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Submission #685515

# Submission time Handle Problem Language Result Execution time Memory
685515 2023-01-24T13:00:23 Z stanislavpolyn Graph (BOI20_graph) C++17
100 / 100
 224 ms 22512 KB 
#include <bits/stdc++.h>

#define fr(i, a, b) for (int i = (a); i <= (b); ++i)
#define rf(i, a, b) for (int i = (a); i >= (b); --i)
#define fe(x, y) for (auto& x : y)

#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define mt make_tuple

#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
#define pw(x) (1LL << (x))

using namespace std;

mt19937_64 rng(228);

#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template <typename T>
using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define fbo find_by_order
#define ook order_of_key

template <typename T>
bool umn(T& a, T b) {
    return a > b ? a = b, 1 : 0;
}
template <typename T>
bool umx(T& a, T b) {
    return a < b ? a = b, 1 : 0;
}

using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <typename T>
using ve = vector<T>;

const int N = 1e5 + 5;
const ld EPS = 1e-10;

bool eq(ld a, ld b) {
    return abs(a - b) <= EPS;
}

int n, m;
ve<pii> g[N];
bool vis[N];

int k[N], b[N];
ve<int> st;
ld X = -1e18;
bool found = 0;
ld ans[N];

void dfs(int v, int p) {
    vis[v] = 1;
    st.pb(v);
//    cout << v << " " << k[v] << " " << b[v] << "\n";

    fe (to, g[v]) {
        if (!vis[to.fi]) {
            b[to.fi] = -b[v] + to.se;
            k[to.fi] = -k[v];

            dfs(to.fi, v);
        } else {
            int needB = -b[v] + to.se;
            int needK = -k[v];

            if (mp(b[to.fi], k[to.fi]) == mp(needB, needK)) {
                continue;
            }
            // x * needK + needB = x * k[to.fi] + b[to.fi]
            // x * (needK - k[to.fi]) = b[to.fi] - needB
            ld nx = ld(b[to.fi] - needB) / (needK - k[to.fi]);

            if (found && !eq(nx, X)) {
                cout << "NO\n";
                exit(0);
            }
            X = nx;
            found = 1;
        }
    }
}

int main() {
#ifdef LOCAL
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#else
    ios::sync_with_stdio(0);
    cin.tie(0);
#endif

    cin >> n >> m;

    fr (i, 1, m) {
        int a, b, c;
        cin >> a >> b >> c;

        g[a].pb({b, c});
        g[b].pb({a, c});
    }

    fr (i, 1, n) {
        if (!vis[i]) {
            st.clear();
            k[i] = 1;
            X = -1e18;
            found = 0;
            dfs(i, 0);

            if (found) {
                fe (cur, st) {
                    ans[cur] = k[cur] * X + b[cur];
                }
            } else {
                auto eval = [&](ld x) {
                    ld sum = 0;
                    fe (cur, st) {
                        sum += abs(k[cur] * x + b[cur]);
                    }
                    return sum;
                };

                fe (cur, st) {
                    assert(k[cur] == 1 || k[cur] == -1);
//                    assert(abs(b[cur]) <= 2);
                }

                ld l = -1e9;
                ld r = 1e9;
                fr (rep, 1, 200) {
                    ld p1 = l + (r - l) / 3;
                    ld p2 = r - (r - l) / 3;

                    if (eval(p1) < eval(p2)) {
                        r = p2;
                    } else {
                        l = p1;
                    }
                }

                fe (cur, st) {
                    ans[cur] = k[cur] * l + b[cur];
                }
            }
        }
    }

    cout << "YES\n";
    cout << fixed << setprecision(14);
    fr (i, 1, n) {
        cout << ans[i] << " ";
    }
    cout << "\n";

    return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB answer = YES
2 Correct 2 ms 2644 KB answer = YES
3 Correct 1 ms 2644 KB answer = YES
4 Correct 2 ms 2644 KB answer = NO
5 Correct 1 ms 2644 KB answer = YES
6 Correct 2 ms 2644 KB answer = YES
7 Correct 1 ms 2644 KB answer = YES
8 Correct 2 ms 2644 KB answer = YES
9 Correct 1 ms 2644 KB answer = NO
10 Correct 1 ms 2644 KB answer = YES
11 Correct 1 ms 2644 KB answer = YES
12 Correct 1 ms 2644 KB answer = NO
13 Correct 2 ms 2644 KB answer = YES
14 Correct 1 ms 2644 KB answer = YES
15 Correct 2 ms 2644 KB answer = YES
16 Correct 1 ms 2644 KB answer = YES
17 Correct 1 ms 2644 KB answer = YES
18 Correct 2 ms 2644 KB answer = YES
19 Correct 1 ms 2644 KB answer = YES
20 Correct 2 ms 2644 KB answer = YES
21 Correct 2 ms 2644 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 2 ms 2644 KB answer = NO

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB answer = YES
2 Correct 2 ms 2644 KB answer = YES
3 Correct 1 ms 2644 KB answer = YES
4 Correct 2 ms 2644 KB answer = NO
5 Correct 1 ms 2644 KB answer = YES
6 Correct 2 ms 2644 KB answer = YES
7 Correct 1 ms 2644 KB answer = YES
8 Correct 2 ms 2644 KB answer = YES
9 Correct 1 ms 2644 KB answer = NO
10 Correct 1 ms 2644 KB answer = YES
11 Correct 1 ms 2644 KB answer = YES
12 Correct 1 ms 2644 KB answer = NO
13 Correct 2 ms 2644 KB answer = YES
14 Correct 1 ms 2644 KB answer = YES
15 Correct 2 ms 2644 KB answer = YES
16 Correct 1 ms 2644 KB answer = YES
17 Correct 1 ms 2644 KB answer = YES
18 Correct 2 ms 2644 KB answer = YES
19 Correct 1 ms 2644 KB answer = YES
20 Correct 2 ms 2644 KB answer = YES
21 Correct 2 ms 2644 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 2 ms 2644 KB answer = NO
24 Correct 2 ms 2644 KB answer = YES
25 Correct 2 ms 2644 KB answer = YES
26 Correct 1 ms 2644 KB answer = YES
27 Correct 2 ms 2644 KB answer = YES
28 Correct 1 ms 2644 KB answer = YES
29 Correct 2 ms 2628 KB answer = YES
30 Correct 2 ms 2644 KB answer = NO
31 Correct 2 ms 2644 KB answer = YES
32 Correct 2 ms 2644 KB answer = YES
33 Correct 2 ms 2644 KB answer = YES
34 Correct 3 ms 2644 KB answer = YES
35 Correct 3 ms 2644 KB answer = YES
36 Correct 3 ms 2644 KB answer = YES

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB answer = YES
2 Correct 2 ms 2644 KB answer = YES
3 Correct 1 ms 2644 KB answer = YES
4 Correct 2 ms 2644 KB answer = NO
5 Correct 1 ms 2644 KB answer = YES
6 Correct 2 ms 2644 KB answer = YES
7 Correct 1 ms 2644 KB answer = YES
8 Correct 2 ms 2644 KB answer = YES
9 Correct 1 ms 2644 KB answer = NO
10 Correct 1 ms 2644 KB answer = YES
11 Correct 1 ms 2644 KB answer = YES
12 Correct 1 ms 2644 KB answer = NO
13 Correct 2 ms 2644 KB answer = YES
14 Correct 1 ms 2644 KB answer = YES
15 Correct 2 ms 2644 KB answer = YES
16 Correct 1 ms 2644 KB answer = YES
17 Correct 1 ms 2644 KB answer = YES
18 Correct 2 ms 2644 KB answer = YES
19 Correct 1 ms 2644 KB answer = YES
20 Correct 2 ms 2644 KB answer = YES
21 Correct 2 ms 2644 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 2 ms 2644 KB answer = NO
24 Correct 2 ms 2644 KB answer = YES
25 Correct 2 ms 2644 KB answer = YES
26 Correct 1 ms 2644 KB answer = YES
27 Correct 2 ms 2644 KB answer = YES
28 Correct 1 ms 2644 KB answer = YES
29 Correct 2 ms 2628 KB answer = YES
30 Correct 2 ms 2644 KB answer = NO
31 Correct 2 ms 2644 KB answer = YES
32 Correct 2 ms 2644 KB answer = YES
33 Correct 2 ms 2644 KB answer = YES
34 Correct 3 ms 2644 KB answer = YES
35 Correct 3 ms 2644 KB answer = YES
36 Correct 3 ms 2644 KB answer = YES
37 Correct 3 ms 2644 KB answer = YES
38 Correct 3 ms 2644 KB answer = YES
39 Correct 3 ms 2644 KB answer = YES
40 Correct 3 ms 2772 KB answer = YES
41 Correct 2 ms 2712 KB answer = NO
42 Correct 4 ms 2752 KB answer = YES
43 Correct 4 ms 2756 KB answer = YES
44 Correct 4 ms 2644 KB answer = YES
45 Correct 4 ms 2772 KB answer = YES
46 Correct 3 ms 2644 KB answer = YES
47 Correct 3 ms 2772 KB answer = YES
48 Correct 3 ms 2772 KB answer = YES

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB answer = YES
2 Correct 2 ms 2644 KB answer = YES
3 Correct 1 ms 2644 KB answer = YES
4 Correct 2 ms 2644 KB answer = NO
5 Correct 1 ms 2644 KB answer = YES
6 Correct 2 ms 2644 KB answer = YES
7 Correct 1 ms 2644 KB answer = YES
8 Correct 2 ms 2644 KB answer = YES
9 Correct 1 ms 2644 KB answer = NO
10 Correct 1 ms 2644 KB answer = YES
11 Correct 1 ms 2644 KB answer = YES
12 Correct 1 ms 2644 KB answer = NO
13 Correct 2 ms 2644 KB answer = YES
14 Correct 1 ms 2644 KB answer = YES
15 Correct 2 ms 2644 KB answer = YES
16 Correct 1 ms 2644 KB answer = YES
17 Correct 1 ms 2644 KB answer = YES
18 Correct 2 ms 2644 KB answer = YES
19 Correct 1 ms 2644 KB answer = YES
20 Correct 2 ms 2644 KB answer = YES
21 Correct 2 ms 2644 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 2 ms 2644 KB answer = NO
24 Correct 2 ms 2644 KB answer = YES
25 Correct 2 ms 2644 KB answer = YES
26 Correct 1 ms 2644 KB answer = YES
27 Correct 2 ms 2644 KB answer = YES
28 Correct 1 ms 2644 KB answer = YES
29 Correct 2 ms 2628 KB answer = YES
30 Correct 2 ms 2644 KB answer = NO
31 Correct 2 ms 2644 KB answer = YES
32 Correct 2 ms 2644 KB answer = YES
33 Correct 2 ms 2644 KB answer = YES
34 Correct 3 ms 2644 KB answer = YES
35 Correct 3 ms 2644 KB answer = YES
36 Correct 3 ms 2644 KB answer = YES
37 Correct 3 ms 2644 KB answer = YES
38 Correct 3 ms 2644 KB answer = YES
39 Correct 3 ms 2644 KB answer = YES
40 Correct 3 ms 2772 KB answer = YES
41 Correct 2 ms 2712 KB answer = NO
42 Correct 4 ms 2752 KB answer = YES
43 Correct 4 ms 2756 KB answer = YES
44 Correct 4 ms 2644 KB answer = YES
45 Correct 4 ms 2772 KB answer = YES
46 Correct 3 ms 2644 KB answer = YES
47 Correct 3 ms 2772 KB answer = YES
48 Correct 3 ms 2772 KB answer = YES
49 Correct 17 ms 3620 KB answer = YES
50 Correct 11 ms 3892 KB answer = YES
51 Correct 18 ms 3912 KB answer = YES
52 Correct 5 ms 3668 KB answer = NO
53 Correct 4 ms 2788 KB answer = YES
54 Correct 5 ms 2832 KB answer = YES
55 Correct 12 ms 3164 KB answer = YES
56 Correct 16 ms 3672 KB answer = YES
57 Correct 19 ms 3544 KB answer = YES
58 Correct 21 ms 3472 KB answer = YES
59 Correct 9 ms 3540 KB answer = YES
60 Correct 18 ms 3656 KB answer = YES
61 Correct 6 ms 3084 KB answer = YES
62 Correct 60 ms 9676 KB answer = NO
63 Correct 72 ms 10444 KB answer = YES
64 Correct 56 ms 10188 KB answer = NO
65 Correct 60 ms 10396 KB answer = YES
66 Correct 5 ms 2772 KB answer = YES

Subtask #5
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB answer = YES
2 Correct 2 ms 2644 KB answer = YES
3 Correct 1 ms 2644 KB answer = YES
4 Correct 2 ms 2644 KB answer = NO
5 Correct 1 ms 2644 KB answer = YES
6 Correct 2 ms 2644 KB answer = YES
7 Correct 1 ms 2644 KB answer = YES
8 Correct 2 ms 2644 KB answer = YES
9 Correct 1 ms 2644 KB answer = NO
10 Correct 1 ms 2644 KB answer = YES
11 Correct 1 ms 2644 KB answer = YES
12 Correct 1 ms 2644 KB answer = NO
13 Correct 2 ms 2644 KB answer = YES
14 Correct 1 ms 2644 KB answer = YES
15 Correct 2 ms 2644 KB answer = YES
16 Correct 1 ms 2644 KB answer = YES
17 Correct 1 ms 2644 KB answer = YES
18 Correct 2 ms 2644 KB answer = YES
19 Correct 1 ms 2644 KB answer = YES
20 Correct 2 ms 2644 KB answer = YES
21 Correct 2 ms 2644 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 2 ms 2644 KB answer = NO
24 Correct 2 ms 2644 KB answer = YES
25 Correct 2 ms 2644 KB answer = YES
26 Correct 1 ms 2644 KB answer = YES
27 Correct 2 ms 2644 KB answer = YES
28 Correct 1 ms 2644 KB answer = YES
29 Correct 2 ms 2628 KB answer = YES
30 Correct 2 ms 2644 KB answer = NO
31 Correct 2 ms 2644 KB answer = YES
32 Correct 2 ms 2644 KB answer = YES
33 Correct 2 ms 2644 KB answer = YES
34 Correct 3 ms 2644 KB answer = YES
35 Correct 3 ms 2644 KB answer = YES
36 Correct 3 ms 2644 KB answer = YES
37 Correct 3 ms 2644 KB answer = YES
38 Correct 3 ms 2644 KB answer = YES
39 Correct 3 ms 2644 KB answer = YES
40 Correct 3 ms 2772 KB answer = YES
41 Correct 2 ms 2712 KB answer = NO
42 Correct 4 ms 2752 KB answer = YES
43 Correct 4 ms 2756 KB answer = YES
44 Correct 4 ms 2644 KB answer = YES
45 Correct 4 ms 2772 KB answer = YES
46 Correct 3 ms 2644 KB answer = YES
47 Correct 3 ms 2772 KB answer = YES
48 Correct 3 ms 2772 KB answer = YES
49 Correct 17 ms 3620 KB answer = YES
50 Correct 11 ms 3892 KB answer = YES
51 Correct 18 ms 3912 KB answer = YES
52 Correct 5 ms 3668 KB answer = NO
53 Correct 4 ms 2788 KB answer = YES
54 Correct 5 ms 2832 KB answer = YES
55 Correct 12 ms 3164 KB answer = YES
56 Correct 16 ms 3672 KB answer = YES
57 Correct 19 ms 3544 KB answer = YES
58 Correct 21 ms 3472 KB answer = YES
59 Correct 9 ms 3540 KB answer = YES
60 Correct 18 ms 3656 KB answer = YES
61 Correct 6 ms 3084 KB answer = YES
62 Correct 60 ms 9676 KB answer = NO
63 Correct 72 ms 10444 KB answer = YES
64 Correct 56 ms 10188 KB answer = NO
65 Correct 60 ms 10396 KB answer = YES
66 Correct 5 ms 2772 KB answer = YES
67 Correct 165 ms 18096 KB answer = YES
68 Correct 155 ms 18068 KB answer = YES
69 Correct 107 ms 17996 KB answer = YES
70 Correct 115 ms 22512 KB answer = YES
71 Correct 84 ms 18048 KB answer = YES
72 Correct 160 ms 12376 KB answer = YES
73 Correct 129 ms 12392 KB answer = YES
74 Correct 78 ms 11944 KB answer = YES
75 Correct 26 ms 9612 KB answer = NO
76 Correct 26 ms 3812 KB answer = YES
77 Correct 41 ms 5068 KB answer = YES
78 Correct 85 ms 6948 KB answer = YES
79 Correct 159 ms 11040 KB answer = YES
80 Correct 121 ms 11936 KB answer = YES
81 Correct 45 ms 11864 KB answer = NO
82 Correct 108 ms 17644 KB answer = YES
83 Correct 134 ms 18260 KB answer = YES
84 Correct 224 ms 18092 KB answer = YES
85 Correct 167 ms 18144 KB answer = YES
86 Correct 102 ms 18352 KB answer = YES
87 Correct 54 ms 11580 KB answer = NO
88 Correct 125 ms 14228 KB answer = YES
89 Correct 103 ms 11220 KB answer = YES
90 Correct 105 ms 11212 KB answer = YES
91 Correct 96 ms 11184 KB answer = YES
92 Correct 61 ms 7616 KB answer = YES
93 Correct 45 ms 7608 KB answer = YES
94 Correct 49 ms 14752 KB answer = NO
95 Correct 44 ms 9500 KB answer = NO
96 Correct 179 ms 20020 KB answer = YES
97 Correct 46 ms 14732 KB answer = NO