Submission #488801

#	Time	Username	Problem	Language	Result	Execution time	Memory
488801		dxz05	Islands (IOI08_islands)	C++14	80 / 100	656 ms	131076 KiB

islands

#pragma GCC optimize("Ofast,O2,O3,unroll-loops")
#pragma GCC target("avx2")

#include <bits/stdc++.h>

using namespace std;

#define SZ(s) ((int)s.size())
#define all(x) (x).begin(), (x).end()
#define lla(x) (x).rbegin(), (x).rend()

clock_t startTime;

double getCurrentTime() {
    return (double) (clock() - startTime) / CLOCKS_PER_SEC;
}

#define MP make_pair

typedef long long ll;
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
const double eps = 0.000001;
const int MOD = 998244353;
const int INF = 1000000101;
const long long LLINF = 1223372000000000555;
const int N = 1e6 + 5;
const int M = 222;

int f[N]; int w[N];
bitset<N> used;
stack<int> st;

vector<int> cycle;

void dfs0(int v){
    if (!cycle.empty()) return;
    used[v] = true;
    st.push(v);

    if (used[f[v]]){
        while (!st.empty()){
            int x = st.top(); st.pop();
            cycle.push_back(x);
            if (x == f[v]) break;
        }
        return;
    }
    if (!cycle.empty()) return;

    dfs0(f[v]);

    if (!st.empty()) st.pop();
}

int parent[N];
int find(int x){
    return (x == parent[x] ? x : parent[x] = find(parent[x]));
}

void unite(int x, int y){
    x = find(x);
    y = find(y);
    if (x == y) return;
    if (rng() & 1) swap(x, y);
    parent[x] = y;
}

vector<pair<int, int>> g[N];

bitset<N> incycle;

void dfs(int v, int p, ll d, int root, vector<int> &tree, vector<ll> &dist){
    tree.push_back(v);
    dist.push_back(d);
    for (auto now : g[v]){
        int u = now.first; int W = now.second;
        if (u != p){
            if (u == root || !incycle[u]) dfs(u, v, d + W, root, tree, dist);
        }
    }
}

ll arr[N];

struct SegTree{
    struct node{
        ll mx;
        ll add;
        node(){
            mx = 0;
            add = 0;
        }
    };

    vector<node> tree;

    int size = 1;

    void build(int v, int tl, int tr, vector<ll> &a){
        if (tl == tr){
            tree[v].mx = a[tl - 1];
            tree[v].add = 0;
            return;
        }
        int tm = (tl + tr) >> 1;
        build(v + v, tl, tm, a);
        build(v + v + 1, tm + 1, tr, a);
        tree[v].mx = max(tree[v + v].mx, tree[v + v + 1].mx);
    }

    void init(vector<ll> &a){
        while (size < a.size()) size *= 2;
        tree.assign(size * 2 + 5, node());
        build(1, 1, size, a);
    }

    void push(int v){
        if (tree[v].add == 0) return;
        tree[v + v].mx += tree[v].add;
        tree[v + v + 1].mx += tree[v].add;
        tree[v + v].add += tree[v].add;
        tree[v + v + 1].add += tree[v].add;
        tree[v].add = 0;
    }

    void add(int l, int r, ll val, int v, int tl, int tr){
        if (l <= tl && tr <= r){
            tree[v].mx += val;
            tree[v].add += val;
            return;
        }
        if (tl > r || tr < l) return;

        push(v);

        int tm = (tl + tr) >> 1;
        add(l, r, val, v + v, tl, tm);
        add(l, r, val, v + v + 1, tm + 1, tr);
        tree[v].mx = max(tree[v + v].mx, tree[v + v + 1].mx);
    }

    void add(int l, int r, ll val){
        add(l, r, val, 1, 1, size);
    }

    ll get(int l, int r, int v, int tl, int tr){
        if (l <= tl && tr <= r) return tree[v].mx;
        if (l > tr || r < tl) return 0;
        push(v);
        int tm = (tl + tr) >> 1;
        return max(get(l, r, v + v, tl, tm), get(l, r, v + v + 1, tm + 1, tr));
    }

    ll get(int l, int r){
        return get(l, r, 1, 1, size);
    }

    ll get(){
        return tree[1].mx;
    }

} ST;

int A(int u, int v){
    if (f[u] == v && f[v] != u) return w[u];
    if (f[u] != v && f[v] == u) return w[v];
    return max(w[u], w[v]);
}

ll component(int root){
    cycle.clear();
    while (!st.empty()) st.pop();

    dfs0(root);

    for (int v : cycle){
        incycle[v] = true;
    }

    ll ans = 0;
    vector<int> tree; vector<ll> dist;
    for (int v : cycle){
        tree.clear();
        dist.clear();
        dfs(v, v, 0, v, tree, dist);

        int i = max_element(all(dist)) - dist.begin();
        ans = max(ans, dist[i]);
        arr[v] = dist[i];
        int u = tree[i];

        tree.clear(), dist.clear();
        dfs(u, u, 0, v, tree, dist);

        ans = max(ans, *max_element(all(dist)));
    }

    int n = cycle.size();

    if (n == 2){
        int u = cycle[0], v = cycle[1];
        ans = max(ans, arr[u] + arr[v] + max(w[u], w[v]));
        return ans;
    }

    vector<ll> a = {arr[cycle[0]]};
    ll sum = 0;
    for (int i = 1; i < n; i++){
        sum += A(cycle[i - 1], cycle[i]);
        a.push_back(arr[cycle[i]] + sum);
    }
    sum += A(cycle[0], cycle.back());

//    for (int x : cycle) cout << x << ' '; cout << endl;
//    for (ll x : a) cout << x << ' '; cout << endl;

    ST.init(a);

    ans = max(ans, arr[cycle[0]] + ST.get(2, n));

    for (int i = 1; i < n; i++){
        int v = cycle[i], u = cycle[i - 1];
        ST.add(1, n, -A(v, u));
        ST.add(i, i, sum);

        ans = max(ans, arr[v] + max(ST.get(1, i), ST.get(i + 2, n)));

//        for (int j = 1; j <= n; j++) cout << ST.get(j, j) << ' '; cout << endl;
    }

    return ans;
}

void solve(int TC) {
    int n;
    cin >> n;

    iota(parent + 1, parent + n + 1, 1);

    for (int i = 1; i <= n; i++){
        cin >> f[i] >> w[i];
        unite(i, f[i]);
        if (f[f[i]] != i){
            g[i].emplace_back(f[i], w[i]);
            g[f[i]].emplace_back(i, w[i]);
        }
    }

    set<int> comp;

    ll ans = 0;
    for (int i = 1; i <= n; i++){
        if (comp.find(find(i)) == comp.end()){
            comp.insert(find(i));
            ll cur = component(i);
            ans += cur;
        }
    }

    cout << ans;

}

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

#ifdef dddxxz
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif

    int TC = 1;
//    cin >> TC;

    for (int test = 1; test <= TC; test++) {
        //debug(test);
        //cout << "Case #" << test << ": ";
        solve(test);
    }

    return 0;
}

Compilation message (stderr)

islands.cpp: In member function 'void SegTree::init(std::vector<long long int>&)':
islands.cpp:112:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  112 |         while (size < a.size()) size *= 2;
      |                ~~~~~^~~~~~~~~~

• Subtask 1: 33 / 33
• Subtask 2: 3 / 3
• Subtask 3: 4 / 4
• Subtask 4: 10 / 10
• Subtask 5: 10 / 10
• Subtask 6: 10 / 10
• Subtask 7: 10 / 10
• Subtask 8: 0 / 10
• Subtask 9: 0 / 10