KB	Output is correct
73	Correct	305 ms	67036 KB	Output is correct
74	Correct	255 ms	55368 KB	Output is correct