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Submission #1030644

# Submission time Handle Problem Language Result Execution time Memory
1030644 2024-07-22T08:05:18 Z thinknoexit Graph (BOI20_graph) C++17
100 / 100
 98 ms 19912 KB 
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 100100;
struct A {
    int v, w;
};
vector<A> adj[N];
double ans[N];
bool ch[N], vis[N];
int col[N], bp = 0, M[N], C[N];
mt19937 rnd(time(NULL));
vector<pair<int, int>> cycle;
void dfs(int v, vector<int>& node) {
    node.push_back(v);
    vis[v] = 1;
    for (auto& x : adj[v]) {
        if (!vis[x.v]) dfs(x.v, node);
    }
}
void dfs_ans(int v) {
    for (auto& x : adj[v]) {
        if (!ch[x.v]) {
            ch[x.v] = 1;
            ans[x.v] = x.w - ans[v];
            dfs_ans(x.v);
        }
    }
}
bool bipartite(int v, int c) {
    if (col[v]) {
        if (col[v] != c) return bp = v, false;
        else return true;
    }
    col[v] = c;
    for (auto& x : adj[v]) {
        if (!bipartite(x.v, 3 - c)) {
            if (bp != 0) cycle.push_back({ v, x.w });
            if (v == bp) bp = 0;
            return false;
        }
    }
    return true;
}
void dfs_eq(int v) {
    ch[v] = 1;
    for (auto& x : adj[v]) {
        if (!ch[x.v]) {
            M[x.v] = -M[v];
            C[x.v] = x.w - C[v];
            dfs_eq(x.v);
        }
        else {
            if (M[x.v] != -M[v] || C[x.v] != x.w - C[v]) {
                cout << "NO";
                exit(0);
            }
        }
    }
}
int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int n, m;
    cin >> n >> m;
    for (int i = 1;i <= m;i++) {
        int u, v, w;
        cin >> u >> v >> w;
        adj[u].push_back({ v, w });
        adj[v].push_back({ u, w });
    }
    for (int i = 1;i <= n;i++) {
        if (vis[i]) continue;
        vector<int> node;
        dfs(i, node);
        bool bipar = bipartite(i, 1);
        if (!bipar) {
            vector<pair<int, int>> c = cycle;
            cycle.clear();
            int root = c.back().first;
            int val = 0;
            for (int i = 0;i < (int)c.size();i++) {
                if (i & 1) val -= c[i].second;
                else val += c[i].second;
            }
            // value at node (root) = val / 2
            ch[root] = 1;
            ans[root] = (double)val / 2;
            dfs_ans(root);
            continue;
        }
        // y = mx + c   
        M[i] = 1, C[i] = 0;
        dfs_eq(i);
        vector<int> v;
        for (auto& x : node) {
            v.push_back(-C[x] / M[x]);
        }
        sort(v.begin(), v.end());
        int crit = v[(node.size() + 1) / 2 - 1];
        for (auto& x : node) {
            ans[x] = crit * M[x] + C[x];
        }
    }
    for (int i = 1;i <= n;i++) {
        for (auto& x : adj[i]) {
            if (ans[i] + ans[x.v] != x.w) {
                cout << "NO";
                return 0;
            }
        }
    }
    cout << "YES\n";
    for (int i = 1;i <= n;i++) {
        cout << ans[i] << ' ';
    }
    return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 2 ms 2724 KB answer = YES
6 Correct 2 ms 2652 KB answer = YES
7 Correct 2 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2648 KB answer = NO
10 Correct 1 ms 2652 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2648 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 2 ms 2724 KB answer = YES
6 Correct 2 ms 2652 KB answer = YES
7 Correct 2 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2648 KB answer = NO
10 Correct 1 ms 2652 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2648 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO
24 Correct 1 ms 2648 KB answer = YES
25 Correct 1 ms 2652 KB answer = YES
26 Correct 1 ms 2652 KB answer = YES
27 Correct 1 ms 2648 KB answer = YES
28 Correct 2 ms 2652 KB answer = YES
29 Correct 1 ms 2652 KB answer = YES
30 Correct 1 ms 2640 KB answer = NO
31 Correct 1 ms 2652 KB answer = YES
32 Correct 1 ms 2652 KB answer = YES
33 Correct 1 ms 2652 KB answer = YES
34 Correct 1 ms 2652 KB answer = YES
35 Correct 1 ms 2652 KB answer = YES
36 Correct 1 ms 2652 KB answer = YES

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 2 ms 2724 KB answer = YES
6 Correct 2 ms 2652 KB answer = YES
7 Correct 2 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2648 KB answer = NO
10 Correct 1 ms 2652 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2648 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO
24 Correct 1 ms 2648 KB answer = YES
25 Correct 1 ms 2652 KB answer = YES
26 Correct 1 ms 2652 KB answer = YES
27 Correct 1 ms 2648 KB answer = YES
28 Correct 2 ms 2652 KB answer = YES
29 Correct 1 ms 2652 KB answer = YES
30 Correct 1 ms 2640 KB answer = NO
31 Correct 1 ms 2652 KB answer = YES
32 Correct 1 ms 2652 KB answer = YES
33 Correct 1 ms 2652 KB answer = YES
34 Correct 1 ms 2652 KB answer = YES
35 Correct 1 ms 2652 KB answer = YES
36 Correct 1 ms 2652 KB answer = YES
37 Correct 1 ms 2652 KB answer = YES
38 Correct 1 ms 2788 KB answer = YES
39 Correct 3 ms 2652 KB answer = YES
40 Correct 2 ms 2652 KB answer = YES
41 Correct 2 ms 2728 KB answer = NO
42 Correct 2 ms 2908 KB answer = YES
43 Correct 2 ms 2908 KB answer = YES
44 Correct 1 ms 2652 KB answer = YES
45 Correct 2 ms 2908 KB answer = YES
46 Correct 1 ms 2652 KB answer = YES
47 Correct 2 ms 2908 KB answer = YES
48 Correct 3 ms 2908 KB answer = YES

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 2 ms 2724 KB answer = YES
6 Correct 2 ms 2652 KB answer = YES
7 Correct 2 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2648 KB answer = NO
10 Correct 1 ms 2652 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2648 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO
24 Correct 1 ms 2648 KB answer = YES
25 Correct 1 ms 2652 KB answer = YES
26 Correct 1 ms 2652 KB answer = YES
27 Correct 1 ms 2648 KB answer = YES
28 Correct 2 ms 2652 KB answer = YES
29 Correct 1 ms 2652 KB answer = YES
30 Correct 1 ms 2640 KB answer = NO
31 Correct 1 ms 2652 KB answer = YES
32 Correct 1 ms 2652 KB answer = YES
33 Correct 1 ms 2652 KB answer = YES
34 Correct 1 ms 2652 KB answer = YES
35 Correct 1 ms 2652 KB answer = YES
36 Correct 1 ms 2652 KB answer = YES
37 Correct 1 ms 2652 KB answer = YES
38 Correct 1 ms 2788 KB answer = YES
39 Correct 3 ms 2652 KB answer = YES
40 Correct 2 ms 2652 KB answer = YES
41 Correct 2 ms 2728 KB answer = NO
42 Correct 2 ms 2908 KB answer = YES
43 Correct 2 ms 2908 KB answer = YES
44 Correct 1 ms 2652 KB answer = YES
45 Correct 2 ms 2908 KB answer = YES
46 Correct 1 ms 2652 KB answer = YES
47 Correct 2 ms 2908 KB answer = YES
48 Correct 3 ms 2908 KB answer = YES
49 Correct 7 ms 3416 KB answer = YES
50 Correct 6 ms 3676 KB answer = YES
51 Correct 10 ms 3676 KB answer = YES
52 Correct 3 ms 3588 KB answer = NO
53 Correct 2 ms 2908 KB answer = YES
54 Correct 2 ms 2908 KB answer = YES
55 Correct 5 ms 3224 KB answer = YES
56 Correct 6 ms 3420 KB answer = YES
57 Correct 7 ms 3420 KB answer = YES
58 Correct 6 ms 3420 KB answer = YES
59 Correct 6 ms 3164 KB answer = YES
60 Correct 6 ms 3552 KB answer = YES
61 Correct 4 ms 2908 KB answer = YES
62 Correct 44 ms 8020 KB answer = NO
63 Correct 41 ms 8020 KB answer = YES
64 Correct 34 ms 8016 KB answer = NO
65 Correct 38 ms 8268 KB answer = YES
66 Correct 2 ms 2904 KB answer = YES

Subtask #5
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 2 ms 2724 KB answer = YES
6 Correct 2 ms 2652 KB answer = YES
7 Correct 2 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2648 KB answer = NO
10 Correct 1 ms 2652 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2648 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO
24 Correct 1 ms 2648 KB answer = YES
25 Correct 1 ms 2652 KB answer = YES
26 Correct 1 ms 2652 KB answer = YES
27 Correct 1 ms 2648 KB answer = YES
28 Correct 2 ms 2652 KB answer = YES
29 Correct 1 ms 2652 KB answer = YES
30 Correct 1 ms 2640 KB answer = NO
31 Correct 1 ms 2652 KB answer = YES
32 Correct 1 ms 2652 KB answer = YES
33 Correct 1 ms 2652 KB answer = YES
34 Correct 1 ms 2652 KB answer = YES
35 Correct 1 ms 2652 KB answer = YES
36 Correct 1 ms 2652 KB answer = YES
37 Correct 1 ms 2652 KB answer = YES
38 Correct 1 ms 2788 KB answer = YES
39 Correct 3 ms 2652 KB answer = YES
40 Correct 2 ms 2652 KB answer = YES
41 Correct 2 ms 2728 KB answer = NO
42 Correct 2 ms 2908 KB answer = YES
43 Correct 2 ms 2908 KB answer = YES
44 Correct 1 ms 2652 KB answer = YES
45 Correct 2 ms 2908 KB answer = YES
46 Correct 1 ms 2652 KB answer = YES
47 Correct 2 ms 2908 KB answer = YES
48 Correct 3 ms 2908 KB answer = YES
49 Correct 7 ms 3416 KB answer = YES
50 Correct 6 ms 3676 KB answer = YES
51 Correct 10 ms 3676 KB answer = YES
52 Correct 3 ms 3588 KB answer = NO
53 Correct 2 ms 2908 KB answer = YES
54 Correct 2 ms 2908 KB answer = YES
55 Correct 5 ms 3224 KB answer = YES
56 Correct 6 ms 3420 KB answer = YES
57 Correct 7 ms 3420 KB answer = YES
58 Correct 6 ms 3420 KB answer = YES
59 Correct 6 ms 3164 KB answer = YES
60 Correct 6 ms 3552 KB answer = YES
61 Correct 4 ms 2908 KB answer = YES
62 Correct 44 ms 8020 KB answer = NO
63 Correct 41 ms 8020 KB answer = YES
64 Correct 34 ms 8016 KB answer = NO
65 Correct 38 ms 8268 KB answer = YES
66 Correct 2 ms 2904 KB answer = YES
67 Correct 52 ms 15192 KB answer = YES
68 Correct 50 ms 16460 KB answer = YES
69 Correct 49 ms 16976 KB answer = YES
70 Correct 98 ms 19912 KB answer = YES
71 Correct 54 ms 16968 KB answer = YES
72 Correct 57 ms 10824 KB answer = YES
73 Correct 63 ms 9672 KB answer = YES
74 Correct 37 ms 10196 KB answer = YES
75 Correct 20 ms 10200 KB answer = NO
76 Correct 8 ms 3676 KB answer = YES
77 Correct 15 ms 4856 KB answer = YES
78 Correct 25 ms 6160 KB answer = YES
79 Correct 49 ms 9556 KB answer = YES
80 Correct 43 ms 10844 KB answer = YES
81 Correct 32 ms 12884 KB answer = NO
82 Correct 67 ms 15696 KB answer = YES
83 Correct 74 ms 16868 KB answer = YES
84 Correct 75 ms 16464 KB answer = YES
85 Correct 90 ms 16472 KB answer = YES
86 Correct 82 ms 16972 KB answer = YES
87 Correct 54 ms 11596 KB answer = NO
88 Correct 96 ms 12896 KB answer = YES
89 Correct 65 ms 8808 KB answer = YES
90 Correct 57 ms 9000 KB answer = YES
91 Correct 58 ms 9044 KB answer = YES
92 Correct 27 ms 6368 KB answer = YES
93 Correct 27 ms 6364 KB answer = YES
94 Correct 42 ms 15308 KB answer = NO
95 Correct 36 ms 8540 KB answer = NO
96 Correct 92 ms 18068 KB answer = YES
97 Correct 28 ms 15308 KB answer = NO