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답안 #594536

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
594536 2022-07-12T16:13:07 Z bogdanvladmihai Pipes (BOI13_pipes) C++14
74.0741 / 100
 372 ms 34500 KB 
#include <bits/stdc++.h>
using namespace std;

/***
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);
    }
}

int 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 / 2;

        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 3 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 269 ms 28580 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 4948 KB Output is correct
8 Correct 3 ms 5032 KB Output is correct
9 Correct 5 ms 5204 KB Output is correct
10 Correct 5 ms 5204 KB Output is correct
11 Correct 5 ms 5204 KB Output is correct
12 Correct 4 ms 5204 KB Output is correct
13 Correct 207 ms 23744 KB Output is correct
14 Correct 258 ms 27144 KB Output is correct
15 Correct 308 ms 28600 KB Output is correct
16 Correct 226 ms 25004 KB Output is correct
17 Correct 274 ms 28396 KB Output is correct
18 Correct 290 ms 28488 KB Output is correct
19 Correct 289 ms 28492 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 4 ms 5204 KB Output is correct
22 Correct 308 ms 28696 KB Output is correct
23 Correct 224 ms 23744 KB Output is correct
24 Correct 271 ms 28568 KB Output is correct
25 Correct 219 ms 24676 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 5 ms 5272 KB Output isn't correct
3 Correct 246 ms 29836 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 3 ms 5020 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Incorrect 3 ms 5012 KB Output isn't correct
8 Incorrect 3 ms 5008 KB Output isn't correct
9 Correct 3 ms 5012 KB Output is correct
10 Correct 2 ms 5008 KB Output is correct
11 Correct 2 ms 5012 KB Output is correct
12 Correct 3 ms 4948 KB Output is correct
13 Correct 2 ms 4948 KB Output is correct
14 Incorrect 3 ms 5008 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 4 ms 5276 KB Output is correct
18 Correct 3 ms 4992 KB Output is correct
19 Correct 3 ms 5020 KB Output is correct
20 Correct 3 ms 5148 KB Output is correct
21 Correct 3 ms 4948 KB Output is correct
22 Incorrect 4 ms 5276 KB Output isn't correct
23 Incorrect 229 ms 27768 KB Output isn't correct
24 Incorrect 316 ms 32184 KB Output isn't correct
25 Correct 234 ms 29848 KB Output is correct
26 Correct 3 ms 4948 KB Output is correct
27 Correct 4 ms 4992 KB Output is correct
28 Correct 3 ms 4948 KB Output is correct
29 Correct 3 ms 5016 KB Output is correct
30 Incorrect 317 ms 31168 KB Output isn't correct
31 Incorrect 307 ms 34500 KB Output isn't correct
32 Incorrect 289 ms 29748 KB Output isn't correct
33 Correct 270 ms 31860 KB Output is correct
34 Correct 3 ms 4948 KB Output is correct
35 Correct 3 ms 5020 KB Output is correct
36 Correct 4 ms 4948 KB Output is correct
37 Correct 2 ms 4948 KB Output is correct
38 Incorrect 332 ms 31696 KB Output isn't correct
39 Incorrect 372 ms 29088 KB Output isn't correct
40 Incorrect 299 ms 31828 KB Output isn't correct
41 Correct 258 ms 33976 KB Output is correct
42 Correct 5 ms 4948 KB Output is correct
43 Correct 3 ms 5020 KB Output is correct
44 Correct 3 ms 5020 KB Output is correct
45 Correct 3 ms 4948 KB Output is correct
46 Incorrect 292 ms 31244 KB Output isn't correct
47 Incorrect 312 ms 31924 KB Output isn't correct
48 Incorrect 308 ms 34188 KB Output isn't correct
49 Correct 255 ms 27756 KB Output is correct
50 Correct 2 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 4948 KB Output is correct
54 Incorrect 341 ms 30744 KB Output isn't correct