oj.uz

Submission #170878

# Submission time Handle Problem Language Result Execution time Memory
170878 2019-12-26T16:14:31 Z nobik Split the Attractions (IOI19_split) C++14
100 / 100
 282 ms 25192 KB 
#include "split.h"
#include <bits/stdc++.h>

using namespace std;

struct Fau {
	int n;

	vector<int> parent;
	vector<vector<int>> bucket;

	Fau(int n): n(n), parent(n), bucket(n) {
		for (int i = 0; i < n; ++i) {
			bucket[i].push_back(i);
			parent[i] = i;
		}
	}

	int Root(int a) {
		return parent[a] == a ? a : Root(parent[a]);
	}

	int Union(int a, int b) {
		a = Root(a);
		b = Root(b);
		if (a == b)
			return a;
		
		if (bucket[a].size() > bucket[b].size())
			swap(a, b);
		
		parent[a] = b;
		bucket[b].insert(bucket[b].end(), bucket[a].begin(), bucket[a].end());
		bucket[a].clear();
		bucket[a].shrink_to_fit();

		return b;
	}

	int Size(int v) {
		return (int) bucket[v].size();
	}
};

struct Solver {
	int n, m;

	vector<vector<pair<int, int>>> graph;
	vector<int> tree_edges;
	vector<int> used, sizes;

	vector<pair<int, int>> component_sizes;

	Solver(int n, const vector<pair<int, int>>& edges, int a, int b, int c)
			: n(n), m(edges.size()), graph(n), tree_edges(m), used(n), sizes(n) {
		component_sizes.emplace_back(a, 1);
		component_sizes.emplace_back(b, 2);
		component_sizes.emplace_back(c, 3);
		sort(component_sizes.begin(), component_sizes.end());

		for (int i = 0; i < m; ++i) {
			int x = edges[i].first, y = edges[i].second;
			graph[x].emplace_back(y, i);
			graph[y].emplace_back(x, i);
		}
	}

	void FindSpanningTree(int v) {
		used[v] = 1;
		sizes[v] = 1;
		for (const auto& edge: graph[v]) {
			int to = edge.first, id = edge.second;
			if (used[to])
				continue;
			
			tree_edges[id] = 1;
			FindSpanningTree(to);
			sizes[v] += sizes[to];
		}
	}

	int FindCentroid(int v, int parent) {
		for (const auto& edge: graph[v]) {
			int to = edge.first, id = edge.second;
			if (to == parent || !tree_edges[id])
				continue;
			
			if (2 * sizes[to] > n)
				return FindCentroid(to, v);
		}

		return v;
	}

	void UniteSubtrees(int centroid, Fau& fau) {
		for (int i = 0; i < n; ++i) {
			if (i == centroid)
				continue;
			
			for (const auto& edge: graph[i]) {
				int to = edge.first, id = edge.second;
				if (to == centroid || !tree_edges[id])
					continue;
				
				fau.Union(i, to);
			}
		}
	}

	vector<int> Solve() {
		FindSpanningTree(0);
		int centroid = FindCentroid(0, -1);

		Fau fau(n);
		UniteSubtrees(centroid, fau);

		
		int max_subtree_vertex = -1, max_subtree_size = -1;
		for (int i = 0; i < n; ++i) {
			if (i == centroid)
				continue;
			
			if (fau.Root(i) == i && fau.Size(i) > max_subtree_size) {
				max_subtree_size = fau.Size(i);
				max_subtree_vertex = i;
			}
		}

		for (int i = 0; i < n; ++i) {
			if (i == centroid)
				continue;
			
			for (const auto& edge: graph[i]) {
				if (max_subtree_size >= component_sizes[0].first)
					break;
				
				int to = edge.first;
				if (to == centroid)
					continue;
				
				int vertex = fau.Union(i, to);
				if (fau.Size(vertex) > max_subtree_size) {
					max_subtree_size = fau.Size(vertex);
					max_subtree_vertex = vertex;
				}
			}
		}

		// Solution was not found!
		if (max_subtree_size < component_sizes[0].first) {
			return vector<int>(n);
		}

		vector<int> result(n, component_sizes.back().second);
		Color(max_subtree_vertex, fau.bucket[max_subtree_vertex], component_sizes[0].first, component_sizes[0].second, result);
		Color(centroid, Complement(fau.bucket[max_subtree_vertex]), component_sizes[1].first, component_sizes[1].second, result);
		return result;
	}

	void Color(int v, const vector<int>& allowed_vertices, int size, int color, vector<int>& colors) {
		vector<int> used(n, 1);
		for (int e: allowed_vertices)
			used[e] = 0;

		queue<int> q;
		q.push(v);
		used[v] = 1;

		while (!q.empty() && size > 0) {
			v = q.front();
			q.pop();
			colors[v] = color;
			--size;

			for (const auto& edge: graph[v]) {
				int to = edge.first;
				if (!used[to]) {
					q.push(to);
					used[to] = 1;
				}
			}
		}
	}

	vector<int> Complement(const vector<int>& a) {
		vector<int> b(n), result;
		for (int e: a) b[e] = 1;
		for (int i = 0; i < n; ++i) {
			if (!b[i])
				result.push_back(i);
		}

		return result;
	}
};

vector<int> find_split(int n, int a, int b, int c, vector<int> p, vector<int> q) {
	int m = static_cast<int>(p.size());
	vector<pair<int, int>> edges;
	for (int i = 0; i < m; ++i) {
		edges.emplace_back(p[i], q[i]);
	}

	Solver solver(n, edges, a, b, c);
	return solver.Solve();
}

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB ok, correct split
2 Correct 2 ms 376 KB ok, correct split
3 Correct 2 ms 376 KB ok, correct split
4 Correct 2 ms 376 KB ok, correct split
5 Correct 2 ms 376 KB ok, correct split
6 Correct 2 ms 376 KB ok, correct split
7 Correct 208 ms 19900 KB ok, correct split
8 Correct 201 ms 18924 KB ok, correct split
9 Correct 138 ms 18540 KB ok, correct split
10 Correct 136 ms 20076 KB ok, correct split
11 Correct 215 ms 20076 KB ok, correct split

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB ok, correct split
2 Correct 2 ms 256 KB ok, correct split
3 Correct 2 ms 376 KB ok, correct split
4 Correct 243 ms 20132 KB ok, correct split
5 Correct 155 ms 16620 KB ok, correct split
6 Correct 147 ms 19180 KB ok, correct split
7 Correct 158 ms 17900 KB ok, correct split
8 Correct 206 ms 21992 KB ok, correct split
9 Correct 141 ms 15468 KB ok, correct split
10 Correct 83 ms 17900 KB ok, correct split
11 Correct 85 ms 18412 KB ok, correct split
12 Correct 89 ms 18924 KB ok, correct split

Subtask #3
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB ok, correct split
2 Correct 141 ms 16780 KB ok, correct split
3 Correct 47 ms 7664 KB ok, correct split
4 Correct 3 ms 376 KB ok, correct split
5 Correct 175 ms 16760 KB ok, correct split
6 Correct 137 ms 16620 KB ok, correct split
7 Correct 148 ms 16492 KB ok, correct split
8 Correct 163 ms 17192 KB ok, correct split
9 Correct 147 ms 16364 KB ok, correct split
10 Correct 42 ms 5872 KB ok, no valid answer
11 Correct 72 ms 8432 KB ok, no valid answer
12 Correct 112 ms 16876 KB ok, no valid answer
13 Correct 135 ms 17132 KB ok, no valid answer
14 Correct 77 ms 16620 KB ok, no valid answer

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB ok, correct split
2 Correct 2 ms 376 KB ok, no valid answer
3 Correct 2 ms 376 KB ok, correct split
4 Correct 2 ms 376 KB ok, correct split
5 Correct 2 ms 380 KB ok, correct split
6 Correct 2 ms 376 KB ok, correct split
7 Correct 2 ms 256 KB ok, correct split
8 Correct 2 ms 376 KB ok, correct split
9 Correct 5 ms 888 KB ok, correct split
10 Correct 5 ms 888 KB ok, correct split
11 Correct 2 ms 376 KB ok, correct split
12 Correct 5 ms 888 KB ok, correct split
13 Correct 2 ms 312 KB ok, correct split
14 Correct 2 ms 276 KB ok, correct split
15 Correct 2 ms 376 KB ok, correct split
16 Correct 2 ms 376 KB ok, correct split
17 Correct 2 ms 376 KB ok, correct split
18 Correct 2 ms 376 KB ok, correct split
19 Correct 3 ms 376 KB ok, correct split
20 Correct 4 ms 504 KB ok, correct split
21 Correct 5 ms 760 KB ok, correct split
22 Correct 4 ms 764 KB ok, correct split
23 Correct 4 ms 760 KB ok, correct split
24 Correct 4 ms 760 KB ok, correct split
25 Correct 4 ms 760 KB ok, correct split
26 Correct 5 ms 888 KB ok, correct split
27 Correct 5 ms 892 KB ok, correct split
28 Correct 5 ms 888 KB ok, correct split
29 Correct 2 ms 376 KB ok, correct split
30 Correct 5 ms 804 KB ok, correct split
31 Correct 3 ms 504 KB ok, correct split
32 Correct 2 ms 376 KB ok, correct split
33 Correct 2 ms 376 KB ok, correct split
34 Correct 5 ms 760 KB ok, correct split
35 Correct 4 ms 888 KB ok, correct split
36 Correct 4 ms 760 KB ok, correct split
37 Correct 5 ms 888 KB ok, correct split
38 Correct 5 ms 888 KB ok, correct split
39 Correct 5 ms 888 KB ok, correct split
40 Correct 5 ms 888 KB ok, correct split
41 Correct 4 ms 508 KB ok, correct split
42 Correct 4 ms 504 KB ok, correct split
43 Correct 5 ms 888 KB ok, correct split
44 Correct 5 ms 888 KB ok, correct split
45 Correct 5 ms 888 KB ok, correct split
46 Correct 4 ms 732 KB ok, correct split
47 Correct 4 ms 760 KB ok, no valid answer
48 Correct 4 ms 760 KB ok, correct split
49 Correct 5 ms 760 KB ok, correct split
50 Correct 2 ms 376 KB ok, no valid answer
51 Correct 2 ms 376 KB ok, no valid answer
52 Correct 4 ms 808 KB ok, no valid answer
53 Correct 6 ms 888 KB ok, no valid answer
54 Correct 4 ms 760 KB ok, no valid answer
55 Correct 5 ms 760 KB ok, no valid answer
56 Correct 5 ms 760 KB ok, no valid answer

Subtask #5
36.0 / 36.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB ok, correct split
2 Correct 2 ms 376 KB ok, correct split
3 Correct 2 ms 376 KB ok, correct split
4 Correct 2 ms 376 KB ok, correct split
5 Correct 2 ms 376 KB ok, correct split
6 Correct 2 ms 376 KB ok, correct split
7 Correct 208 ms 19900 KB ok, correct split
8 Correct 201 ms 18924 KB ok, correct split
9 Correct 138 ms 18540 KB ok, correct split
10 Correct 136 ms 20076 KB ok, correct split
11 Correct 215 ms 20076 KB ok, correct split
12 Correct 2 ms 256 KB ok, correct split
13 Correct 2 ms 256 KB ok, correct split
14 Correct 2 ms 376 KB ok, correct split
15 Correct 243 ms 20132 KB ok, correct split
16 Correct 155 ms 16620 KB ok, correct split
17 Correct 147 ms 19180 KB ok, correct split
18 Correct 158 ms 17900 KB ok, correct split
19 Correct 206 ms 21992 KB ok, correct split
20 Correct 141 ms 15468 KB ok, correct split
21 Correct 83 ms 17900 KB ok, correct split
22 Correct 85 ms 18412 KB ok, correct split
23 Correct 89 ms 18924 KB ok, correct split
24 Correct 2 ms 376 KB ok, correct split
25 Correct 141 ms 16780 KB ok, correct split
26 Correct 47 ms 7664 KB ok, correct split
27 Correct 3 ms 376 KB ok, correct split
28 Correct 175 ms 16760 KB ok, correct split
29 Correct 137 ms 16620 KB ok, correct split
30 Correct 148 ms 16492 KB ok, correct split
31 Correct 163 ms 17192 KB ok, correct split
32 Correct 147 ms 16364 KB ok, correct split
33 Correct 42 ms 5872 KB ok, no valid answer
34 Correct 72 ms 8432 KB ok, no valid answer
35 Correct 112 ms 16876 KB ok, no valid answer
36 Correct 135 ms 17132 KB ok, no valid answer
37 Correct 77 ms 16620 KB ok, no valid answer
38 Correct 2 ms 256 KB ok, correct split
39 Correct 2 ms 376 KB ok, no valid answer
40 Correct 2 ms 376 KB ok, correct split
41 Correct 2 ms 376 KB ok, correct split
42 Correct 2 ms 380 KB ok, correct split
43 Correct 2 ms 376 KB ok, correct split
44 Correct 2 ms 256 KB ok, correct split
45 Correct 2 ms 376 KB ok, correct split
46 Correct 5 ms 888 KB ok, correct split
47 Correct 5 ms 888 KB ok, correct split
48 Correct 2 ms 376 KB ok, correct split
49 Correct 5 ms 888 KB ok, correct split
50 Correct 2 ms 312 KB ok, correct split
51 Correct 2 ms 276 KB ok, correct split
52 Correct 2 ms 376 KB ok, correct split
53 Correct 2 ms 376 KB ok, correct split
54 Correct 2 ms 376 KB ok, correct split
55 Correct 2 ms 376 KB ok, correct split
56 Correct 3 ms 376 KB ok, correct split
57 Correct 4 ms 504 KB ok, correct split
58 Correct 5 ms 760 KB ok, correct split
59 Correct 4 ms 764 KB ok, correct split
60 Correct 4 ms 760 KB ok, correct split
61 Correct 4 ms 760 KB ok, correct split
62 Correct 4 ms 760 KB ok, correct split
63 Correct 5 ms 888 KB ok, correct split
64 Correct 5 ms 892 KB ok, correct split
65 Correct 5 ms 888 KB ok, correct split
66 Correct 2 ms 376 KB ok, correct split
67 Correct 5 ms 804 KB ok, correct split
68 Correct 3 ms 504 KB ok, correct split
69 Correct 2 ms 376 KB ok, correct split
70 Correct 2 ms 376 KB ok, correct split
71 Correct 5 ms 760 KB ok, correct split
72 Correct 4 ms 888 KB ok, correct split
73 Correct 4 ms 760 KB ok, correct split
74 Correct 5 ms 888 KB ok, correct split
75 Correct 5 ms 888 KB ok, correct split
76 Correct 5 ms 888 KB ok, correct split
77 Correct 5 ms 888 KB ok, correct split
78 Correct 4 ms 508 KB ok, correct split
79 Correct 4 ms 504 KB ok, correct split
80 Correct 5 ms 888 KB ok, correct split
81 Correct 5 ms 888 KB ok, correct split
82 Correct 5 ms 888 KB ok, correct split
83 Correct 4 ms 732 KB ok, correct split
84 Correct 4 ms 760 KB ok, no valid answer
85 Correct 4 ms 760 KB ok, correct split
86 Correct 5 ms 760 KB ok, correct split
87 Correct 2 ms 376 KB ok, no valid answer
88 Correct 2 ms 376 KB ok, no valid answer
89 Correct 4 ms 808 KB ok, no valid answer
90 Correct 6 ms 888 KB ok, no valid answer
91 Correct 4 ms 760 KB ok, no valid answer
92 Correct 5 ms 760 KB ok, no valid answer
93 Correct 5 ms 760 KB ok, no valid answer
94 Correct 181 ms 19404 KB ok, correct split
95 Correct 226 ms 25192 KB ok, correct split
96 Correct 282 ms 23016 KB ok, correct split
97 Correct 49 ms 7536 KB ok, correct split
98 Correct 50 ms 7920 KB ok, correct split
99 Correct 72 ms 10092 KB ok, correct split
100 Correct 206 ms 25164 KB ok, correct split
101 Correct 179 ms 23276 KB ok, correct split
102 Correct 163 ms 22140 KB ok, correct split
103 Correct 142 ms 21480 KB ok, correct split
104 Correct 152 ms 22796 KB ok, correct split
105 Correct 74 ms 11756 KB ok, correct split
106 Correct 145 ms 23372 KB ok, correct split
107 Correct 145 ms 18528 KB ok, correct split
108 Correct 135 ms 18540 KB ok, correct split
109 Correct 212 ms 24172 KB ok, correct split
110 Correct 207 ms 24708 KB ok, correct split
111 Correct 233 ms 24304 KB ok, correct split
112 Correct 198 ms 24168 KB ok, correct split
113 Correct 196 ms 24180 KB ok, correct split
114 Correct 19 ms 2804 KB ok, correct split
115 Correct 17 ms 2552 KB ok, correct split
116 Correct 216 ms 24524 KB ok, correct split
117 Correct 193 ms 24004 KB ok, correct split
118 Correct 152 ms 16492 KB ok, correct split
119 Correct 149 ms 17596 KB ok, correct split
120 Correct 147 ms 18440 KB ok, correct split
121 Correct 142 ms 17332 KB ok, no valid answer
122 Correct 134 ms 18028 KB ok, no valid answer
123 Correct 236 ms 23224 KB ok, no valid answer
124 Correct 217 ms 24044 KB ok, no valid answer
125 Correct 122 ms 18924 KB ok, no valid answer
126 Correct 74 ms 15852 KB ok, no valid answer
127 Correct 146 ms 19568 KB ok, no valid answer