제출 #1303455

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1303455		hypersphere	Graph (BOI20_graph)	C++20	100 / 100	129 ms	37124 KiB

Graph

#include <bits/stdc++.h>
using namespace std;

#define ll long long
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

ll rand(ll l, ll r) {
    return uniform_int_distribution<ll>(l, r)(rng);
}

const ll INF = 1e18;
const ll mod = 1e9 + 22071997;

ll binpow(ll base, ll exp, ll mod) {
    ll ans = 1;
    ll mult = base;
    while(exp) {
        if(exp & 1) ans = (ans * mult) % mod;
        mult = (mult * mult) % mod;
        exp >>= 1;
    }
    return ans;
} 

ll gcd(ll a, ll b) {
    if(b == 0) return a;
    return gcd(b, a%b);
}

struct LinearEq {
    double x, c;
    LinearEq(double _x = 0, double _c = 0) : x(_x), c(_c) {

    }

    LinearEq operator + (const LinearEq& other) {
        return LinearEq(x + other.x, c + other.c);
    }

    LinearEq operator - (const LinearEq& other) {
        return LinearEq(x - other.x, c - other.c);
    }
};

const int N = 1e5 + 5;
int n, m;
vector<pair<int, double>> adj[N];
bool vis[N];
LinearEq eq[N];
double val[N];

void gather_nodes(vector<int>& nodes, int node) {
    vis[node] = true;
    nodes.push_back(node);

    for(pair<int, double> v : adj[node]) {
        if(vis[v.first]) continue;
        gather_nodes(nodes, v.first);
    }
}

void spread_equation(int node) {
    vis[node] = true;
    for(pair<int, double> v : adj[node]) {
        if(!vis[v.first]) {
            eq[v.first] = LinearEq(0, v.second) - eq[node];
            spread_equation(v.first);
        } 
    }
}

void gather_equations(vector<LinearEq>& equations, int node) {
    vis[node] = true;
    for(pair<int, double> v : adj[node]) {
        equations.push_back(eq[node] + eq[v.first] - LinearEq(0, v.second));
        if(!vis[v.first]) {
            gather_equations(equations, v.first);
        } 
    }
}

void spread_value(double x, int node) {
    val[node] = x * eq[node].x + eq[node].c;
    vis[node] = true;
    for(pair<int, double> v : adj[node]) {
        if(!vis[v.first]) spread_value(x, v.first);
    }
}

bool valid_for_whole_graph = true;
void solve_component(int node) {
    vector<int> nodes;
    gather_nodes(nodes, node);

    for(int i : nodes) {
        vis[i] = false;
    }
    eq[node] = LinearEq(1, 0);
    spread_equation(node);

    for(int i : nodes) {
        vis[i] = false;
    }
    vector<LinearEq> equations;
    gather_equations(equations, node);

    
    vector<double> solutions;
    //cout << "System of equations: \n";
    for(LinearEq& e : equations) {
        //cout << e.x << "x + " << e.c << " = 0\n"; 
        if(fabs(e.x) <= 1e-9) {
            if(fabs(e.c) > 1e-9) {
                valid_for_whole_graph = false;
                return;
            }
        }
        else {
            solutions.push_back(-e.c / e.x);
        }
    }
    if(solutions.size() >= 1) {
        sort(solutions.begin(), solutions.end());
        solutions.erase(unique(solutions.begin(), solutions.end()), solutions.end());
    }
    double x;
    if(solutions.size() >= 2) {
        valid_for_whole_graph = false;
        return;
    }
    else if(solutions.size() == 1) {
        x = solutions.front();
    } else {
        // Get the median of all solutions
        vector<double> candidates;
        for(int i : nodes) {
            candidates.push_back(-eq[i].c / eq[i].x);
        }
        //cout << "HI\n" << flush;
        sort(candidates.begin(), candidates.end());
        int id = (int)candidates.size() / 2;

        x = candidates[id];
    }

    for(int i : nodes) {
        vis[i] = false;
    }
    spread_value(x, node);
}


void solve() {
    memset(vis, 0, sizeof(vis));
    cin >> n >> m;
    cout << fixed << setprecision(8);
    for(int i = 0; i < m; i++) {
        int a, b, t;
        cin >> a >> b >> t;
        adj[a].push_back({b, t});
        adj[b].push_back({a, t});
    }

    for(int i = 1; i <= n; i++) {
        if(vis[i]) continue;
        solve_component(i);
        if(!valid_for_whole_graph) break;
    }

    if(!valid_for_whole_graph) {
        cout << "NO\n";
        return;
    }
    cout << "YES\n";
    for(int i = 1; i <= n; i++) cout << val[i] << " ";
}

int main() {
    //freopen("COLLECT.INP", "r", stdin);
    //freopen("COLLECT.OUT", "w", stdout);
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    int tests = 1;
    //cin >> tests;

    while(tests--) solve();
}

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