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Submission #1036098

# Submission time Handle Problem Language Result Execution time Memory
1036098 2024-07-27T03:34:22 Z thinknoexit Islands (IOI08_islands) C++17
90 / 100
 679 ms 131072 KB 
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 1001000;
vector<pair<int, int>> adj[N];
int deg[N];
bool cycle[N], vis[N];
ll dp[2][N], qs[N], a[N];
ll res = 0;
void dfs(int v, int p = -1) {
    dp[0][v] = dp[1][v] = 0;
    for (auto& x : adj[v]) {
        if (x.first == p || cycle[x.first]) continue;
        dfs(x.first, v);
        dp[1][v] = max(dp[1][v], dp[0][x.first] + x.second);
        if (dp[1][v] > dp[0][v]) swap(dp[0][v], dp[1][v]);
    }
    res = max(res, dp[0][v] + dp[1][v]);
}
int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int n;
    cin >> n;
    for (int i = 1;i <= n;i++) {
        int a, x;
        cin >> a >> x;
        adj[i].push_back({ a, x });
        adj[a].push_back({ i, x });
        deg[i]++, deg[a]++;
    }
    // find cycle using kahn's algorithm
    {
        queue<int> q;
        for (int i = 1;i <= n;i++) {
            cycle[i] = 1;
            if (deg[i] == 1) q.push(i);
        }
        while (!q.empty()) {
            int v = q.front();
            q.pop();
            cycle[v] = 0;
            for (auto& x : adj[v]) {
                if (--deg[x.first] == 1) q.push(x.first);
            }
        }
    }
    ll ans = 0;
    // for each component find the longest path and sum up to answer
    for (int i = 1;i <= n;i++) {
        if (!cycle[i] || vis[i]) continue;
        vector<pair<int, int>> c;
        c.push_back({ 0, 0 });
        int now = i, p = -1;
        while (1) {
            bool ch = 0;
            vis[now] = 1;
            for (auto& x : adj[now]) {
                if (!cycle[x.first] || x.first == p) continue;
                c.push_back({ now, x.second });
                if (!vis[x.first]) {
                    p = now;
                    ch = 1;
                    now = x.first;
                    break;
                }
            }
            if (!ch) {
                if ((int)c.size() == 2) { // parallel edge
                    multiset<int> s;
                    for (auto& x : adj[now]) {
                        if (!cycle[x.first]) continue;
                        s.insert(x.second);
                    }
                    s.erase(s.find(c.back().second));
                    c.push_back({ now, *s.begin() });
                }
                break;
            }
        }
        // c is list of cycle in order
        res = 0;
        int sz = c.size() - 1;
        for (int i = 1;i <= sz;i++) {
            dfs(c[i].first);
            qs[i] = qs[i - 1] + c[i - 1].second;
            a[i] = dp[0][c[i].first];
        }
        ll mx = -1e18, mx2 = -1e18;
        ll sk = c[sz].second;
        for (int i = 1;i <= sz;i++) {
            res = max(res, mx + qs[i] + a[i]);
            res = max(res, mx2 + qs[sz] - qs[i] + a[i] + sk);
            mx = max(mx, -qs[i] + a[i]);
            mx2 = max(mx2, qs[i] + a[i]);
        }
        ans += res;
        //cout << res << ' ';
    }
    cout << ans;
    return 0;
}

Subtask #1
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 23896 KB Output is correct
2 Correct 10 ms 23896 KB Output is correct
3 Correct 10 ms 23828 KB Output is correct
4 Correct 10 ms 23900 KB Output is correct
5 Correct 9 ms 23900 KB Output is correct
6 Correct 9 ms 23900 KB Output is correct
7 Correct 10 ms 24012 KB Output is correct
8 Correct 9 ms 23800 KB Output is correct
9 Correct 12 ms 23896 KB Output is correct
10 Correct 11 ms 23900 KB Output is correct
11 Correct 10 ms 23900 KB Output is correct

Subtask #2
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 23900 KB Output is correct
2 Correct 10 ms 23900 KB Output is correct

Subtask #3
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 24156 KB Output is correct
2 Correct 11 ms 24372 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 24972 KB Output is correct
2 Correct 20 ms 26820 KB Output is correct
3 Correct 16 ms 25460 KB Output is correct
4 Correct 16 ms 24668 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 24 ms 28120 KB Output is correct
2 Correct 36 ms 31356 KB Output is correct

Subtask #6
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 53 ms 38908 KB Output is correct
2 Correct 56 ms 41168 KB Output is correct
3 Correct 66 ms 46132 KB Output is correct

Subtask #7
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 95 ms 52608 KB Output is correct
2 Correct 119 ms 64664 KB Output is correct
3 Correct 121 ms 69364 KB Output is correct
4 Correct 162 ms 79960 KB Output is correct

Subtask #8
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 206 ms 103216 KB Output is correct
2 Correct 526 ms 109664 KB Output is correct
3 Correct 197 ms 82756 KB Output is correct
4 Correct 227 ms 102280 KB Output is correct
5 Correct 212 ms 103096 KB Output is correct
6 Correct 679 ms 95604 KB Output is correct
7 Correct 250 ms 112248 KB Output is correct

Subtask #9
0 / 10.0

# Verdict Execution time Memory Grader output
1 Runtime error 250 ms 131072 KB Execution killed with signal 9
2 Halted 0 ms 0 KB -