oj.uz

Submission #198112

# Submission time Handle Problem Language Result Execution time Memory
198112 2020-01-24T18:13:01 Z model_code Dynamic Diameter (CEOI19_diameter) C++17
100 / 100
 1354 ms 53476 KB 
#include <bits/stdc++.h>
using namespace std;

class Solver {
	using wgt = long long;

	class IntervalTree {
		using wgt = long long;

		static constexpr wgt no_val = -(1LL<<60);

		struct node {
			wgt val, add;
		};

		int b;
		vector<node> T;

		inline __attribute__((always_inline)) void upd(int i, bool leaf) {
			wgt add = T[i].add;
			if(add == 0) return;
			T[i].val += add;
			T[i].add = 0;
			if(!leaf) {
				T[2*i].add += add;
				T[2*i+1].add += add;
			}
		}

		void get_internal(int l, int r, int i, int n_l, int n_r, wgt & max_val) {
			if(n_l >= r || l >= n_r) return;
			upd(i, n_l+1 == n_r);
			if((n_l == l && n_r == r) || T[i].val <= max_val) {
				max_val = max(max_val, T[i].val);
				return;
			}
			int c = (n_l + n_r) / 2;
			get_internal(l, min(r, c), 2*i, n_l, c, max_val);
			get_internal(max(l, c), r, 2*i+1, c, n_r, max_val);
		}

	public:
		IntervalTree() {}

		IntervalTree(int N) {
			b = 1;
			while(b < N) b *= 2;
			T.resize(2*b+1, {0, 0});
		}

		void add(int l, int r, wgt w_add, int i = 1, int n_l = 0, int n_r = 0) {
			if(i == 1) n_r = b;
			if(n_l == l && n_r == r) {
				T[i].add += w_add;
				upd(i, n_l+1 == n_r);
				return;
			}
			upd(i, n_l+1 == n_r);
			if(n_l >= r || l >= n_r) return;
			int c = (n_l + n_r) / 2;
			add(l, min(r, c), w_add, 2*i, n_l, c);
			add(max(l, c), r, w_add, 2*i+1, c, n_r);
			T[i].val = max(T[2*i].val, T[2*i+1].val);
		}

		void put(int pos, wgt w, int i = 1, int n_l = 0, int n_r = 0) {
			if(i == 1) n_r = b;
			if(n_l == pos && n_r == pos+1) {
				T[i].val = w;
				T[i].add = 0;
				return;
			}
			upd(i, n_l+1 == n_r);
			if(n_l > pos || pos >= n_r) return;
			int c = (n_l + n_r) / 2;
			if(pos < c) {
				upd(2*i+1, c+1 == n_r);
				put(pos, w, 2*i, n_l, c);
			}
			else {
				upd(2*i, n_l+1 == c);
				put(pos, w, 2*i+1, c, n_r);
			}
			T[i].val = max(T[2*i].val, T[2*i+1].val);
		}

		pair<wgt, int> get(int l, int r, bool with_id = false) { // max [l..r)
			wgt ret = no_val;
			get_internal(l, r, 1, 0, b, ret);
			if(!with_id) return {ret, 0};
			int cur = 1, n_l = 0, n_r = b;
			while(n_l+1 != n_r) {
				int c = (n_l + n_r) / 2;
				upd(2*cur, n_l+1 == c);
				if(T[2*cur].val == ret) {
					cur = 2*cur;
					n_r = c;
				}
				else {
					upd(2*cur+1, c+1 == n_r);
					n_l = c;
					cur = 2*cur+1;
				}
			}
			return {ret, n_l};
		}

		wgt get_pos(int pos) { // max [pos]
			int cur = 1, n_l = 0, n_r = b;
			while(true) {
				upd(cur, n_l+1 == n_r);
				if(n_l+1 == n_r) {
					return T[cur].val;
					break;
				}
				int c = (n_l + n_r) / 2;
				if(pos < c) {
					n_r = c;
					cur = 2*cur;
				}
				else {
					n_l = c;
					cur = 2*cur+1;
				}
			}
			return no_val;
		}
	};

	int N, R, P; // R = root, P = number of paths
	vector<int> par;
	vector< vector<int> > G; // sons
	vector< pair<int, int> > interval_renumbering;
	vector<int> v_from_interval_id;
	vector<int> subtree_size;
	vector< vector<int> > paths;
	vector<int> path_id, path_pos; // paths[path_id[i]][path_pos[i]] == i
	vector< vector< vector< pair<int, int> > > > down_edges; // light edges (child, index in tree) + dummy self-loops
	vector<int> down_edge_id;
	vector< vector<int> > last_down_edge; // largest index of light edge from (parent) + 1

	vector<wgt> W;
	IntervalTree max_dist_down;
	vector<IntervalTree> tree_over_path;

	void DFS_construct(int v, const vector< vector< pair<int, wgt> > > & G_) {
		interval_renumbering[v].second = interval_renumbering[v].first+1;
		v_from_interval_id[interval_renumbering[v].first] = v;
		subtree_size[v] = 1;
		int max_subtree_size = 0, son_in_path = -1;
		for(auto p : G_[v]) if(par[p.first] == -1) {
			int w = p.first;
			par[w] = v;
			G[v].push_back(w);
			W[w] = p.second;
			interval_renumbering[w].first = interval_renumbering[v].second;
			DFS_construct(w, G_);
			interval_renumbering[v].second = interval_renumbering[w].second;
			max_dist_down.add(interval_renumbering[w].first, interval_renumbering[w].second, p.second);
			subtree_size[v] += subtree_size[w];
			if(subtree_size[w] > max_subtree_size) {
				max_subtree_size = subtree_size[w];
				son_in_path = w;
			}
		}
		if(son_in_path == -1) {
			path_id[v] = P++;
			paths.push_back({});
		}
		else path_id[v] = path_id[son_in_path];
		paths[path_id[v]].push_back(v);
	}

	wgt get_max_dist_down(int v) {
		return max_dist_down.get(interval_renumbering[v].first, interval_renumbering[v].second).first;
	}

	wgt get_dep(int v) {
		return max_dist_down.get_pos(interval_renumbering[v].first);
	}

public:
	Solver(vector< vector< pair<int, wgt> > > & G_) : N(G_.size()), R(0), P(0) {
		par.resize(N, -1);
		G.resize(N);
		interval_renumbering.resize(N, {0, 0});
		subtree_size.resize(N);
		path_id.resize(N);
		path_pos.resize(N);
		W.resize(N, 0);
		v_from_interval_id.resize(N);
		max_dist_down = IntervalTree(N);

		par[R] = R;
		DFS_construct(R, G_);
		for(int i = 0; i < P; i++) reverse(begin(paths[i]), end(paths[i]));

		tree_over_path.resize(P);
		down_edges.resize(P);
		last_down_edge.resize(P);
		down_edge_id.resize(N);
		for(int i = 0; i < P; i++) {
			int num_edges = 0, L = paths[i].size();
			down_edges[i].resize(L);
			last_down_edge[i].resize(L);
			for(int j = 0; j < L; j++) {
				path_pos[paths[i][j]] = j;
				for(auto son : G[paths[i][j]]) if(path_id[son] != i) {
					down_edge_id[son] = num_edges;
					down_edges[i][j].push_back({son, num_edges++});
				}
				down_edges[i][j].push_back({paths[i][j], num_edges++});
				last_down_edge[i][j] = num_edges;
			}
			tree_over_path[i] = IntervalTree(num_edges);
			wgt dist_from_top = 0;
			for(int j = 0; j < L; j++) {
				if(j > 0) dist_from_top += W[paths[i][j]];
				for(auto edge : down_edges[i][j]) {
					wgt val = 0;
					if(edge.first != paths[i][j])
						val = get_max_dist_down(edge.first) - get_dep(edge.first) + W[edge.first];
					tree_over_path[i].put(edge.second, val - dist_from_top);
				}
			}
		}
	}

	void update(int u, int v, wgt w) {
		if(par[u] == v) swap(u, v);
		// update weight(par[v]--v) to w
		max_dist_down.add(interval_renumbering[v].first, interval_renumbering[v].second, w-W[v]);
		if(path_id[v] == path_id[u])
			tree_over_path[path_id[v]].add(last_down_edge[path_id[u]][path_pos[u]], last_down_edge[path_id[u]].back(), W[v]-w);
		W[v] = w;
		v = paths[path_id[v]][0];
		while(v != R) {
			int v_old = v;
			v = par[v];
			int r = last_down_edge[path_id[v]][path_pos[v]];
			wgt dist_from_top = -tree_over_path[path_id[v]].get_pos(r-1);
			tree_over_path[path_id[v]].put(down_edge_id[v_old], get_max_dist_down(v_old) - get_dep(v) - dist_from_top);
			v = paths[path_id[v]][0];
		}
	}

	wgt query() {
		// return diameter
		pair<wgt, int> p = max_dist_down.get(0, N, true);
		int v = v_from_interval_id[p.second];
		wgt ret = p.first, dist_up = 0;
		int last_edge_id = -1;
		while(true) {
			int r = last_down_edge[path_id[v]][path_pos[v]];
			wgt dist_from_top = -tree_over_path[path_id[v]].get_pos(r-1);
			ret = max(ret, dist_up + dist_from_top + tree_over_path[path_id[v]].get(0, last_edge_id).first);
			ret = max(ret, dist_up + dist_from_top + tree_over_path[path_id[v]].get(last_edge_id+1, r).first);
			if(path_pos[v]+1 < (int)paths[path_id[v]].size())
				ret = max(ret, dist_up + get_max_dist_down(paths[path_id[v]][path_pos[v]+1]) - get_dep(v));
			dist_up += dist_from_top;
			v = paths[path_id[v]][0];
			if(v == R) break;
			last_edge_id = down_edge_id[v];
			dist_up += W[v];
			v = par[v];
		}
		return ret;
	}
};

int main() {
	cin.sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(10);
	int N, Q;
	long long W;
	cin >> N >> Q >> W;
	vector< pair<int, int> > E(N-1);
	vector< vector< pair<int, long long> > > G(N);
	for(int i = 0; i < N-1; i++) {
		int u, v;
		long long w;
		cin >> u >> v >> w;
		G[--u].push_back({--v, w});
		G[v].push_back({u, w});
		E[i] = {u, v};
	}
	Solver solver(G);
	long long last = 0;
	for(int i = 0; i < Q; i++) {
		long long e, w;
		cin >> e >> w;
		e = (e + last) % (N-1);
		w = (w + last) % W;
		int u = E[e].first, v = E[e].second;
		solver.update(u, v, w);
		last = solver.query();
		cout << last << "\n";
	}
	return 0;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 348 KB Output is correct
2 Correct 2 ms 348 KB Output is correct
3 Correct 2 ms 348 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 2 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 2 ms 376 KB Output is correct
10 Correct 2 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 3 ms 376 KB Output is correct
13 Correct 2 ms 348 KB Output is correct
14 Correct 2 ms 348 KB Output is correct
15 Correct 2 ms 376 KB Output is correct
16 Correct 2 ms 348 KB Output is correct
17 Correct 2 ms 376 KB Output is correct
18 Correct 2 ms 376 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 348 KB Output is correct
2 Correct 2 ms 348 KB Output is correct
3 Correct 2 ms 348 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 2 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 2 ms 376 KB Output is correct
10 Correct 2 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 3 ms 376 KB Output is correct
13 Correct 2 ms 348 KB Output is correct
14 Correct 2 ms 348 KB Output is correct
15 Correct 2 ms 376 KB Output is correct
16 Correct 2 ms 348 KB Output is correct
17 Correct 2 ms 376 KB Output is correct
18 Correct 2 ms 376 KB Output is correct
19 Correct 16 ms 760 KB Output is correct
20 Correct 15 ms 760 KB Output is correct
21 Correct 14 ms 820 KB Output is correct
22 Correct 10 ms 760 KB Output is correct
23 Correct 32 ms 2556 KB Output is correct
24 Correct 27 ms 2424 KB Output is correct
25 Correct 23 ms 2580 KB Output is correct
26 Correct 18 ms 3004 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 376 KB Output is correct
3 Correct 4 ms 376 KB Output is correct
4 Correct 19 ms 456 KB Output is correct
5 Correct 83 ms 732 KB Output is correct
6 Correct 2 ms 380 KB Output is correct
7 Correct 3 ms 632 KB Output is correct
8 Correct 3 ms 632 KB Output is correct
9 Correct 5 ms 632 KB Output is correct
10 Correct 29 ms 764 KB Output is correct
11 Correct 135 ms 1008 KB Output is correct
12 Correct 11 ms 3096 KB Output is correct
13 Correct 12 ms 3108 KB Output is correct
14 Correct 14 ms 3064 KB Output is correct
15 Correct 47 ms 3192 KB Output is correct
16 Correct 200 ms 3680 KB Output is correct
17 Correct 192 ms 52836 KB Output is correct
18 Correct 190 ms 52792 KB Output is correct
19 Correct 199 ms 52836 KB Output is correct
20 Correct 251 ms 52900 KB Output is correct
21 Correct 499 ms 53476 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 760 KB Output is correct
2 Correct 30 ms 760 KB Output is correct
3 Correct 134 ms 1000 KB Output is correct
4 Correct 263 ms 1400 KB Output is correct
5 Correct 29 ms 4728 KB Output is correct
6 Correct 67 ms 4856 KB Output is correct
7 Correct 258 ms 4984 KB Output is correct
8 Correct 507 ms 5584 KB Output is correct
9 Correct 110 ms 21680 KB Output is correct
10 Correct 163 ms 21752 KB Output is correct
11 Correct 422 ms 22280 KB Output is correct
12 Correct 731 ms 22448 KB Output is correct
13 Correct 213 ms 43112 KB Output is correct
14 Correct 298 ms 43180 KB Output is correct
15 Correct 609 ms 43684 KB Output is correct
16 Correct 1024 ms 44132 KB Output is correct
17 Correct 1354 ms 43816 KB Output is correct

Subtask #5
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 916 ms 42744 KB Output is correct
2 Correct 948 ms 42524 KB Output is correct
3 Correct 1077 ms 42640 KB Output is correct
4 Correct 958 ms 42864 KB Output is correct
5 Correct 937 ms 43944 KB Output is correct
6 Correct 866 ms 48612 KB Output is correct
7 Correct 742 ms 46332 KB Output is correct
8 Correct 716 ms 46084 KB Output is correct
9 Correct 720 ms 46508 KB Output is correct
10 Correct 697 ms 46348 KB Output is correct
11 Correct 739 ms 46988 KB Output is correct
12 Correct 594 ms 51708 KB Output is correct
13 Correct 575 ms 49592 KB Output is correct
14 Correct 650 ms 49552 KB Output is correct
15 Correct 546 ms 49592 KB Output is correct
16 Correct 544 ms 49596 KB Output is correct
17 Correct 525 ms 50004 KB Output is correct
18 Correct 496 ms 51924 KB Output is correct
19 Correct 509 ms 49472 KB Output is correct
20 Correct 512 ms 49608 KB Output is correct
21 Correct 537 ms 49524 KB Output is correct
22 Correct 536 ms 49728 KB Output is correct
23 Correct 552 ms 50092 KB Output is correct
24 Correct 513 ms 51816 KB Output is correct

Subtask #6
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 348 KB Output is correct
2 Correct 2 ms 348 KB Output is correct
3 Correct 2 ms 348 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 2 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 2 ms 376 KB Output is correct
10 Correct 2 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 3 ms 376 KB Output is correct
13 Correct 2 ms 348 KB Output is correct
14 Correct 2 ms 348 KB Output is correct
15 Correct 2 ms 376 KB Output is correct
16 Correct 2 ms 348 KB Output is correct
17 Correct 2 ms 376 KB Output is correct
18 Correct 2 ms 376 KB Output is correct
19 Correct 16 ms 760 KB Output is correct
20 Correct 15 ms 760 KB Output is correct
21 Correct 14 ms 820 KB Output is correct
22 Correct 10 ms 760 KB Output is correct
23 Correct 32 ms 2556 KB Output is correct
24 Correct 27 ms 2424 KB Output is correct
25 Correct 23 ms 2580 KB Output is correct
26 Correct 18 ms 3004 KB Output is correct
27 Correct 2 ms 376 KB Output is correct
28 Correct 2 ms 376 KB Output is correct
29 Correct 4 ms 376 KB Output is correct
30 Correct 19 ms 456 KB Output is correct
31 Correct 83 ms 732 KB Output is correct
32 Correct 2 ms 380 KB Output is correct
33 Correct 3 ms 632 KB Output is correct
34 Correct 3 ms 632 KB Output is correct
35 Correct 5 ms 632 KB Output is correct
36 Correct 29 ms 764 KB Output is correct
37 Correct 135 ms 1008 KB Output is correct
38 Correct 11 ms 3096 KB Output is correct
39 Correct 12 ms 3108 KB Output is correct
40 Correct 14 ms 3064 KB Output is correct
41 Correct 47 ms 3192 KB Output is correct
42 Correct 200 ms 3680 KB Output is correct
43 Correct 192 ms 52836 KB Output is correct
44 Correct 190 ms 52792 KB Output is correct
45 Correct 199 ms 52836 KB Output is correct
46 Correct 251 ms 52900 KB Output is correct
47 Correct 499 ms 53476 KB Output is correct
48 Correct 6 ms 760 KB Output is correct
49 Correct 30 ms 760 KB Output is correct
50 Correct 134 ms 1000 KB Output is correct
51 Correct 263 ms 1400 KB Output is correct
52 Correct 29 ms 4728 KB Output is correct
53 Correct 67 ms 4856 KB Output is correct
54 Correct 258 ms 4984 KB Output is correct
55 Correct 507 ms 5584 KB Output is correct
56 Correct 110 ms 21680 KB Output is correct
57 Correct 163 ms 21752 KB Output is correct
58 Correct 422 ms 22280 KB Output is correct
59 Correct 731 ms 22448 KB Output is correct
60 Correct 213 ms 43112 KB Output is correct
61 Correct 298 ms 43180 KB Output is correct
62 Correct 609 ms 43684 KB Output is correct
63 Correct 1024 ms 44132 KB Output is correct
64 Correct 1354 ms 43816 KB Output is correct
65 Correct 916 ms 42744 KB Output is correct
66 Correct 948 ms 42524 KB Output is correct
67 Correct 1077 ms 42640 KB Output is correct
68 Correct 958 ms 42864 KB Output is correct
69 Correct 937 ms 43944 KB Output is correct
70 Correct 866 ms 48612 KB Output is correct
71 Correct 742 ms 46332 KB Output is correct
72 Correct 716 ms 46084 KB Output is correct
73 Correct 720 ms 46508 KB Output is correct
74 Correct 697 ms 46348 KB Output is correct
75 Correct 739 ms 46988 KB Output is correct
76 Correct 594 ms 51708 KB Output is correct
77 Correct 575 ms 49592 KB Output is correct
78 Correct 650 ms 49552 KB Output is correct
79 Correct 546 ms 49592 KB Output is correct
80 Correct 544 ms 49596 KB Output is correct
81 Correct 525 ms 50004 KB Output is correct
82 Correct 496 ms 51924 KB Output is correct
83 Correct 509 ms 49472 KB Output is correct
84 Correct 512 ms 49608 KB Output is correct
85 Correct 537 ms 49524 KB Output is correct
86 Correct 536 ms 49728 KB Output is correct
87 Correct 552 ms 50092 KB Output is correct
88 Correct 513 ms 51816 KB Output is correct
89 Correct 846 ms 42484 KB Output is correct
90 Correct 848 ms 42784 KB Output is correct
91 Correct 743 ms 45176 KB Output is correct
92 Correct 717 ms 43560 KB Output is correct
93 Correct 601 ms 48884 KB Output is correct
94 Correct 627 ms 43732 KB Output is correct
95 Correct 564 ms 45712 KB Output is correct
96 Correct 546 ms 42400 KB Output is correct
97 Correct 551 ms 45552 KB Output is correct
98 Correct 526 ms 49116 KB Output is correct
99 Correct 616 ms 44020 KB Output is correct
100 Correct 556 ms 44020 KB Output is correct