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답안 #594527

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
594527 2022-07-12T16:03:47 Z bogdanvladmihai Pipes (BOI13_pipes) C++14
44.0741 / 100
 373 ms 37132 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 calculated[MAXN + 1], 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;
        edges[i] = make_pair(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();

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

        calculated[id] = true;
        weight[id] = 2 * 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() > 1) {
            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())];
        calculated[id] = true;
        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)];

            calculated[id] = true;
            weight[id] = 2 * 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 << weight[i] << " ";
    }
    cout << "\n";

    return 0;
}

Subtask #1
0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Incorrect 3 ms 4948 KB Output isn't correct
2 Incorrect 3 ms 5024 KB Output isn't correct
3 Incorrect 4 ms 5280 KB Output isn't correct
4 Incorrect 279 ms 30692 KB Output isn't correct
5 Incorrect 3 ms 4948 KB Output isn't correct
6 Incorrect 3 ms 4948 KB Output isn't correct
7 Incorrect 3 ms 5016 KB Output isn't correct
8 Incorrect 2 ms 5012 KB Output isn't correct
9 Incorrect 4 ms 5276 KB Output isn't correct
10 Incorrect 4 ms 5204 KB Output isn't correct
11 Incorrect 5 ms 5280 KB Output isn't correct
12 Incorrect 5 ms 5204 KB Output isn't correct
13 Incorrect 235 ms 25428 KB Output isn't correct
14 Incorrect 278 ms 29276 KB Output isn't correct
15 Incorrect 333 ms 30748 KB Output isn't correct
16 Incorrect 247 ms 27056 KB Output isn't correct
17 Incorrect 291 ms 30704 KB Output isn't correct
18 Incorrect 308 ms 30844 KB Output isn't correct
19 Incorrect 302 ms 31200 KB Output isn't correct
20 Incorrect 3 ms 5016 KB Output isn't correct
21 Incorrect 4 ms 5152 KB Output isn't correct
22 Incorrect 298 ms 30804 KB Output isn't correct
23 Incorrect 207 ms 25356 KB Output isn't correct
24 Incorrect 331 ms 30752 KB Output isn't correct
25 Incorrect 245 ms 26448 KB Output isn't 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 5332 KB Output isn't correct
3 Correct 242 ms 31884 KB Output is correct
4 Correct 3 ms 4976 KB Output is correct
5 Correct 4 ms 4948 KB Output is correct
6 Correct 4 ms 5028 KB Output is correct
7 Incorrect 3 ms 5016 KB Output isn't correct
8 Incorrect 3 ms 4948 KB Output isn't correct
9 Correct 4 ms 5012 KB Output is correct
10 Correct 4 ms 4948 KB Output is correct
11 Correct 3 ms 4948 KB Output is correct
12 Correct 2 ms 4948 KB Output is correct
13 Correct 3 ms 4948 KB Output is correct
14 Incorrect 2 ms 4948 KB Output isn't correct
15 Incorrect 5 ms 5284 KB Output isn't correct
16 Incorrect 4 ms 5204 KB Output isn't correct
17 Correct 4 ms 5204 KB Output is correct
18 Correct 2 ms 4948 KB Output is correct
19 Correct 3 ms 5020 KB Output is correct
20 Correct 2 ms 4948 KB Output is correct
21 Correct 3 ms 5020 KB Output is correct
22 Incorrect 4 ms 5204 KB Output isn't correct
23 Incorrect 302 ms 29948 KB Output isn't correct
24 Incorrect 292 ms 34624 KB Output isn't correct
25 Correct 251 ms 31884 KB Output is correct
26 Correct 3 ms 4948 KB Output is correct
27 Correct 3 ms 4948 KB Output is correct
28 Correct 3 ms 4948 KB Output is correct
29 Correct 3 ms 4948 KB Output is correct
30 Incorrect 307 ms 33916 KB Output isn't correct
31 Incorrect 373 ms 37132 KB Output isn't correct
32 Incorrect 294 ms 32032 KB Output isn't correct
33 Correct 282 ms 34044 KB Output is correct
34 Correct 3 ms 4948 KB Output is correct
35 Correct 3 ms 4948 KB Output is correct
36 Correct 3 ms 5028 KB Output is correct
37 Correct 3 ms 4948 KB Output is correct
38 Incorrect 298 ms 34348 KB Output isn't correct
39 Incorrect 282 ms 31444 KB Output isn't correct
40 Incorrect 332 ms 34400 KB Output isn't correct
41 Correct 235 ms 36176 KB Output is correct
42 Correct 3 ms 5076 KB Output is correct
43 Correct 3 ms 5028 KB Output is correct
44 Correct 3 ms 4948 KB Output is correct
45 Correct 3 ms 4948 KB Output is correct
46 Incorrect 315 ms 34164 KB Output isn't correct
47 Incorrect 288 ms 34432 KB Output isn't correct
48 Incorrect 346 ms 36852 KB Output isn't correct
49 Correct 243 ms 29780 KB Output is correct
50 Correct 2 ms 4948 KB Output is correct
51 Correct 3 ms 4948 KB Output is correct
52 Correct 3 ms 4948 KB Output is correct
53 Correct 3 ms 4948 KB Output is correct
54 Incorrect 312 ms 33472 KB Output isn't correct