oj.uz

Submission #868711

# Submission time Handle Problem Language Result Execution time Memory
868711 2023-11-01T17:11:06 Z mzh Šarenlist (COCI22_sarenlist) C++17
110 / 110
 41 ms 468 KB 
#include <bits/stdc++.h>
 
using namespace std;
 
/*
    this problem can be solved using inclusion exclusion
    but the implementation is a little tricky
    it's annoying that we need to color edges in this problem
    how do we handle this?
 
    number the edges, make an adjacency list containing (dest, edge index)
    for each path, get its set of edges using dfs
    when processing a subset, make a dsu on sets of edges
    add/subtract k^sets
*/
 
constexpr int MOD = 1e9 + 7;
 
constexpr int N = 60, M = 15;
 
pair<int, int> edges[N];
vector<pair<int, int>> adj[N];
pair<int, int> paths[M];
 
pair<int, int> from[N];
 
void dfs(int u, int p) {
    for (auto [v, idx] : adj[u]) {
        if (v != p) {
            from[v] = {u, idx};
            dfs(v, u);
        }
    }
}
 
int dsu[N];
int comps = 0;
 
int find(int x) {
    return dsu[x] < 0 ? x : dsu[x] = find(dsu[x]);
}
 
void unite(int x, int y) {
    x = find(x);
    y = find(y);
 
    if (x == y) {
        return;
    }
    if (-dsu[x] < -dsu[y]) {
        swap(x, y);
    }
 
    dsu[x] += dsu[y];
    dsu[y] = x;
    comps--;
}

int pow_k[N]; 

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
 
    int n, m, k;
    cin >> n >> m >> k;
 
    for (int i = 0; i < n - 1; i++) {
        auto &[u, v] = edges[i];
        cin >> u >> v;
        u--; v--;
        adj[u].push_back({v, i});
        adj[v].push_back({u, i});
    }
 
    for (int i = 0; i < m; i++) {
        auto &[a, b] = paths[i];
        cin >> a >> b;
        a--; b--;
    }

    pow_k[0] = 1;
    for (int i = 1; i < n; i++) {
        pow_k[i] = 1ll * pow_k[i - 1] * k % MOD;
    }
 
    long long ans = 0;
    for (int i = 0; i < (1 << m); i++) {
        fill(dsu, dsu + n - 1, -1);
        comps = n - 1;
 
        for (int j = 0; j < m; j++) {
            if ((i >> j) & 1) {
                auto [a, b] = paths[j];
                from[a].first = a;
                dfs(a, -1);
                for (int x = b; from[x].first != a; x = from[x].first) {
                    unite(from[x].second, from[from[x].first].second);
                }
            }
        }
 
        if (__builtin_popcount(i) & 1) {
            ans = (ans - pow_k[comps] + MOD) % MOD;
        } else {
            ans = (ans + pow_k[comps]) % MOD;
        }
    }
    cout << ans << '\n';
    
    return 0;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 344 KB Output is correct
6 Correct 0 ms 348 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 6 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 460 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 4 ms 456 KB Output is correct
6 Correct 5 ms 456 KB Output is correct
7 Correct 1 ms 348 KB Output is correct

Subtask #5
65.0 / 65.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 344 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 6 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 460 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 4 ms 456 KB Output is correct
25 Correct 5 ms 456 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 27 ms 348 KB Output is correct
28 Correct 0 ms 344 KB Output is correct
29 Correct 0 ms 348 KB Output is correct
30 Correct 30 ms 468 KB Output is correct
31 Correct 7 ms 348 KB Output is correct
32 Correct 3 ms 348 KB Output is correct
33 Correct 1 ms 344 KB Output is correct
34 Correct 3 ms 348 KB Output is correct
35 Correct 15 ms 456 KB Output is correct
36 Correct 41 ms 348 KB Output is correct
37 Correct 18 ms 348 KB Output is correct