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Submission #522104

# Submission time Handle Problem Language Result Execution time Memory
522104 2022-02-03T20:33:10 Z blue Road Closures (APIO21_roads) C++17
31 / 100
 2000 ms 28884 KB 
#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
using namespace std;

using vi = vector<int>;
using vvi = vector<vi>;
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;
using pii = pair<int, int>;
#define sz(x) int(x.size())

const int mx = 100'000;
const ll INF = 1'000'000'000'000'000'000LL;


int N;
vi U, V, W;

vi edge[mx];
vi deg(mx, 0);
vi deg_occ[mx];

vi depth(mx);
vi parent(mx, -1);

ll wt_sum = 0;

vi par_wt(mx);



void dfs1(int u, int p)
{
    for(int e: edge[u])
    {
        int v = U[e] + V[e] - u;
        int w = W[e];
        if(v == p) continue;

        par_wt[v] = w;

        depth[v] = depth[u] + 1;
        parent[v] = u;
        dfs1(v, u);
    }
}





struct DS
{
    multiset<ll> values;

    ll minSum(int z)
    {
        if(z > sz(values)) return INF;

        if(z <= 0) return 0;

        int ct = 0;
        ll res = 0;

        for(ll v : values)
        {
            res += v;
            ct++;
            if(ct == z) break;
        }

        return res;
    }

    void insert(ll v) 
    {
        values.insert(v);
    }

    int size()
    {
        return sz(values);
    }
};







vll minimum_closure_costs(int N_, vi U_, vi V_, vi W_)
{   
    N = N_;
    U = U_;
    V = V_;
    W = W_;

    for(int e = 0; e < N-1; e++)
    {
        edge[U[e]].push_back(e);
        edge[V[e]].push_back(e);

        deg[U[e]]++;
        deg[V[e]]++;

        wt_sum += W[e];
    }

    for(int i = 0; i < N; i++)
        deg_occ[deg[i]].push_back(i);

    for(int i = 0; i < N; i++)
    {
        sort(edge[i].begin(), edge[i].end(), [] (int e, int f)
        {
            return deg[U[e]] + deg[V[e]] > deg[U[f]] + deg[V[f]];
        });
    }


    dfs1(0, -1);

    set<pii> it_list;

    for(int i = 0; i < N; i++) it_list.insert({-depth[i], i});


    vll res(N, 0);

    res[0] = wt_sum;

                     // root deg <= K-1
    vll dp0(N), dp1(N);
    //root deg <= K

    DS extra_edges[N];

    vi intdeg = deg;
    for(int i = 1; i < N; i++)
        intdeg[i]--;

    for(int k = 1; k < N; k++)
    {
        // cerr << "\n\n\n\n\n";
        // cerr << "k = " << k << '\n';
        for(int u: deg_occ[k]) //deg_occ[0] is empty
        {
            // cerr << "eliminating " << u << '\n';
            it_list.erase({-depth[u], u});
            for(int e : edge[u])
            {
                int v = U[e] + V[e] - u;
                int w = W[e];
                if(parent[v] != u)
                    extra_edges[v].insert(w);
                // cerr << "extra edges " << v << " -> insert " << w << '\n';
            }
        }

        for(auto p: it_list)
        {
            // cerr << "\n\n";
            int u = p.second;
            // cerr << "u = " << u << '\n';

            // cerr << "ee = ";
            // for(ll y : extra_edges[u].values) cerr << y << ' ';
                // cerr << '\n';

            dp0[u] = dp1[u] = INF;

            ll basicCost = 0;

            vector<ll> upgrades;

            for(auto e: edge[u])
            {
                int v = U[e] + V[e] - u;
                ll w = W[e];

                if(v == parent[u]) continue;

                if(deg[v] <= k) break;

                basicCost += dp1[v];
                upgrades.push_back(dp0[v] + w - dp1[v]);
            }

            sort(upgrades.begin(), upgrades.end());

            ll upgrade_total = 0;

            dp0[u] = min(dp0[u], basicCost + extra_edges[u].minSum(intdeg[u] - k));
            dp1[u] = min(dp1[u], basicCost + extra_edges[u].minSum(intdeg[u] - (k-1)));

            // cerr << "pre : " << dp0[u] << ' ' << dp1[u] << '\n';

            // cerr << basicCost << '\n';

            // cerr << "ee size = " << sz(extra_edges[u]) << ", query val = " << intdeg[u] - k << '\n';




            for(int cct = 0; cct < sz(upgrades); cct++)
            {
                // cerr << "cct = " << cct << '\n';
                upgrade_total += upgrades[cct];
                dp0[u] = min(dp0[u], basicCost + upgrade_total + extra_edges[u].minSum(intdeg[u] - k - (cct+1)));
                dp1[u] = min(dp1[u], basicCost + upgrade_total + extra_edges[u].minSum(intdeg[u] - (k-1) - (cct+1)));
                // cerr << "! " << intdeg[u] - k - (cct+1) << ' ' << intdeg[u] - (k-1) - (cct+1) << '\n';
                // cerr << cct << " , " << basicCost + upgrade_total + extra_edges[u].minSum(intdeg[u] - k - (cct+1)) << ' ' << basicCost + upgrade_total + extra_edges[u].minSum(intdeg[u] - (k-1) - (cct+1)) << '\n';
            }

            if(u == 0) 
            {
                    // cerr << "adding " << dp0[u] << " a to res " << k << '\n'; 
                res[k] += dp0[u];
            }
            else if(deg[parent[u]] <= k)
            {
                // cerr << "adding " << min(dp1[u], dp0[u] + par_wt[u]) << " b to res " << k << '\n'; 
                res[k] += min(dp1[u], dp0[u] + par_wt[u]);
            }

            // cerr << u << " : " << parent[u] << ' ' << dp0[u] << ' ' << dp1[u] << '\n';
        }
    }


    return res;
}

Subtask #1
0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 6860 KB Output is correct
2 Correct 34 ms 7244 KB Output is correct
3 Correct 38 ms 7244 KB Output is correct
4 Correct 27 ms 7244 KB Output is correct
5 Correct 4 ms 6860 KB Output is correct
6 Correct 4 ms 6988 KB Output is correct
7 Correct 4 ms 6884 KB Output is correct
8 Correct 24 ms 7244 KB Output is correct
9 Correct 31 ms 7244 KB Output is correct
10 Correct 4 ms 6988 KB Output is correct
11 Correct 4 ms 6988 KB Output is correct
12 Execution timed out 2086 ms 18452 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 6860 KB Output is correct
2 Correct 77 ms 25076 KB Output is correct
3 Correct 86 ms 27468 KB Output is correct
4 Correct 92 ms 28856 KB Output is correct
5 Correct 91 ms 28792 KB Output is correct
6 Correct 5 ms 7244 KB Output is correct
7 Correct 5 ms 7372 KB Output is correct
8 Correct 5 ms 7244 KB Output is correct
9 Correct 4 ms 6988 KB Output is correct
10 Correct 4 ms 6988 KB Output is correct
11 Correct 4 ms 6988 KB Output is correct
12 Correct 51 ms 20032 KB Output is correct
13 Correct 85 ms 28864 KB Output is correct
14 Correct 3 ms 6860 KB Output is correct
15 Correct 82 ms 26684 KB Output is correct
16 Correct 86 ms 28884 KB Output is correct

Subtask #3
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 6860 KB Output is correct
2 Correct 3 ms 6860 KB Output is correct
3 Correct 3 ms 6860 KB Output is correct
4 Correct 4 ms 6860 KB Output is correct
5 Correct 3 ms 6988 KB Output is correct
6 Correct 4 ms 6988 KB Output is correct
7 Correct 4 ms 6988 KB Output is correct
8 Correct 4 ms 6988 KB Output is correct
9 Correct 4 ms 6988 KB Output is correct
10 Correct 4 ms 6988 KB Output is correct
11 Correct 4 ms 6988 KB Output is correct
12 Correct 4 ms 6988 KB Output is correct
13 Correct 4 ms 6988 KB Output is correct
14 Correct 4 ms 6948 KB Output is correct
15 Correct 4 ms 6988 KB Output is correct
16 Correct 3 ms 6860 KB Output is correct
17 Correct 4 ms 6988 KB Output is correct
18 Correct 3 ms 6988 KB Output is correct
19 Correct 4 ms 6988 KB Output is correct
20 Correct 5 ms 6988 KB Output is correct
21 Correct 3 ms 6860 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 6860 KB Output is correct
2 Correct 3 ms 6860 KB Output is correct
3 Correct 3 ms 6860 KB Output is correct
4 Correct 4 ms 6860 KB Output is correct
5 Correct 3 ms 6988 KB Output is correct
6 Correct 4 ms 6988 KB Output is correct
7 Correct 4 ms 6988 KB Output is correct
8 Correct 4 ms 6988 KB Output is correct
9 Correct 4 ms 6988 KB Output is correct
10 Correct 4 ms 6988 KB Output is correct
11 Correct 4 ms 6988 KB Output is correct
12 Correct 4 ms 6988 KB Output is correct
13 Correct 4 ms 6988 KB Output is correct
14 Correct 4 ms 6948 KB Output is correct
15 Correct 4 ms 6988 KB Output is correct
16 Correct 3 ms 6860 KB Output is correct
17 Correct 4 ms 6988 KB Output is correct
18 Correct 3 ms 6988 KB Output is correct
19 Correct 4 ms 6988 KB Output is correct
20 Correct 5 ms 6988 KB Output is correct
21 Correct 3 ms 6860 KB Output is correct
22 Correct 3 ms 6860 KB Output is correct
23 Correct 5 ms 7080 KB Output is correct
24 Correct 6 ms 7244 KB Output is correct
25 Correct 5 ms 7284 KB Output is correct
26 Correct 6 ms 7232 KB Output is correct
27 Correct 13 ms 7244 KB Output is correct
28 Correct 11 ms 7360 KB Output is correct
29 Correct 6 ms 7244 KB Output is correct
30 Correct 7 ms 7244 KB Output is correct
31 Correct 6 ms 7244 KB Output is correct
32 Correct 17 ms 7328 KB Output is correct
33 Correct 5 ms 7232 KB Output is correct
34 Correct 5 ms 7376 KB Output is correct
35 Correct 6 ms 7244 KB Output is correct
36 Correct 34 ms 7244 KB Output is correct
37 Correct 39 ms 7332 KB Output is correct
38 Correct 26 ms 7244 KB Output is correct
39 Correct 4 ms 6860 KB Output is correct
40 Correct 4 ms 6860 KB Output is correct
41 Correct 4 ms 6860 KB Output is correct
42 Correct 4 ms 6988 KB Output is correct
43 Correct 3 ms 6988 KB Output is correct
44 Correct 4 ms 6988 KB Output is correct
45 Correct 4 ms 6988 KB Output is correct
46 Correct 4 ms 6988 KB Output is correct
47 Correct 4 ms 6988 KB Output is correct
48 Correct 4 ms 6988 KB Output is correct
49 Correct 3 ms 6988 KB Output is correct
50 Correct 4 ms 6860 KB Output is correct
51 Correct 4 ms 6988 KB Output is correct
52 Correct 4 ms 6988 KB Output is correct
53 Correct 5 ms 7244 KB Output is correct
54 Correct 6 ms 7244 KB Output is correct
55 Correct 12 ms 7356 KB Output is correct
56 Correct 25 ms 7372 KB Output is correct
57 Correct 33 ms 7244 KB Output is correct
58 Correct 3 ms 6860 KB Output is correct
59 Correct 4 ms 6988 KB Output is correct
60 Correct 4 ms 6988 KB Output is correct
61 Correct 4 ms 6988 KB Output is correct
62 Correct 4 ms 6988 KB Output is correct
63 Correct 4 ms 6860 KB Output is correct
64 Correct 6 ms 7248 KB Output is correct
65 Correct 6 ms 7244 KB Output is correct
66 Correct 6 ms 7244 KB Output is correct
67 Correct 20 ms 7244 KB Output is correct
68 Correct 6 ms 7244 KB Output is correct

Subtask #5
0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 209 ms 25080 KB Output is correct
2 Correct 190 ms 24748 KB Output is correct
3 Correct 768 ms 26516 KB Output is correct
4 Correct 198 ms 25724 KB Output is correct
5 Correct 516 ms 26428 KB Output is correct
6 Execution timed out 2073 ms 26052 KB Time limit exceeded
7 Halted 0 ms 0 KB -

Subtask #6
0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 209 ms 25080 KB Output is correct
2 Correct 190 ms 24748 KB Output is correct
3 Correct 768 ms 26516 KB Output is correct
4 Correct 198 ms 25724 KB Output is correct
5 Correct 516 ms 26428 KB Output is correct
6 Execution timed out 2073 ms 26052 KB Time limit exceeded
7 Halted 0 ms 0 KB -

Subtask #7
0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 6860 KB Output is correct
2 Correct 34 ms 7244 KB Output is correct
3 Correct 38 ms 7244 KB Output is correct
4 Correct 27 ms 7244 KB Output is correct
5 Correct 4 ms 6860 KB Output is correct
6 Correct 4 ms 6988 KB Output is correct
7 Correct 4 ms 6884 KB Output is correct
8 Correct 24 ms 7244 KB Output is correct
9 Correct 31 ms 7244 KB Output is correct
10 Correct 4 ms 6988 KB Output is correct
11 Correct 4 ms 6988 KB Output is correct
12 Execution timed out 2086 ms 18452 KB Time limit exceeded
13 Halted 0 ms 0 KB -