Submission #685515

#	Time	Username	Problem	Language	Result	Execution time	Memory
685515		stanislavpolyn	Graph (BOI20_graph)	C++17	100 / 100	224 ms	22512 KiB

Graph

#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 / 5
• Subtask 2: 12 / 12
• Subtask 3: 17 / 17
• Subtask 4: 24 / 24
• Subtask 5: 42 / 42