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Submission #340185

# Submission time Handle Problem Language Result Execution time Memory
340185 2020-12-27T09:14:05 Z blue Graph (BOI20_graph) C++11
100 / 100
 421 ms 27232 KB 
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

/*
- Values in different connected components are independent of each other.
- When DFS'ing a CC, the starting vertex has a value of x
- For every edge (a, b, c)
    If b is unexplored, value[b] = c - value[a]
    If b is explored, but the equation c = value[a] + value[b] gives no additional information, do nothing
    If b is explored, and the equation gives additional information, use it to compute x.
    Check for contradictions later.
*/

int N, M;
vector<int> edge[100001];
vector<int> color[100001];

vector<double> x_coeff(100001, 0.0);
vector<double> c_coeff(100001, 0.0);

vector<int> cc(100001, 0);
int cc_count = 0;
vector<double> xval(1);

vector<double> findx;

void dfs(int u)
{
    findx.push_back(c_coeff[u] * x_coeff[u] * -1.0);
    for(int i = 0; i < edge[u].size(); i++)
    {
        int v = edge[u][i];
        int c = color[u][i];

        if(!cc[v])
        {
            cc[v] = cc_count;
            x_coeff[v] = -1.0 * x_coeff[u];
            c_coeff[v] = double(c) - c_coeff[u];
            dfs(v);
        }
        else
        {
            if(x_coeff[u] + x_coeff[v] == 0.0) continue;
            xval.back() = (double(c) - (c_coeff[u] + c_coeff[v]))/(x_coeff[u] + x_coeff[v]);
        }
    }
}

int main()
{
    int N, M;
    cin >> N >> M;

    int a, b, c;
    for(int i = 1; i <= M; i++)
    {
        cin >> a >> b >> c;

        edge[a].push_back(b);
        color[a].push_back(c);

        edge[b].push_back(a);
        color[b].push_back(c);
    }

    for(int i = 1; i <= N; i++)
    {
        if(cc[i]) continue;
        cc_count++;
        cc[i] = cc_count;
        x_coeff[i] = 1.0;
        xval.push_back(-9999.9);
        findx.clear();
        dfs(i);
        if(xval.back() == -9999.9)
        {
            sort(findx.begin(), findx.end());
            xval.back() = findx[findx.size()/2];
        }
    }

    double val[N+1];
    for(int i = 1; i <= N; i++) val[i] = x_coeff[i] * xval[cc[i]] + c_coeff[i];
    for(int i = 1; i <= N; i++)
    {
        for(int j = 0; j < edge[i].size(); j++)
        {
            if(val[i] + val[edge[i][j]] != color[i][j])
            {
                cout << "NO\n";
                return 0;
            }
        }
    }
    cout << "YES\n";
    for(int i = 1; i <= N; i++) cout << val[i] << ' ';
    cout << '\n';
}

Compilation message

Graph.cpp: In function 'void dfs(int)':
Graph.cpp:32:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   32 |     for(int i = 0; i < edge[u].size(); i++)
      |                    ~~^~~~~~~~~~~~~~~~
Graph.cpp: In function 'int main()':
Graph.cpp:89:26: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   89 |         for(int j = 0; j < edge[i].size(); j++)
      |                        ~~^~~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7020 KB answer = YES
2 Correct 5 ms 7020 KB answer = YES
3 Correct 6 ms 7040 KB answer = YES
4 Correct 4 ms 7020 KB answer = NO
5 Correct 5 ms 7020 KB answer = YES
6 Correct 5 ms 7040 KB answer = YES
7 Correct 5 ms 7020 KB answer = YES
8 Correct 5 ms 7020 KB answer = YES
9 Correct 5 ms 7020 KB answer = NO
10 Correct 5 ms 7020 KB answer = YES
11 Correct 5 ms 7040 KB answer = YES
12 Correct 5 ms 7020 KB answer = NO
13 Correct 5 ms 7020 KB answer = YES
14 Correct 5 ms 7020 KB answer = YES
15 Correct 5 ms 6892 KB answer = YES
16 Correct 5 ms 7020 KB answer = YES
17 Correct 5 ms 7020 KB answer = YES
18 Correct 5 ms 7020 KB answer = YES
19 Correct 5 ms 7020 KB answer = YES
20 Correct 5 ms 7020 KB answer = YES
21 Correct 5 ms 7040 KB answer = YES
22 Correct 5 ms 7020 KB answer = NO
23 Correct 5 ms 7020 KB answer = NO

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7020 KB answer = YES
2 Correct 5 ms 7020 KB answer = YES
3 Correct 6 ms 7040 KB answer = YES
4 Correct 4 ms 7020 KB answer = NO
5 Correct 5 ms 7020 KB answer = YES
6 Correct 5 ms 7040 KB answer = YES
7 Correct 5 ms 7020 KB answer = YES
8 Correct 5 ms 7020 KB answer = YES
9 Correct 5 ms 7020 KB answer = NO
10 Correct 5 ms 7020 KB answer = YES
11 Correct 5 ms 7040 KB answer = YES
12 Correct 5 ms 7020 KB answer = NO
13 Correct 5 ms 7020 KB answer = YES
14 Correct 5 ms 7020 KB answer = YES
15 Correct 5 ms 6892 KB answer = YES
16 Correct 5 ms 7020 KB answer = YES
17 Correct 5 ms 7020 KB answer = YES
18 Correct 5 ms 7020 KB answer = YES
19 Correct 5 ms 7020 KB answer = YES
20 Correct 5 ms 7020 KB answer = YES
21 Correct 5 ms 7040 KB answer = YES
22 Correct 5 ms 7020 KB answer = NO
23 Correct 5 ms 7020 KB answer = NO
24 Correct 5 ms 7020 KB answer = YES
25 Correct 5 ms 7020 KB answer = YES
26 Correct 5 ms 7020 KB answer = YES
27 Correct 5 ms 7020 KB answer = YES
28 Correct 5 ms 7020 KB answer = YES
29 Correct 5 ms 7020 KB answer = YES
30 Correct 5 ms 7020 KB answer = NO
31 Correct 5 ms 7020 KB answer = YES
32 Correct 5 ms 7020 KB answer = YES
33 Correct 5 ms 7020 KB answer = YES
34 Correct 5 ms 7020 KB answer = YES
35 Correct 5 ms 7020 KB answer = YES
36 Correct 5 ms 7040 KB answer = YES

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7020 KB answer = YES
2 Correct 5 ms 7020 KB answer = YES
3 Correct 6 ms 7040 KB answer = YES
4 Correct 4 ms 7020 KB answer = NO
5 Correct 5 ms 7020 KB answer = YES
6 Correct 5 ms 7040 KB answer = YES
7 Correct 5 ms 7020 KB answer = YES
8 Correct 5 ms 7020 KB answer = YES
9 Correct 5 ms 7020 KB answer = NO
10 Correct 5 ms 7020 KB answer = YES
11 Correct 5 ms 7040 KB answer = YES
12 Correct 5 ms 7020 KB answer = NO
13 Correct 5 ms 7020 KB answer = YES
14 Correct 5 ms 7020 KB answer = YES
15 Correct 5 ms 6892 KB answer = YES
16 Correct 5 ms 7020 KB answer = YES
17 Correct 5 ms 7020 KB answer = YES
18 Correct 5 ms 7020 KB answer = YES
19 Correct 5 ms 7020 KB answer = YES
20 Correct 5 ms 7020 KB answer = YES
21 Correct 5 ms 7040 KB answer = YES
22 Correct 5 ms 7020 KB answer = NO
23 Correct 5 ms 7020 KB answer = NO
24 Correct 5 ms 7020 KB answer = YES
25 Correct 5 ms 7020 KB answer = YES
26 Correct 5 ms 7020 KB answer = YES
27 Correct 5 ms 7020 KB answer = YES
28 Correct 5 ms 7020 KB answer = YES
29 Correct 5 ms 7020 KB answer = YES
30 Correct 5 ms 7020 KB answer = NO
31 Correct 5 ms 7020 KB answer = YES
32 Correct 5 ms 7020 KB answer = YES
33 Correct 5 ms 7020 KB answer = YES
34 Correct 5 ms 7020 KB answer = YES
35 Correct 5 ms 7020 KB answer = YES
36 Correct 5 ms 7040 KB answer = YES
37 Correct 5 ms 7020 KB answer = YES
38 Correct 5 ms 7032 KB answer = YES
39 Correct 5 ms 7020 KB answer = YES
40 Correct 6 ms 7020 KB answer = YES
41 Correct 6 ms 7032 KB answer = NO
42 Correct 6 ms 7020 KB answer = YES
43 Correct 6 ms 7020 KB answer = YES
44 Correct 6 ms 7020 KB answer = YES
45 Correct 6 ms 7020 KB answer = YES
46 Correct 5 ms 7148 KB answer = YES
47 Correct 7 ms 7148 KB answer = YES
48 Correct 6 ms 7148 KB answer = YES

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7020 KB answer = YES
2 Correct 5 ms 7020 KB answer = YES
3 Correct 6 ms 7040 KB answer = YES
4 Correct 4 ms 7020 KB answer = NO
5 Correct 5 ms 7020 KB answer = YES
6 Correct 5 ms 7040 KB answer = YES
7 Correct 5 ms 7020 KB answer = YES
8 Correct 5 ms 7020 KB answer = YES
9 Correct 5 ms 7020 KB answer = NO
10 Correct 5 ms 7020 KB answer = YES
11 Correct 5 ms 7040 KB answer = YES
12 Correct 5 ms 7020 KB answer = NO
13 Correct 5 ms 7020 KB answer = YES
14 Correct 5 ms 7020 KB answer = YES
15 Correct 5 ms 6892 KB answer = YES
16 Correct 5 ms 7020 KB answer = YES
17 Correct 5 ms 7020 KB answer = YES
18 Correct 5 ms 7020 KB answer = YES
19 Correct 5 ms 7020 KB answer = YES
20 Correct 5 ms 7020 KB answer = YES
21 Correct 5 ms 7040 KB answer = YES
22 Correct 5 ms 7020 KB answer = NO
23 Correct 5 ms 7020 KB answer = NO
24 Correct 5 ms 7020 KB answer = YES
25 Correct 5 ms 7020 KB answer = YES
26 Correct 5 ms 7020 KB answer = YES
27 Correct 5 ms 7020 KB answer = YES
28 Correct 5 ms 7020 KB answer = YES
29 Correct 5 ms 7020 KB answer = YES
30 Correct 5 ms 7020 KB answer = NO
31 Correct 5 ms 7020 KB answer = YES
32 Correct 5 ms 7020 KB answer = YES
33 Correct 5 ms 7020 KB answer = YES
34 Correct 5 ms 7020 KB answer = YES
35 Correct 5 ms 7020 KB answer = YES
36 Correct 5 ms 7040 KB answer = YES
37 Correct 5 ms 7020 KB answer = YES
38 Correct 5 ms 7032 KB answer = YES
39 Correct 5 ms 7020 KB answer = YES
40 Correct 6 ms 7020 KB answer = YES
41 Correct 6 ms 7032 KB answer = NO
42 Correct 6 ms 7020 KB answer = YES
43 Correct 6 ms 7020 KB answer = YES
44 Correct 6 ms 7020 KB answer = YES
45 Correct 6 ms 7020 KB answer = YES
46 Correct 5 ms 7148 KB answer = YES
47 Correct 7 ms 7148 KB answer = YES
48 Correct 6 ms 7148 KB answer = YES
49 Correct 20 ms 8044 KB answer = YES
50 Correct 22 ms 8428 KB answer = YES
51 Correct 20 ms 8428 KB answer = YES
52 Correct 18 ms 8428 KB answer = NO
53 Correct 7 ms 7020 KB answer = YES
54 Correct 8 ms 7276 KB answer = YES
55 Correct 12 ms 7532 KB answer = YES
56 Correct 20 ms 8044 KB answer = YES
57 Correct 19 ms 7916 KB answer = YES
58 Correct 21 ms 7916 KB answer = YES
59 Correct 18 ms 7916 KB answer = YES
60 Correct 20 ms 7916 KB answer = YES
61 Correct 13 ms 7532 KB answer = YES
62 Correct 180 ms 14720 KB answer = NO
63 Correct 192 ms 14828 KB answer = YES
64 Correct 181 ms 14700 KB answer = NO
65 Correct 193 ms 14828 KB answer = YES
66 Correct 8 ms 7148 KB answer = YES

Subtask #5
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 7020 KB answer = YES
2 Correct 5 ms 7020 KB answer = YES
3 Correct 6 ms 7040 KB answer = YES
4 Correct 4 ms 7020 KB answer = NO
5 Correct 5 ms 7020 KB answer = YES
6 Correct 5 ms 7040 KB answer = YES
7 Correct 5 ms 7020 KB answer = YES
8 Correct 5 ms 7020 KB answer = YES
9 Correct 5 ms 7020 KB answer = NO
10 Correct 5 ms 7020 KB answer = YES
11 Correct 5 ms 7040 KB answer = YES
12 Correct 5 ms 7020 KB answer = NO
13 Correct 5 ms 7020 KB answer = YES
14 Correct 5 ms 7020 KB answer = YES
15 Correct 5 ms 6892 KB answer = YES
16 Correct 5 ms 7020 KB answer = YES
17 Correct 5 ms 7020 KB answer = YES
18 Correct 5 ms 7020 KB answer = YES
19 Correct 5 ms 7020 KB answer = YES
20 Correct 5 ms 7020 KB answer = YES
21 Correct 5 ms 7040 KB answer = YES
22 Correct 5 ms 7020 KB answer = NO
23 Correct 5 ms 7020 KB answer = NO
24 Correct 5 ms 7020 KB answer = YES
25 Correct 5 ms 7020 KB answer = YES
26 Correct 5 ms 7020 KB answer = YES
27 Correct 5 ms 7020 KB answer = YES
28 Correct 5 ms 7020 KB answer = YES
29 Correct 5 ms 7020 KB answer = YES
30 Correct 5 ms 7020 KB answer = NO
31 Correct 5 ms 7020 KB answer = YES
32 Correct 5 ms 7020 KB answer = YES
33 Correct 5 ms 7020 KB answer = YES
34 Correct 5 ms 7020 KB answer = YES
35 Correct 5 ms 7020 KB answer = YES
36 Correct 5 ms 7040 KB answer = YES
37 Correct 5 ms 7020 KB answer = YES
38 Correct 5 ms 7032 KB answer = YES
39 Correct 5 ms 7020 KB answer = YES
40 Correct 6 ms 7020 KB answer = YES
41 Correct 6 ms 7032 KB answer = NO
42 Correct 6 ms 7020 KB answer = YES
43 Correct 6 ms 7020 KB answer = YES
44 Correct 6 ms 7020 KB answer = YES
45 Correct 6 ms 7020 KB answer = YES
46 Correct 5 ms 7148 KB answer = YES
47 Correct 7 ms 7148 KB answer = YES
48 Correct 6 ms 7148 KB answer = YES
49 Correct 20 ms 8044 KB answer = YES
50 Correct 22 ms 8428 KB answer = YES
51 Correct 20 ms 8428 KB answer = YES
52 Correct 18 ms 8428 KB answer = NO
53 Correct 7 ms 7020 KB answer = YES
54 Correct 8 ms 7276 KB answer = YES
55 Correct 12 ms 7532 KB answer = YES
56 Correct 20 ms 8044 KB answer = YES
57 Correct 19 ms 7916 KB answer = YES
58 Correct 21 ms 7916 KB answer = YES
59 Correct 18 ms 7916 KB answer = YES
60 Correct 20 ms 7916 KB answer = YES
61 Correct 13 ms 7532 KB answer = YES
62 Correct 180 ms 14720 KB answer = NO
63 Correct 192 ms 14828 KB answer = YES
64 Correct 181 ms 14700 KB answer = NO
65 Correct 193 ms 14828 KB answer = YES
66 Correct 8 ms 7148 KB answer = YES
67 Correct 158 ms 23648 KB answer = YES
68 Correct 152 ms 23520 KB answer = YES
69 Correct 148 ms 23648 KB answer = YES
70 Correct 242 ms 27232 KB answer = YES
71 Correct 157 ms 23776 KB answer = YES
72 Correct 223 ms 16736 KB answer = YES
73 Correct 221 ms 16736 KB answer = YES
74 Correct 127 ms 16740 KB answer = YES
75 Correct 92 ms 16612 KB answer = NO
76 Correct 24 ms 8300 KB answer = YES
77 Correct 45 ms 9448 KB answer = YES
78 Correct 97 ms 11236 KB answer = YES
79 Correct 185 ms 15460 KB answer = YES
80 Correct 128 ms 16740 KB answer = YES
81 Correct 144 ms 19552 KB answer = NO
82 Correct 239 ms 23136 KB answer = YES
83 Correct 229 ms 23776 KB answer = YES
84 Correct 231 ms 23776 KB answer = YES
85 Correct 158 ms 23648 KB answer = YES
86 Correct 153 ms 23648 KB answer = YES
87 Correct 188 ms 17768 KB answer = NO
88 Correct 265 ms 18916 KB answer = YES
89 Correct 191 ms 15976 KB answer = YES
90 Correct 195 ms 15976 KB answer = YES
91 Correct 211 ms 16104 KB answer = YES
92 Correct 99 ms 12008 KB answer = YES
93 Correct 101 ms 11880 KB answer = YES
94 Correct 186 ms 23392 KB answer = NO
95 Correct 159 ms 15720 KB answer = NO
96 Correct 421 ms 24032 KB answer = YES
97 Correct 111 ms 23392 KB answer = NO