oj.uz

Submission #154397

# Submission time Handle Problem Language Result Execution time Memory
154397 2019-09-21T16:58:22 Z rama_pang Split the Attractions (IOI19_split) C++14
100 / 100
 198 ms 20720 KB 
#include "split.h"
#include <bits/stdc++.h>
using namespace std;

struct disj { //disjoint set union find data structure
    vector<int> p, sz;
    disj(int n) { p.resize(n); iota(p.begin(), p.end(), 0); sz.assign(n, 1); }
    int par(int n) { return (p[n] == n)? n : p[n] = par(p[n]); }
};

void centroid(int n, int p, vector<vector<int>> &G, int &cent, vector<int> &sz_dfs) { //find centroid of tree
    bool is_centroid = true;
    for (auto i : G[n]) {
        if (i == p) continue;
        centroid(i, n, G, cent, sz_dfs);
        if (sz_dfs[i] > G.size() / 2) is_centroid = false;
        sz_dfs[n] += sz_dfs[i];
    }
    if (G.size() - sz_dfs[n] > G.size() / 2) is_centroid = false;
    if (is_centroid) cent = n;
}

int find_size(int n, int p, int id, vector<vector<int>> &G, disj &a, vector<int> &sz_dfs) { //find size of subtree
    a.p[n] = id;
    int res = 1;
    for (auto i : G[n]) {
        if (i == p) continue;
        sz_dfs[n] += find_size(i, n, id, G, a, sz_dfs);
    }
    return sz_dfs[n];
}

void dfs_color(int n, int p, int &cnt, int color, vector<vector<int>> &G, vector<int> &res, int except) { //coloring by dfs
    if (n == except) return;
    if (cnt > 0) {
        cnt--;
        res[n] = color;
    }
    for (auto i : G[n]) {
        if (i == p) continue;
        if (res[i] != 0) continue;
        if (cnt <= 0) break;
        dfs_color(i, n, cnt, color, G, res, except);
    }
}

vector<int> find_split(int n, int a, int b, int c, vector<int> p, vector<int> q) {
	vector<int> res(n, 0);
    vector<pair<int, int>> tmp = {{a, 1}, {b, 2}, {c, 3}}; sort(tmp.begin(), tmp.end()); //assume a <= b <= c
    disj ds(n);
    vector<pair<int, int>> edge;
    vector<vector<int>> G(n);
    vector<int> sz_dfs(n, 1);

    for (int i = 0; i < p.size(); i++) edge.push_back({p[i], q[i]});
    for (auto i : edge) { //create (random) spanning tree
        int p1 = ds.par(i.first), p2 = ds.par(i.second);
        if (p1 != p2) {
            ds.p[p1] = p2;
            G[i.first].push_back(i.second); G[i.second].push_back(i.first);
        }
    }

    int center; centroid(0, 0, G, center, sz_dfs); //find centroid of spanning tree
    int max_subtree = 0;
    vector<int> subtrees;
    disj anc(n);
    sz_dfs.assign(n, 1);
    bool done = false; //check if a is already found
    int lim = tmp[0].first;
    //finding and coloring
    for (auto i : G[center]) {
        if (done) break;
        max_subtree = max(max_subtree, sz_dfs[i] = find_size(i, center, i, G, anc, sz_dfs));
        anc.sz[i] = sz_dfs[i];
        if (max_subtree >= tmp[0].first) { //pick if subtree of centroid has size >= a; b is guaranteed (centroid to all nodes in other subtrees), c is leftover
            dfs_color(i, center, tmp[0].first, tmp[0].second, G, res, -1);
            done = true;
        }
    }
    for (auto i : edge) if (!done) { //a <= n / 3
        if (i.first == center || i.second == center) continue;
        int p1 = anc.par(i.first), p2 = anc.par(i.second); //worst case coloring scenario: dfs coloring of a through all child of centroid -> centroid trapped
        if (p1 == p2) continue; //for worst case scenario, all subtrees < a (since a cannot be chosen from a single subtree)
        G[i.first].push_back(i.second); G[i.second].push_back(i.first); //a+b+c -(2a-2) - 1(centroid) = b + c - a + 1 = sizeof connected subtrees left from centroid
        max_subtree = max(max_subtree, anc.sz[p1] + anc.sz[p2]); //assume b (needed size of subtree) > b + c - a + 2 (centroid-connected subtree left)
        anc.sz[p1] += anc.sz[p2]; anc.sz[p2] = 0; anc.p[p2] = p1; //then a - 2 > c, however a <= c. Contradiction. Thus coloring always works
        if (max_subtree >= tmp[0].first) { //connect subtrees of spanning tree -> if component has size >= a, then found a
            dfs_color(p1, center, tmp[0].first, tmp[0].second, G, res, center);
            done = true;
        }
    }

    dfs_color(center, -1, tmp[1].first, tmp[1].second, G, res, -1); //since centroid isn't used and it is connected to all nodes, it can be used to get b
    for (int i = 0; i < n; i++) res[i] = (res[i] == 0)? tmp[2].second : res[i]; //leftover for c
    if (max_subtree < lim) res.assign(n, 0); //if max connected subtree has size < a, then there is no solution
	
    return res;
}

Compilation message

split.cpp: In function 'void centroid(int, int, std::vector<std::vector<int> >&, int&, std::vector<int>&)':
split.cpp:16:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         if (sz_dfs[i] > G.size() / 2) is_centroid = false;
split.cpp: In function 'int find_size(int, int, int, std::vector<std::vector<int> >&, disj&, std::vector<int>&)':
split.cpp:25:9: warning: unused variable 'res' [-Wunused-variable]
     int res = 1;
         ^~~
split.cpp: In function 'std::vector<int> find_split(int, int, int, int, std::vector<int>, std::vector<int>)':
split.cpp:55:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 0; i < p.size(); i++) edge.push_back({p[i], q[i]});
                     ~~^~~~~~~~~~

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 256 KB ok, correct split
5 Correct 2 ms 256 KB ok, correct split
6 Correct 2 ms 376 KB ok, correct split
7 Correct 148 ms 20716 KB ok, correct split
8 Correct 116 ms 17900 KB ok, correct split
9 Correct 129 ms 17132 KB ok, correct split
10 Correct 130 ms 20720 KB ok, correct split
11 Correct 143 ms 19300 KB ok, correct split

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB ok, correct split
2 Correct 2 ms 256 KB ok, correct split
3 Correct 2 ms 376 KB ok, correct split
4 Correct 122 ms 13568 KB ok, correct split
5 Correct 111 ms 11780 KB ok, correct split
6 Correct 120 ms 20688 KB ok, correct split
7 Correct 140 ms 17772 KB ok, correct split
8 Correct 148 ms 14884 KB ok, correct split
9 Correct 114 ms 11884 KB ok, correct split
10 Correct 73 ms 11728 KB ok, correct split
11 Correct 70 ms 11624 KB ok, correct split
12 Correct 81 ms 12012 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 109 ms 11832 KB ok, correct split
3 Correct 42 ms 4848 KB ok, correct split
4 Correct 2 ms 376 KB ok, correct split
5 Correct 121 ms 14828 KB ok, correct split
6 Correct 130 ms 14572 KB ok, correct split
7 Correct 138 ms 14416 KB ok, correct split
8 Correct 148 ms 15824 KB ok, correct split
9 Correct 144 ms 14444 KB ok, correct split
10 Correct 31 ms 4108 KB ok, no valid answer
11 Correct 46 ms 6000 KB ok, no valid answer
12 Correct 93 ms 12012 KB ok, no valid answer
13 Correct 114 ms 11884 KB ok, no valid answer
14 Correct 80 ms 12140 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 256 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 256 KB ok, correct split
7 Correct 2 ms 256 KB ok, correct split
8 Correct 2 ms 376 KB ok, correct split
9 Correct 16 ms 760 KB ok, correct split
10 Correct 5 ms 632 KB ok, correct split
11 Correct 2 ms 376 KB ok, correct split
12 Correct 5 ms 632 KB ok, correct split
13 Correct 2 ms 376 KB ok, correct split
14 Correct 2 ms 256 KB ok, correct split
15 Correct 2 ms 256 KB ok, correct split
16 Correct 2 ms 376 KB ok, correct split
17 Correct 2 ms 256 KB ok, correct split
18 Correct 3 ms 380 KB ok, correct split
19 Correct 3 ms 376 KB ok, correct split
20 Correct 3 ms 504 KB ok, correct split
21 Correct 4 ms 632 KB ok, correct split
22 Correct 4 ms 632 KB ok, correct split
23 Correct 4 ms 760 KB ok, correct split
24 Correct 4 ms 680 KB ok, correct split
25 Correct 4 ms 636 KB ok, correct split
26 Correct 4 ms 656 KB ok, correct split
27 Correct 5 ms 780 KB ok, correct split
28 Correct 5 ms 632 KB ok, correct split
29 Correct 2 ms 376 KB ok, correct split
30 Correct 4 ms 632 KB ok, correct split
31 Correct 3 ms 376 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 632 KB ok, correct split
35 Correct 4 ms 632 KB ok, correct split
36 Correct 4 ms 632 KB ok, correct split
37 Correct 5 ms 632 KB ok, correct split
38 Correct 5 ms 804 KB ok, correct split
39 Correct 5 ms 696 KB ok, correct split
40 Correct 5 ms 632 KB ok, correct split
41 Correct 4 ms 500 KB ok, correct split
42 Correct 3 ms 504 KB ok, correct split
43 Correct 5 ms 632 KB ok, correct split
44 Correct 5 ms 760 KB ok, correct split
45 Correct 5 ms 632 KB ok, correct split
46 Correct 4 ms 632 KB ok, correct split
47 Correct 4 ms 632 KB ok, no valid answer
48 Correct 4 ms 632 KB ok, correct split
49 Correct 4 ms 632 KB ok, correct split
50 Correct 2 ms 276 KB ok, no valid answer
51 Correct 2 ms 376 KB ok, no valid answer
52 Correct 4 ms 632 KB ok, no valid answer
53 Correct 5 ms 632 KB ok, no valid answer
54 Correct 4 ms 636 KB ok, no valid answer
55 Correct 4 ms 632 KB ok, no valid answer
56 Correct 5 ms 632 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 256 KB ok, correct split
5 Correct 2 ms 256 KB ok, correct split
6 Correct 2 ms 376 KB ok, correct split
7 Correct 148 ms 20716 KB ok, correct split
8 Correct 116 ms 17900 KB ok, correct split
9 Correct 129 ms 17132 KB ok, correct split
10 Correct 130 ms 20720 KB ok, correct split
11 Correct 143 ms 19300 KB ok, correct split
12 Correct 2 ms 376 KB ok, correct split
13 Correct 2 ms 256 KB ok, correct split
14 Correct 2 ms 376 KB ok, correct split
15 Correct 122 ms 13568 KB ok, correct split
16 Correct 111 ms 11780 KB ok, correct split
17 Correct 120 ms 20688 KB ok, correct split
18 Correct 140 ms 17772 KB ok, correct split
19 Correct 148 ms 14884 KB ok, correct split
20 Correct 114 ms 11884 KB ok, correct split
21 Correct 73 ms 11728 KB ok, correct split
22 Correct 70 ms 11624 KB ok, correct split
23 Correct 81 ms 12012 KB ok, correct split
24 Correct 2 ms 376 KB ok, correct split
25 Correct 109 ms 11832 KB ok, correct split
26 Correct 42 ms 4848 KB ok, correct split
27 Correct 2 ms 376 KB ok, correct split
28 Correct 121 ms 14828 KB ok, correct split
29 Correct 130 ms 14572 KB ok, correct split
30 Correct 138 ms 14416 KB ok, correct split
31 Correct 148 ms 15824 KB ok, correct split
32 Correct 144 ms 14444 KB ok, correct split
33 Correct 31 ms 4108 KB ok, no valid answer
34 Correct 46 ms 6000 KB ok, no valid answer
35 Correct 93 ms 12012 KB ok, no valid answer
36 Correct 114 ms 11884 KB ok, no valid answer
37 Correct 80 ms 12140 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 256 KB ok, correct split
41 Correct 2 ms 376 KB ok, correct split
42 Correct 2 ms 376 KB ok, correct split
43 Correct 2 ms 256 KB ok, correct split
44 Correct 2 ms 256 KB ok, correct split
45 Correct 2 ms 376 KB ok, correct split
46 Correct 16 ms 760 KB ok, correct split
47 Correct 5 ms 632 KB ok, correct split
48 Correct 2 ms 376 KB ok, correct split
49 Correct 5 ms 632 KB ok, correct split
50 Correct 2 ms 376 KB ok, correct split
51 Correct 2 ms 256 KB ok, correct split
52 Correct 2 ms 256 KB ok, correct split
53 Correct 2 ms 376 KB ok, correct split
54 Correct 2 ms 256 KB ok, correct split
55 Correct 3 ms 380 KB ok, correct split
56 Correct 3 ms 376 KB ok, correct split
57 Correct 3 ms 504 KB ok, correct split
58 Correct 4 ms 632 KB ok, correct split
59 Correct 4 ms 632 KB ok, correct split
60 Correct 4 ms 760 KB ok, correct split
61 Correct 4 ms 680 KB ok, correct split
62 Correct 4 ms 636 KB ok, correct split
63 Correct 4 ms 656 KB ok, correct split
64 Correct 5 ms 780 KB ok, correct split
65 Correct 5 ms 632 KB ok, correct split
66 Correct 2 ms 376 KB ok, correct split
67 Correct 4 ms 632 KB ok, correct split
68 Correct 3 ms 376 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 632 KB ok, correct split
72 Correct 4 ms 632 KB ok, correct split
73 Correct 4 ms 632 KB ok, correct split
74 Correct 5 ms 632 KB ok, correct split
75 Correct 5 ms 804 KB ok, correct split
76 Correct 5 ms 696 KB ok, correct split
77 Correct 5 ms 632 KB ok, correct split
78 Correct 4 ms 500 KB ok, correct split
79 Correct 3 ms 504 KB ok, correct split
80 Correct 5 ms 632 KB ok, correct split
81 Correct 5 ms 760 KB ok, correct split
82 Correct 5 ms 632 KB ok, correct split
83 Correct 4 ms 632 KB ok, correct split
84 Correct 4 ms 632 KB ok, no valid answer
85 Correct 4 ms 632 KB ok, correct split
86 Correct 4 ms 632 KB ok, correct split
87 Correct 2 ms 276 KB ok, no valid answer
88 Correct 2 ms 376 KB ok, no valid answer
89 Correct 4 ms 632 KB ok, no valid answer
90 Correct 5 ms 632 KB ok, no valid answer
91 Correct 4 ms 636 KB ok, no valid answer
92 Correct 4 ms 632 KB ok, no valid answer
93 Correct 5 ms 632 KB ok, no valid answer
94 Correct 128 ms 12396 KB ok, correct split
95 Correct 169 ms 15336 KB ok, correct split
96 Correct 156 ms 14184 KB ok, correct split
97 Correct 36 ms 4848 KB ok, correct split
98 Correct 37 ms 5104 KB ok, correct split
99 Correct 53 ms 6120 KB ok, correct split
100 Correct 148 ms 15352 KB ok, correct split
101 Correct 133 ms 14220 KB ok, correct split
102 Correct 136 ms 14312 KB ok, correct split
103 Correct 129 ms 14080 KB ok, correct split
104 Correct 126 ms 15708 KB ok, correct split
105 Correct 61 ms 7404 KB ok, correct split
106 Correct 114 ms 15464 KB ok, correct split
107 Correct 106 ms 11752 KB ok, correct split
108 Correct 109 ms 11808 KB ok, correct split
109 Correct 198 ms 14864 KB ok, correct split
110 Correct 166 ms 15380 KB ok, correct split
111 Correct 161 ms 15468 KB ok, correct split
112 Correct 169 ms 15720 KB ok, correct split
113 Correct 171 ms 15628 KB ok, correct split
114 Correct 15 ms 1908 KB ok, correct split
115 Correct 14 ms 1780 KB ok, correct split
116 Correct 132 ms 15336 KB ok, correct split
117 Correct 138 ms 15208 KB ok, correct split
118 Correct 124 ms 11884 KB ok, correct split
119 Correct 143 ms 11832 KB ok, correct split
120 Correct 148 ms 15340 KB ok, correct split
121 Correct 121 ms 11892 KB ok, no valid answer
122 Correct 111 ms 11912 KB ok, no valid answer
123 Correct 167 ms 15288 KB ok, no valid answer
124 Correct 181 ms 15440 KB ok, no valid answer
125 Correct 115 ms 13088 KB ok, no valid answer
126 Correct 70 ms 11116 KB ok, no valid answer
127 Correct 120 ms 13928 KB ok, no valid answer