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Submission #852805

# Submission time Handle Problem Language Result Execution time Memory
852805 2023-09-22T18:06:52 Z lorenzoferrari Islands (IOI08_islands) C++17
80 / 100
 1043 ms 131072 KB 
#include "bits/stdc++.h"
using namespace std;
using LL = long long;

static constexpr int N = 1e6+5;

vector<vector<array<int, 3>>> adj;
vector<array<int, 2>> par;
bitset<N> vis, cyc;
int cycle_node = -1;
int back_edge = -1;

void dfs(int v, int pi) {
    vis[v] = true;
    for (auto [u, w, i] : adj[v]) {
        if (i == pi) continue;   // deal with cycles of length 2
        if (!vis[u]) {
            par[u] = {v, w};
            dfs(u, i);
        } else if (vis[u] && cycle_node == -1) {
            cycle_node = v;
            par[u] = {v, w};
            back_edge = i;
        }
    }
}

void find_diam(int v, int p, LL dist, array<LL, 2>& max_dist) {
    max_dist = max(max_dist, array<LL, 2>{dist, v});
    for (auto [u, w, i] : adj[v]) {
        if (u == p || i == back_edge) continue;
        find_diam(u, v, dist + w, max_dist);
    }
}

LL height(int v, int p) {
    LL ans = 0;
    for (auto [u, w, i] : adj[v]) {
        if (u == p || i == back_edge) continue;
        if (cyc[u]) continue;
        ans = max(ans, w + height(u, v));
    }
    return ans;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int n; cin >> n;
    adj.resize(n+1);
    par.resize(n+1);

    for (int v = 1, u, w; v <= n; ++v) {
        cin >> u >> w;
        adj[v].push_back({u, w, v});
        adj[u].push_back({v, w, v});
    }

    LL ans = 0;
    for (int v = 1; v <= n; ++v) {
        if (!vis[v]) {
            // first dfs
            dfs(v, -1);

            // diameter
            array<LL, 2> max_dist{0, v};
            find_diam(v, -1, 0, max_dist);
            int u = max_dist[1];
            max_dist = {0, u};
            find_diam(u, -1, 0, max_dist);
            LL diameter = max_dist[0];

            // path traversing the cycle
            LL a = cycle_node;
            LL cycle_length = 0;
            while (par[a][0] != cycle_node) {
                cyc[a] = true;
                cycle_length += par[a][1];
                a = par[a][0];
            }
            cyc[a] = true;
            cycle_length += par[a][1];

            a = cycle_node;
            LL max1 = -1e9, max2 = -1e9;
            LL prv1 = height(a, -1);
            LL prv2 = prv1;
            while (par[a][0] != cycle_node) {
                auto [b, w] = par[a];
                prv1 += w;
                prv2 -= w;
                LL h = height(b, -1);
                max1 = max(max1, prv1 + h);
                max2 = max(max2, prv2 + h);
                prv1 = max(prv1, h);
                prv2 = max(prv2, h);
                a = b;
            }
            LL cycle_path = max(max1, cycle_length + max2);

            // increase the answer by the maximum path in the current cc
            ans += max(diameter, cycle_path);

            cycle_node = -1;    // reset
            back_edge = -1;
        }
    }

    cout << ans << "\n";
}

Subtask #1
33.0 / 33.0

# 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 0 ms 348 KB Output is correct
4 Correct 0 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 344 KB Output is correct
9 Correct 0 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 600 KB Output is correct

Subtask #2
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 344 KB Output is correct

Subtask #3
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 604 KB Output is correct
2 Correct 2 ms 860 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1628 KB Output is correct
2 Correct 12 ms 4444 KB Output is correct
3 Correct 8 ms 1884 KB Output is correct
4 Correct 4 ms 1116 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 17 ms 5936 KB Output is correct
2 Correct 25 ms 9308 KB Output is correct

Subtask #6
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 64 ms 17236 KB Output is correct
2 Correct 60 ms 22100 KB Output is correct
3 Correct 83 ms 33360 KB Output is correct

Subtask #7
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 100 ms 30288 KB Output is correct
2 Correct 148 ms 57284 KB Output is correct
3 Correct 164 ms 62776 KB Output is correct
4 Correct 201 ms 84632 KB Output is correct

Subtask #8
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 212 ms 75328 KB Output is correct
2 Correct 780 ms 128408 KB Output is correct
3 Correct 191 ms 60648 KB Output is correct
4 Correct 298 ms 102820 KB Output is correct
5 Correct 278 ms 104592 KB Output is correct
6 Correct 1043 ms 70508 KB Output is correct
7 Runtime error 268 ms 131072 KB Execution killed with signal 9
8 Halted 0 ms 0 KB -

Subtask #9
0 / 10.0

# Verdict Execution time Memory Grader output
1 Runtime error 273 ms 131072 KB Execution killed with signal 9
2 Halted 0 ms 0 KB -