oj.uz

Submission #366673

# Submission time Handle Problem Language Result Execution time Memory
366673 2021-02-14T23:13:43 Z 12tqian Constellation 3 (JOI20_constellation3) C++17
100 / 100
 1222 ms 96080 KB 
#include <bits/stdc++.h>

using namespace std;

#define f1r(i, a, b) for (int i = a; i < b; ++i)
#define f0r(i, a) f1r(i, 0, a)
#define each(t, a) for (auto& t : a)

#define mp make_pair
#define f first
#define s second
#define pb push_back
#define eb emplace_back
#define sz(x) (int) (x).size()
#define all(x) begin(x), end(x)

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;

template <class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template <class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }

const int INF = 1e9;

struct IntervalUnion {
    std::set<std::pair<int, int>> le, ri;

    void reset() {
        le.clear();
        ri.clear();
    }

    // inserts an interval while returning the intervals it intersected with
    std::vector<std::pair<int, int>> insert(std::pair<int, int> x) {
        std::set<std::pair<int, int>> bad;
        std::vector<std::pair<int, int>> ret;
        std::pair<int, int> use1 = std::make_pair(x.first, -INF), use2 = std::make_pair(x.second, INF);
        auto it1 = le.lower_bound(use1);
        auto it2 = ri.lower_bound(use2);
        if (it2 != ri.end()) {
            int lo = (*it2).second, hi = (*it2).first;
            if (lo <= x.first && x.second <= hi) {
                ret.emplace_back(std::make_pair(lo, hi));
                int mn = x.first, mx = x.second;
                for (auto b: ret) {
                    le.erase(b); ri.erase(std::make_pair(b.second, b.first));
                    mn = std::min(mn, b.first); mx = std::max(mx, b.second);
                }
                le.insert(std::make_pair(mn, mx)); ri.insert(std::make_pair(mx, mn));
                return ret;
            }
        }
        if (it1 != le.end()) {
            while (it1 != le.end()) {
                auto val = (*it1);
                if (val.first <= x.second) bad.insert(val);
                else break;
                it1 = next(it1);
            }
        }
        if (it2 != ri.begin()) {
            it2 = prev(it2);
            while (true) {
                auto val = (*it2);
                if (val.first >= x.first) bad.insert(std::make_pair(val.second, val.first));
                else break;
                if (it2 == ri.begin()) break;
                it2 = prev(it2);
            }
        }
        for (auto b: bad) ret.emplace_back(b);
        int mn = x.first, mx = x.second;
        for (auto b: ret) {
            le.erase(b); ri.erase(std::make_pair(b.second, b.first));
            mn = std::min(mn, b.first); mx = std::max(mx, b.second);
        }
        le.insert(std::make_pair(mn, mx)); ri.insert(std::make_pair(mx, mn));
        return ret;
    }
};

template <class T> struct SparseTable {
    std::vector<T> v;
    std::vector<std::vector<int>> jump;

    int level(int x) { return 31 - __builtin_clz(x); }

    int comb(int a, int b) {
        return v[a] == v[b] ? std::min(a, b) : (v[a] > v[b] ? a : b);
    }

    void init(const std::vector<T>& _v) {
        v = _v;
        jump = {std::vector<int>((int) v.size())};
        iota(jump[0].begin(), jump[0].end(), 0);
        for (int j = 1; (1 << j) <= (int) v.size(); j++) {
            jump.push_back(std::vector<int>((int) v.size() - (1 << j) + 1));
            for (int i = 0; i < (int) jump[j].size(); i++) {
                jump[j][i] = comb(jump[j - 1][i], jump[j - 1][i + (1 << (j - 1))]);
            }
        }
    }

    int index(int l, int r) {
        assert(l <= r);
        int d = level(r - l + 1);
        return comb(jump[d][l], jump[d][r - (1 << d) + 1]);
    }

    T query(int l, int r) {
        return v[index(l, r)];
    }
};


template <class T> struct LazySeg {
    std::vector<T> sum, lazy;
    int sz;

    void init(int sz_) {
        sz = 1;
        while (sz < sz_) sz *= 2;
        sum.assign(2 * sz, 0);
        lazy.assign(2 * sz, 0);
    }

    void push(int ind, int L, int R) {
        sum[ind] += (R - L + 1) * lazy[ind];
        if (L != R) {
            lazy[2 * ind] += lazy[ind];
            lazy[2 * ind + 1] += lazy[ind];
        }
        lazy[ind] = 0;
    }

    void pull(int ind) {
        sum[ind] = sum[2 * ind] + sum[2 * ind + 1];
    }

    void build() {
        for (int i = sz - 1; i >= 1; i--) {
            pull(i);
        }
    }

    void upd(int lo, int hi, T inc, int ind = 1, int L = 0, int R = -1) {
        if (R == -1) R += sz;
        push(ind, L, R);
        if (hi < L || R < lo) return ;
        if (lo <= L && R <= hi) {
            lazy[ind] = inc;
            push(ind, L, R);
            return;
        }
        int M = (L + R) / 2;
        upd(lo, hi, inc, 2 * ind, L, M);
        upd(lo, hi, inc, 2 * ind + 1, M + 1, R);
        pull(ind);
    }

    T qsum(int lo, int hi, int ind = 1, int L = 0, int R = -1) {
        if (R == -1) R += sz;
        push(ind, L, R);
        if (lo > R || L > hi) return 0;
        if (lo <= L && R <= hi) return sum[ind];
        int M = (L + R) / 2;
        return qsum(lo, hi, 2 * ind, L, M) + qsum(lo, hi, 2 * ind + 1, M + 1, R);
    }
};

const bool VALUES_IN_VERTICES = true;

template <class T> class HeavyLight {
    std::vector<int> parent, heavy, depth, root, tree_pos;
    int ti = 0;
    vpi ranges;
    LazySeg<T> tree;
    LazySeg<T> subtree;

    template <class G> int dfs(const G& graph, int v) {
        int size = 1, max_subtree = 0;
        ranges[v].f = ti++;
        for (int u : graph[v]) if (u != parent[v]) {
            parent[u] = v;
            depth[u] = depth[v] + 1;
            int subtree = dfs(graph, u);
            if (subtree > max_subtree) heavy[v] = u, max_subtree = subtree;
            size += subtree;
        }
        ranges[v].s = ti - 1;
        return size;
    }

    template <class B> void process_path(int u, int v, B op) {
        for (; root[u] != root[v]; v = parent[root[v]]) {
            if (depth[root[u]] > depth[root[v]]) std::swap(u, v);
            op(tree_pos[root[v]], tree_pos[v]);
        }
        if (depth[u] > depth[v]) std::swap(u, v);
        op(tree_pos[u] + (VALUES_IN_VERTICES ? 0 : 1), tree_pos[v]);
    }

public:
    template <class G>
    void init(const G& graph, vi roots) {
        int n = (int) graph.size();
        heavy.assign(n, -1);
        parent.assign(n, 0);
        depth.assign(n, 0);
        root.assign(n, 0);
        tree_pos.assign(n, 0);
        ranges.resize(n);
        tree.init(n);
        subtree.init(n);
        each(r, roots) {
            parent[r] = -1;
            depth[r] = 0;
            dfs(graph, r);
        }   
        for (int i = 0, current_pos = 0; i < n; ++i)
            if (parent[i] == -1 || heavy[parent[i]] != i)
            for (int j = i; j != -1; j = heavy[j]) {
                root[j] = i;
                tree_pos[j] = current_pos++;
            }
    }

    void modify_path(int u, int v, const T& value) {
        process_path(u, v, [this, &value](int l, int r) { tree.upd(l, r, value); });
    }

    T query_path(int u, int v) {
        T res = 0;
        process_path(u, v, [this, &res](int l, int r) { res += tree.qsum(l, r); });
        return res;
    }
};

template <class T> struct RangeSetSeg {
    const T UNUSED = -1;
    std::vector<T> sum, lazy;
    int sz;

    // lazy stores what to set to
    void init(int sz_) {
        sz = 1;
        while (sz < sz_) sz *= 2;
        sum.assign(2 * sz, 0);
        lazy.assign(2 * sz, UNUSED);
    }

    void push(int ind, int L, int R) {
        if (L != R) {
            if(lazy[ind] != UNUSED){
                for(int i = 0; i < 2; i++){
                    lazy[2 * ind + i] = lazy[ind];
                }
            }
        }
        if (lazy[ind] != UNUSED) sum[ind] = (R - L + 1) * lazy[ind];
        lazy[ind] = UNUSED;
    }

    void pull(int ind) { sum[ind] = sum[2 * ind] + sum[2 * ind + 1]; }

    void range_set(int lo, int hi, T inc, int ind = 1, int L = 0, int R = -1) {
        if (R == -1) R += sz;
        push(ind, L, R);
        if (hi < L || R < lo) return;
        if (lo <= L && R <= hi) {
            lazy[ind] = inc;
            push(ind, L, R); return;
        }
        int M = (L + R) / 2;
        range_set(lo, hi, inc, 2 * ind, L, M); range_set(lo, hi, inc, 2 * ind + 1, M + 1, R);
        pull(ind);
    }

    T qsum(int lo, int hi, int ind = 1, int L = 0, int R = -1) {
        if (R == -1) R += sz;
        push(ind, L, R); if (lo > R || L > hi) return 0;
        if (lo <= L && R <= hi) return sum[ind];
        int M = (L + R) / 2;
        return qsum(lo, hi, 2 * ind, L, M) + qsum(lo, hi, 2 * ind + 1, M + 1, R);
    }
};

int main() {
    cin.tie(0)->sync_with_stdio(0);
    int n, m;
    cin >> n;
    vi a(n);
    f0r(i, n) cin >> a[i], a[i]--;
    SparseTable<int> ST;
    ST.init(a);
    cin >> m;
    vector<array<int, 4>> ivals;
    f0r(i, m) {
        int x, y, c; 
        cin >> x >> y >> c;
        x--;
        y--;
        int L, R;
        int lo = 0;
        int hi = x;
        while (hi - lo > 1) {
            int mid = (lo + hi) >> 1;
            if (ST.query(mid, x) < y) hi = mid;
            else lo = mid + 1;
        }
        if (ST.query(lo, x) < y) L = lo;
        else L = hi;
        lo = x;
        hi = n - 1;
        while (hi - lo > 1) {
            int mid = (lo + hi) >> 1;
            if (ST.query(x, mid) < y) lo = mid;
            else hi = mid - 1;
        }
        if (ST.query(x, hi) < y) R = hi;
        else R = lo;
        ivals.pb({L, R, c, x});
        // cout << L << " IVAL " << R << endl;
    }
    IntervalUnion IU;
    vector<pi> nodes;
    f0r(i, m) {
        nodes.pb({ivals[i][0], ivals[i][1]});
    }
    sort(all(nodes));
    nodes.erase(unique(all(nodes)), nodes.end());
    int sz = sz(nodes);
    vector<vi> in(sz), out(sz), g(sz);
    vl c(m);
    f0r(i, m) {
        c[i] = ivals[i][2];
    }
    sort(all(ivals), [](array<int, 4> a, array<int, 4> b) {
        return a[1] - a[0] < b[1] - b[0];
    });
    auto get_pos = [&](pi x) {
        return lower_bound(all(nodes), x) - nodes.begin();
    };
    // cout << "EDGE -------------------" << endl;
    f0r(i, m) {
        int l = ivals[i][0];
        int r = ivals[i][1];
        auto res = IU.insert({l, r});
        int oi = get_pos({l, r});
        each(ii, res) {
            int ni = get_pos(ii);
            if (ni == oi) continue;
            out[oi].pb(ni);
            in[ni].pb(oi);
            // cout << oi << " " << ni << endl;
            g[oi].pb(ni);
            g[ni].pb(oi);
        }
    }
    // cout << "---------------" << endl;
    vector<vpi> tags(sz); // pair of bad, cost

    f0r(i, m) { 
        int id = get_pos({ivals[i][0], ivals[i][1]});
        tags[id].eb(ivals[i][3], ivals[i][2]);
    }
    vi roots;
    f0r(i, sz) {
        if (sz(in[i]) == 0) {
            roots.pb(i);
        }
        // cout << i << " IN: ";
        // each(x, in[i]) cout << x << " ";
        // cout << endl;
        // cout << i << " OUT: ";
        // each(x, out[i]) cout << x << " ";
        // cout << endl;
        // cout << "---------------" << endl;
    }
    HeavyLight<ll> H, P;
    H.init(g, roots);
    P.init(g, roots);
    vi rev(n);
    RangeSetSeg<int> range_seg;
    range_seg.init(n);
    // f0r(i, sz(nodes)) {
    //     cout << i << ": " << nodes[i].f << " " << nodes[i].s << " NODE" << endl;
    // }
    vi par(sz);
    function<void(int)> dfs_tags = [&](int u) {
        range_seg.range_set(nodes[u].f, nodes[u].s, u);
        each(v, out[u]) {
            dfs_tags(v);
            par[v] = u;
        }
    };
    each(r, roots) {
        par[r] = -1;
        dfs_tags(r);
    }
    f0r(i, n) {
        rev[i] = range_seg.qsum(i, i);
    }

    f0r(i, sz) {
        // cout << i <<  ": ";
        each(tag, tags[i]) {
            tag.f = rev[tag.f];
            // cout << tag.f << " " << tag.s << endl;
        }
        // cout << "-----------" << endl;
    }
    vl dp(sz);
    function<void(int)> dfs = [&](int u) {
        ll best = 0;
        each(v, out[u]) {
            dfs(v);
            best += H.query_path(v, v);
        }
        each(tag, tags[u]) {
            int bad = tag.f;
            int cost = tag.s;
            // cout << u << " " << bad << " " << sz << endl;
            ll val = P.query_path(u, bad);            
            // if (u == 0 && cost == 8) {
            //     cout << val <<" VAL " << endl;
            // }
            if (u != bad) {
                val -= (H.query_path(u, bad) - dp[u]);
            }
            val += cost;
            ckmax(best, val);
        }

        dp[u] = best;
        // cout << "DP: " << u << " " << best << endl;
        H.modify_path(u, u, best);
        if (par[u] != -1) P.modify_path(par[u], par[u], best);
    };
    ll res = 0;
    each(r, roots) {
        dfs(r);
        res += dp[r];
        // cout << dp[r] << " HUUH" << endl;
    }
    ll ans = 0;
    each(e, c) ans += e;
    ans -= res;
    cout << ans << '\n';
    return 0;
}

/**
 * Each star has an interval
 * intervals can't partial intersect, must fully contain
 * you want no intersecting intervals
 * min cost to make no intersecting intervals
 * each interval has a cost
 * each interval is like in a tree structure right
 * 
 */

Subtask #1
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB Output is correct
2 Correct 1 ms 492 KB Output is correct
3 Correct 1 ms 492 KB Output is correct
4 Correct 2 ms 492 KB Output is correct
5 Correct 1 ms 492 KB Output is correct
6 Correct 1 ms 492 KB Output is correct
7 Correct 1 ms 492 KB Output is correct
8 Correct 1 ms 492 KB Output is correct
9 Correct 2 ms 492 KB Output is correct
10 Correct 1 ms 492 KB Output is correct
11 Correct 1 ms 492 KB Output is correct
12 Correct 1 ms 492 KB Output is correct
13 Correct 1 ms 512 KB Output is correct
14 Correct 1 ms 364 KB Output is correct
15 Correct 2 ms 364 KB Output is correct
16 Correct 1 ms 492 KB Output is correct
17 Correct 1 ms 492 KB Output is correct
18 Correct 1 ms 492 KB Output is correct
19 Correct 1 ms 364 KB Output is correct
20 Correct 1 ms 364 KB Output is correct
21 Correct 1 ms 492 KB Output is correct
22 Correct 1 ms 364 KB Output is correct

Subtask #2
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB Output is correct
2 Correct 1 ms 492 KB Output is correct
3 Correct 1 ms 492 KB Output is correct
4 Correct 2 ms 492 KB Output is correct
5 Correct 1 ms 492 KB Output is correct
6 Correct 1 ms 492 KB Output is correct
7 Correct 1 ms 492 KB Output is correct
8 Correct 1 ms 492 KB Output is correct
9 Correct 2 ms 492 KB Output is correct
10 Correct 1 ms 492 KB Output is correct
11 Correct 1 ms 492 KB Output is correct
12 Correct 1 ms 492 KB Output is correct
13 Correct 1 ms 512 KB Output is correct
14 Correct 1 ms 364 KB Output is correct
15 Correct 2 ms 364 KB Output is correct
16 Correct 1 ms 492 KB Output is correct
17 Correct 1 ms 492 KB Output is correct
18 Correct 1 ms 492 KB Output is correct
19 Correct 1 ms 364 KB Output is correct
20 Correct 1 ms 364 KB Output is correct
21 Correct 1 ms 492 KB Output is correct
22 Correct 1 ms 364 KB Output is correct
23 Correct 6 ms 876 KB Output is correct
24 Correct 6 ms 1004 KB Output is correct
25 Correct 7 ms 1024 KB Output is correct
26 Correct 6 ms 1004 KB Output is correct
27 Correct 6 ms 1004 KB Output is correct
28 Correct 7 ms 1004 KB Output is correct
29 Correct 7 ms 1024 KB Output is correct
30 Correct 7 ms 1004 KB Output is correct
31 Correct 6 ms 1004 KB Output is correct
32 Correct 6 ms 1004 KB Output is correct
33 Correct 5 ms 1004 KB Output is correct
34 Correct 5 ms 1132 KB Output is correct
35 Correct 5 ms 876 KB Output is correct
36 Correct 3 ms 620 KB Output is correct
37 Correct 3 ms 620 KB Output is correct
38 Correct 5 ms 1132 KB Output is correct
39 Correct 6 ms 768 KB Output is correct
40 Correct 6 ms 1132 KB Output is correct
41 Correct 5 ms 748 KB Output is correct
42 Correct 6 ms 768 KB Output is correct
43 Correct 5 ms 1152 KB Output is correct
44 Correct 5 ms 748 KB Output is correct

Subtask #3
65.0 / 65.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB Output is correct
2 Correct 1 ms 492 KB Output is correct
3 Correct 1 ms 492 KB Output is correct
4 Correct 2 ms 492 KB Output is correct
5 Correct 1 ms 492 KB Output is correct
6 Correct 1 ms 492 KB Output is correct
7 Correct 1 ms 492 KB Output is correct
8 Correct 1 ms 492 KB Output is correct
9 Correct 2 ms 492 KB Output is correct
10 Correct 1 ms 492 KB Output is correct
11 Correct 1 ms 492 KB Output is correct
12 Correct 1 ms 492 KB Output is correct
13 Correct 1 ms 512 KB Output is correct
14 Correct 1 ms 364 KB Output is correct
15 Correct 2 ms 364 KB Output is correct
16 Correct 1 ms 492 KB Output is correct
17 Correct 1 ms 492 KB Output is correct
18 Correct 1 ms 492 KB Output is correct
19 Correct 1 ms 364 KB Output is correct
20 Correct 1 ms 364 KB Output is correct
21 Correct 1 ms 492 KB Output is correct
22 Correct 1 ms 364 KB Output is correct
23 Correct 6 ms 876 KB Output is correct
24 Correct 6 ms 1004 KB Output is correct
25 Correct 7 ms 1024 KB Output is correct
26 Correct 6 ms 1004 KB Output is correct
27 Correct 6 ms 1004 KB Output is correct
28 Correct 7 ms 1004 KB Output is correct
29 Correct 7 ms 1024 KB Output is correct
30 Correct 7 ms 1004 KB Output is correct
31 Correct 6 ms 1004 KB Output is correct
32 Correct 6 ms 1004 KB Output is correct
33 Correct 5 ms 1004 KB Output is correct
34 Correct 5 ms 1132 KB Output is correct
35 Correct 5 ms 876 KB Output is correct
36 Correct 3 ms 620 KB Output is correct
37 Correct 3 ms 620 KB Output is correct
38 Correct 5 ms 1132 KB Output is correct
39 Correct 6 ms 768 KB Output is correct
40 Correct 6 ms 1132 KB Output is correct
41 Correct 5 ms 748 KB Output is correct
42 Correct 6 ms 768 KB Output is correct
43 Correct 5 ms 1152 KB Output is correct
44 Correct 5 ms 748 KB Output is correct
45 Correct 1213 ms 74200 KB Output is correct
46 Correct 1191 ms 73560 KB Output is correct
47 Correct 1222 ms 73992 KB Output is correct
48 Correct 1190 ms 73600 KB Output is correct
49 Correct 1164 ms 72976 KB Output is correct
50 Correct 1143 ms 72560 KB Output is correct
51 Correct 1189 ms 73072 KB Output is correct
52 Correct 1204 ms 74452 KB Output is correct
53 Correct 1178 ms 73436 KB Output is correct
54 Correct 940 ms 86356 KB Output is correct
55 Correct 846 ms 71016 KB Output is correct
56 Correct 792 ms 66176 KB Output is correct
57 Correct 763 ms 62712 KB Output is correct
58 Correct 511 ms 33392 KB Output is correct
59 Correct 497 ms 33652 KB Output is correct
60 Correct 568 ms 96080 KB Output is correct
61 Correct 977 ms 50772 KB Output is correct
62 Correct 886 ms 86156 KB Output is correct
63 Correct 906 ms 45736 KB Output is correct
64 Correct 941 ms 49588 KB Output is correct
65 Correct 906 ms 85864 KB Output is correct
66 Correct 927 ms 44916 KB Output is correct