Submission #652537

#	Time	Username	Problem	Language	Result	Execution time	Memory
652537		1zaid1	Graph (BOI20_graph)	C++17	100 / 100	610 ms	58768 KiB

Graph

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define endl '\n';
 
const int M = 1e5+5, MOD = 1e9+7;
int p[M], d[M], loop, vis[M], f[M];
vector<pair<int, int>> node[M];
bitset<100005> is;
vector<int> tmp;
double cost[M];

void dfs(int s, int dp = 0) {
    vis[s] = 1;
    d[s] = dp++;
    tmp.push_back(s);
    for (auto [i, x]:node[s]) {
        if (!vis[i]) {
            p[i] = s;
            dfs(i, dp);
        } else if (!loop && (dp-d[i])%2) {
            loop = s;
            p[i] = s;
        }
    }
}

double eval(int s, double a, int cnt = 0) {
    double ans = abs(a);
    cost[s] = a;
    is[s] = 1;
    for (auto [i, x]:node[s]) {
        if (!is[i]) ans += abs(eval(i, x-a));
    } return ans;
}

bool check(vector<int> v) {
    for (int y:v) {
        for (auto [i, x]:node[y]) {
            if (abs(cost[y] + cost[i]-x) >= 1e-6)  return 0;
        }
    } return true;
}

void dfs2(int s, int d = 0) {
    is[s] = true;
    for (auto [i, x]:node[s]) {
        if (!is[i]) {
            f[i] = f[s]+(d?x:-x);
            dfs2(i, !d);
        }
    }
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);
    
    int n, m;
    cin >> n >> m;

    map<pair<int, int>, int> ed;
    for (int i = 1; i <= m; i++) {
        int a, b, c;
        cin >> a >> b >> c;
        if (a > b) swap(a, b);
        if (ed[{a, b}] && ed[{a, b}] != c) {
            cout << "NO" << endl;
            return 0;
        } else if (ed[{a, b}]) continue;

        ed[{a, b}] = ed[{b, a}] = c;
        node[a].push_back({b, c});
        node[b].push_back({a, c});
    }

    for (int k = 1; k <= n; k++) {
        if (!vis[k] && node[k].size()) {
            dfs(k);

            if (loop) {
                vector<int> lp = {loop};
                for (int x = p[loop]; x != loop; x = p[x]) lp.push_back(x);
                lp.push_back(loop);

                double sum = 0;
                for (int i = 0, f = 1; i < lp.size()-1; i++, f ^= 1) {
                    if (f) sum += ed[{min(lp[i], lp[i+1]), max(lp[i], lp[i+1])}];
                    else   sum -= ed[{min(lp[i], lp[i+1]), max(lp[i], lp[i+1])}];
                }

                eval(loop, sum/2);
            } else {
                eval(k, 0);
                if (!check(tmp)) {
                    cout << "NO" << endl;
                    return 0;
                }

                is = 0;
                dfs2(k);
                map<int, int> fr, ir;
                for (int i:tmp) fr[f[i]]++;
                for (int i:tmp) ir[f[i]] = i;
                int sum = 0;
                for (auto [a, b]:fr) sum += a*b;
                
                vector<int> nor; for (int i:tmp) nor.push_back(-f[i]);
                sort(nor.begin(), nor.end());

                double ans;
                if (nor.size()%2) ans = nor[nor.size()/2];
                else ans = (nor[nor.size()/2] + nor[nor.size()/2-1])/2;
                is = 0;
                eval(k, ans);
            }

            if (!check(tmp)) {
                cout << "NO" << endl;
                return 0;
            }

            tmp = {};
            loop = 0;
        }
    }

    cout << "YES" << fixed << setprecision(6) << endl;
    for (int i = 1; i <= n; i++) cout << cost[i] << ' '; cout << endl;
 
    return 0;
}
 
/*
3 3
1 1 2
2 2 1
2 3 2
 
4 5
1 4 2
3 2 1
2 1 2
3 4 1
1 3 2

3 2
2 1 2
3 2 1

4 4
1 2 1
2 3 2
1 3 2
3 4 1
*/

Compilation message (stderr)

Graph.cpp: In function 'int main()':
Graph.cpp:86:42: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   86 |                 for (int i = 0, f = 1; i < lp.size()-1; i++, f ^= 1) {
      |                                        ~~^~~~~~~~~~~~~
Graph.cpp:128:5: warning: this 'for' clause does not guard... [-Wmisleading-indentation]
  128 |     for (int i = 1; i <= n; i++) cout << cost[i] << ' '; cout << endl;
      |     ^~~
Graph.cpp:128:58: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'for'
  128 |     for (int i = 1; i <= n; i++) cout << cost[i] << ' '; cout << endl;
      |                                                          ^~~~

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