Submission #852810

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
852810	2023-09-22T18:17:39 Z	lorenzoferrari	Islands (IOI08_islands)	C++17	90 / 100	1229 ms	131072 KB

islands

#include "bits/stdc++.h"
using namespace std;
using LL = long long;

static constexpr int N = 1e6+5;

vector<vector<int>> adj;
static array<int, 2> par[N];
static array<int, 2> edges[N];
bitset<N> vis, cyc;
int cycle_node = -1;
int back_edge = -1;

void dfs(int v, int pi) {
    vis[v] = true;
    for (auto i : adj[v]) {
        auto [uv, w] = edges[i];
        int u = uv^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 i : adj[v]) {
        auto [uv, w] = edges[i];
        int u = uv^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 i : adj[v]) {
        auto [uv, w] = edges[i];
        int u = uv^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);

    for (int v = 1, u, w; v <= n; ++v) {
        cin >> u >> w;
        edges[v] = {u^v, w};
        adj[v].push_back(v);
        adj[u].push_back(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	1 ms	4444 KB	Output is correct
2	Correct	1 ms	4444 KB	Output is correct
3	Correct	1 ms	4584 KB	Output is correct
4	Correct	1 ms	4444 KB	Output is correct
5	Correct	1 ms	4444 KB	Output is correct
6	Correct	1 ms	4444 KB	Output is correct
7	Correct	1 ms	4444 KB	Output is correct
8	Correct	1 ms	4444 KB	Output is correct
9	Correct	1 ms	4444 KB	Output is correct
10	Correct	1 ms	4444 KB	Output is correct
11	Correct	1 ms	4444 KB	Output is correct

Subtask #2
3.0 / 3.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	4696 KB	Output is correct
2	Correct	1 ms	4444 KB	Output is correct

Subtask #3
4.0 / 4.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	4444 KB	Output is correct
2	Correct	2 ms	4956 KB	Output is correct

Subtask #4
10.0 / 10.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	6 ms	5576 KB	Output is correct
2	Correct	13 ms	7772 KB	Output is correct
3	Correct	9 ms	5788 KB	Output is correct
4	Correct	4 ms	4956 KB	Output is correct

Subtask #5
10.0 / 10.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	18 ms	11096 KB	Output is correct
2	Correct	26 ms	13660 KB	Output is correct

Subtask #6
10.0 / 10.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	61 ms	19428 KB	Output is correct
2	Correct	75 ms	26220 KB	Output is correct
3	Correct	87 ms	34424 KB	Output is correct

Subtask #7
10.0 / 10.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	108 ms	34192 KB	Output is correct
2	Correct	141 ms	56980 KB	Output is correct
3	Correct	189 ms	72260 KB	Output is correct
4	Correct	200 ms	86320 KB	Output is correct

Subtask #8
10.0 / 10.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	211 ms	74936 KB	Output is correct
2	Correct	851 ms	118608 KB	Output is correct
3	Correct	199 ms	60240 KB	Output is correct
4	Correct	285 ms	99580 KB	Output is correct
5	Correct	286 ms	99800 KB	Output is correct
6	Correct	1229 ms	69232 KB	Output is correct
7	Correct	325 ms	131072 KB	Output is correct

Subtask #9
0 / 10.0

#	Verdict	Execution time	Memory	Grader output
1	Runtime error	243 ms	131072 KB	Execution killed with signal 9
2	Halted	0 ms	0 KB	-

Submission #852810

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