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답안 #594538

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
594538 2022-07-12T16:14:18 Z bogdanvladmihai Pipes (BOI13_pipes) C++14
74.0741 / 100
 348 ms 35272 KB 
#include <bits/stdc++.h>
using namespace std;

#define int long long

/***
N equations and M unknowns - can only have a unique solution if M <= N
Since M >= N - 1 =>
* the graph is a tree, in wich case we can solve the problem
* the graph is a tree with a simple cycle (N edges). Solve the problem for leafs and solve from a cycle

Solve for a cycle:
* even length: multiple solution (for each node do +1 on one edge and -1 on the other)
* odd length: unique solution, do some math stuff and deduce first edge

N = the number of nodes that are left are the process

sum(1) = W(n, 1) + W(1, 2)
sum(2) = W(1, 2) + W(2, 3)

sum(1) = W(n, 1) + sum(2) - W(2, 3)
sum(1) = W(n, 1) + sum(2) - sum(3) + sum(4) - ... - sum(N) + W(n, 1)
2 * W(n, 1) = sum(1) - sum(2) + sum(3) - sum(4) + .... + sum(N)

***/

const int MAXN = 1000 * 100;

int n, m;
set<int> g[MAXN + 1];
pair<int, int> edges[MAXN + 1];
map<pair<int, int>, int> edgeId;
int weight[MAXN + 1], sum[MAXN + 1];
bool visited[MAXN + 1];

vector<int> cycle;
void dfs(int u, int dad = -1) {
    visited[u] = true;
    cycle.push_back(u);

    for (const int &v : g[u]) {
        if (v == dad || visited[v]) {
            continue;
        }

        dfs(v, u);
    }
}

signed main() {
    cin >> n >> m;

    if (m > n) {
        cout << "0\n";
        return 0;
    }

    for (int i = 1; i <= n; i++) {
        cin >> sum[i];
    }
    for (int i = 0; i < m; i++) {
        int u, v; cin >> u >> v;

        edgeId[make_pair(u, v)] = edgeId[make_pair(v, u)] = i;

        g[u].insert(v);
        g[v].insert(u);
    }

    queue<int> q;
    for (int i = 1; i <= n; i++) {
        if ((int)g[i].size() == 1) {
            q.push(i);
        }
    }

    while (!q.empty()) {
        int u = q.front();
        q.pop();

        if ((int)g[u].size() > 0) {
            int v = *g[u].begin();
            int id = edgeId[make_pair(u, v)];

            weight[id] = sum[u];
            sum[v] -= weight[id];

            g[u].erase(v);
            g[v].erase(u);
            if ((int)g[v].size() == 1) {
                q.push(v);
            }
        }
    }

    for (int i = 1; i <= n; i++) {
        if ((int)g[i].size() > 0) {
            dfs(i);
            break;
        }
    }

    if ((int)cycle.size() > 0 && (int)cycle.size() % 2 == 0) {
        cout << "0\n";
        return 0;
    }

    if ((int)cycle.size() > 0) {
        int s = 0;
        for (int i = 0; i < (int)cycle.size(); i++) {
            if (i % 2 == 0) {
                s += sum[cycle[i]];
            } else {
                s -= sum[cycle[i]];
            }
        }

        int id = edgeId[make_pair(cycle[0], cycle.back())];
        weight[id] = s / 4;

        g[cycle[0]].erase(cycle.back());
        g[cycle.back()].erase(cycle[0]);

        sum[cycle[0]] -= weight[id];
        sum[cycle.back()] -= weight[id];

        q.push(cycle[0]);
        q.push(cycle.back());
        while (!q.empty()) {
            int u = q.front();
            q.pop();

            int v = *g[u].begin();
            int id = edgeId[make_pair(u, v)];

            weight[id] = sum[u];
            sum[v] -= weight[id];

            g[u].erase(v);
            g[v].erase(u);
            if ((int)g[v].size() == 1) {
                q.push(v);
            }
        }
    }

    for (int i = 0; i < m; i++) {
        cout << 2 * weight[i] << " ";
    }
    cout << "\n";

    return 0;
}

Subtask #1
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 3 ms 4948 KB Output is correct
3 Correct 4 ms 5204 KB Output is correct
4 Correct 288 ms 29100 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 3 ms 4932 KB Output is correct
8 Correct 3 ms 4948 KB Output is correct
9 Correct 4 ms 5204 KB Output is correct
10 Correct 4 ms 5204 KB Output is correct
11 Correct 4 ms 5204 KB Output is correct
12 Correct 6 ms 5204 KB Output is correct
13 Correct 215 ms 24176 KB Output is correct
14 Correct 267 ms 27892 KB Output is correct
15 Correct 348 ms 29236 KB Output is correct
16 Correct 233 ms 25548 KB Output is correct
17 Correct 273 ms 29116 KB Output is correct
18 Correct 293 ms 29220 KB Output is correct
19 Correct 274 ms 28896 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 4 ms 5216 KB Output is correct
22 Correct 268 ms 29304 KB Output is correct
23 Correct 202 ms 24264 KB Output is correct
24 Correct 280 ms 29436 KB Output is correct
25 Correct 218 ms 25168 KB Output is correct

Subtask #2
44.0740740741 / 70.0

# 결과 실행 시간 메모리 Grader output
1 Incorrect 3 ms 4948 KB Output isn't correct
2 Incorrect 4 ms 5204 KB Output isn't correct
3 Correct 228 ms 30600 KB Output is correct
4 Correct 2 ms 4948 KB Output is correct
5 Correct 2 ms 4948 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Incorrect 2 ms 4948 KB Output isn't correct
8 Incorrect 2 ms 4948 KB Output isn't correct
9 Correct 2 ms 4948 KB Output is correct
10 Correct 3 ms 4948 KB Output is correct
11 Correct 2 ms 4948 KB Output is correct
12 Correct 2 ms 4948 KB Output is correct
13 Correct 2 ms 4948 KB Output is correct
14 Incorrect 2 ms 4948 KB Output isn't correct
15 Incorrect 4 ms 5204 KB Output isn't correct
16 Incorrect 4 ms 5204 KB Output isn't correct
17 Correct 3 ms 5292 KB Output is correct
18 Correct 3 ms 4948 KB Output is correct
19 Correct 2 ms 4948 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 2 ms 4948 KB Output is correct
22 Incorrect 4 ms 5204 KB Output isn't correct
23 Incorrect 236 ms 28316 KB Output isn't correct
24 Incorrect 297 ms 32832 KB Output isn't correct
25 Correct 233 ms 30612 KB Output is correct
26 Correct 3 ms 4948 KB Output is correct
27 Correct 2 ms 4948 KB Output is correct
28 Correct 3 ms 4948 KB Output is correct
29 Correct 2 ms 4948 KB Output is correct
30 Incorrect 277 ms 31824 KB Output isn't correct
31 Incorrect 296 ms 35272 KB Output isn't correct
32 Incorrect 281 ms 30476 KB Output isn't correct
33 Correct 249 ms 32760 KB Output is correct
34 Correct 2 ms 4948 KB Output is correct
35 Correct 3 ms 4948 KB Output is correct
36 Correct 2 ms 4948 KB Output is correct
37 Correct 3 ms 4948 KB Output is correct
38 Incorrect 301 ms 32452 KB Output isn't correct
39 Incorrect 279 ms 29828 KB Output isn't correct
40 Incorrect 292 ms 32692 KB Output isn't correct
41 Correct 225 ms 34788 KB Output is correct
42 Correct 2 ms 4948 KB Output is correct
43 Correct 3 ms 4948 KB Output is correct
44 Correct 2 ms 4948 KB Output is correct
45 Correct 2 ms 4948 KB Output is correct
46 Incorrect 289 ms 31928 KB Output isn't correct
47 Incorrect 295 ms 32708 KB Output isn't correct
48 Incorrect 298 ms 35064 KB Output isn't correct
49 Correct 252 ms 28492 KB Output is correct
50 Correct 3 ms 4948 KB Output is correct
51 Correct 2 ms 4948 KB Output is correct
52 Correct 2 ms 4948 KB Output is correct
53 Correct 3 ms 4976 KB Output is correct
54 Incorrect 280 ms 31424 KB Output isn't correct