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Submission #852804

# Submission time Handle Problem Language Result Execution time Memory
852804 2023-09-22T18:05:02 Z lorenzoferrari Islands (IOI08_islands) C++17
80 / 100
 1049 ms 131072 KB 
#include "bits/stdc++.h"
using namespace std;
using LL = long long;

static constexpr int N = 1e6+5;

static vector<array<int, 3>> adj[N];
static array<int, 2> par[N];
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;
    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
        }
    }

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

Subtask #1
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 27480 KB Output is correct
2 Correct 5 ms 27736 KB Output is correct
3 Correct 5 ms 27740 KB Output is correct
4 Correct 5 ms 27484 KB Output is correct
5 Correct 6 ms 27740 KB Output is correct
6 Correct 6 ms 27484 KB Output is correct
7 Correct 5 ms 27484 KB Output is correct
8 Correct 5 ms 27740 KB Output is correct
9 Correct 6 ms 27740 KB Output is correct
10 Correct 6 ms 27740 KB Output is correct
11 Correct 5 ms 27740 KB Output is correct

Subtask #2
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 27740 KB Output is correct
2 Correct 6 ms 27740 KB Output is correct

Subtask #3
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 27740 KB Output is correct
2 Correct 7 ms 27996 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 28504 KB Output is correct
2 Correct 19 ms 30552 KB Output is correct
3 Correct 13 ms 28504 KB Output is correct
4 Correct 10 ms 27996 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 24 ms 31572 KB Output is correct
2 Correct 30 ms 33372 KB Output is correct

Subtask #6
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 66 ms 37824 KB Output is correct
2 Correct 67 ms 42320 KB Output is correct
3 Correct 90 ms 52748 KB Output is correct

Subtask #7
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 104 ms 47012 KB Output is correct
2 Correct 144 ms 70740 KB Output is correct
3 Correct 169 ms 75344 KB Output is correct
4 Correct 230 ms 96044 KB Output is correct

Subtask #8
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 214 ms 90304 KB Output is correct
2 Correct 769 ms 131072 KB Output is correct
3 Correct 224 ms 77728 KB Output is correct
4 Correct 304 ms 115460 KB Output is correct
5 Correct 305 ms 116824 KB Output is correct
6 Correct 1049 ms 86508 KB Output is correct
7 Runtime error 275 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 -