Submission #1030644

#	Time	Username	Problem	Language	Result	Execution time	Memory
1030644		thinknoexit	Graph (BOI20_graph)	C++17	100 / 100	98 ms	19912 KiB

Graph

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