Submission #1101936

#	Time	Username	Problem	Language	Result	Execution time	Memory
1101936		crafticat	Graph (BOI20_graph)	C++17	0 / 100	1089 ms	336 KiB

Graph

#include "bits/stdc++.h"

using namespace std;
template<typename T>
using V = vector<T>;
using vi = V<int>;
using vvi = V<vi>;
using pi = pair<int,int>;
using vpi = V<pi>;

#define F0R(i, n) for(int i = 0; i < n;i++)
#define FOR(i,a, n) for(int i = a; i < n;i++)
#define pb push_back

V<bool> vis;
V<int> nodes;
double determine = -1;
bool determineInit = false, possible = true;
V<vpi> g;
double ep = 0.000000001;

struct info {
    int a, m;
    bool init = false;

    info() {

    }
    info(int a, int m) : a(a), m(m) {
        init = true;
    }
    bool operator==(info other) const {
        return a == other.a && m == other.m;
    }
    bool operator!=(info other) {
        return !(a == other.a && m == other.m);
    }
    info operator-(info other) const {
        return {a - other.a,m- other.m};
    }
    double eval(double x) {
        return a + m * x;
    }
};
V<info> dat;
V<double> ans;

void calc(int a, int b, int edge) {
    auto d2 = info(edge,0) - dat[b];
    if (dat[a].m == d2.m && dat[a].a == d2.a) return;
    if (dat[a].m == d2.m && dat[a].a != d2.a) {
        possible = false;
        return;
    }
    double results = (dat[a].a - d2.a) / ((double) d2.m - dat[a].m);
    if (determineInit && abs(results - determine) > ep) possible = false;
    else {
        determine = results;
        determineInit = true;
    }
}

void solve(int x, int edge, int par) {
    nodes.pb(x);
    vis[x] = true;

    if (par == -1) dat[x] = info(0,1);
    else {
        dat[x] = info(edge, 0) - dat[par];
    }

    for (auto &[v,cost] : g[x]) {
        if (vis[v]) {
            if (dat[v].init)
                calc(v, x, cost);
            continue;
        }

        solve(v, cost, x);
    }
}

double eval(double x) {
    double result = 0;
    for (auto v : nodes) {
        result += abs(dat[v].eval(x));
    }
    return result;
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(nullptr);

    int n, m; cin >> n >> m;
    g.resize(n + 1);

    F0R(i, m) {
        int a, b, c; cin >> a >> b >> c;
        g[a].pb({b,c});
        g[b].pb({a,c});
    }

    vis.resize(n + 1);
    dat.resize(n + 1);
    ans.resize(n + 1);

    FOR(i, 1, n + 1) {
        if (vis[i]) continue;
        solve(i, -1, -1);

        if (!possible) {
            cout << "NO\n";
            return 0;
        }
        if (!determineInit) {
            // Binary search results
            double l = -1e9, r = 1e9;
            while (r > l + ep) {
                double mid = l + (r - l + ep) / 2;
                if (eval(mid + ep) < eval(mid)) {
                    l = mid + ep;
                } else {
                    r = mid;
                }
            }

            determine = l;
        }
        for (auto x : nodes)
            ans[x] = dat[x].eval(determine);

        determine = -1;
        possible = true;
        determineInit = false;

        nodes.clear();
    }

    cout << "YES\n";
    FOR(i, 1, n + 1) {
        cout << fixed << setprecision(6) << ans[i] << " ";
    }

    return 0;
}

• Subtask 1: 0 / 5
• Subtask 2: 0 / 12
• Subtask 3: 0 / 17
• Subtask 4: 0 / 24
• Subtask 5: 0 / 42