Submission #594527

#	Time	Username	Problem	Language	Result	Execution time	Memory
594527		bogdanvladmihai	Pipes (BOI13_pipes)	C++14	44.07 / 100	373 ms	37132 KiB

pipes

#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
• Subtask 2: 44.074074074074076 / 70