oj.uz

Submission #366674

# Submission time Handle Problem Language Result Execution time Memory
366674 2021-02-14T23:23:24 Z 12tqian Constellation 3 (JOI20_constellation3) C++17
100 / 100
 1286 ms 91992 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; }
 template <class T> struct IntervalUnion {
    const T INF = std::numeric_limits<T>::max();
    std::set<std::pair<T, T>> le, ri;

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

    // inserts an interval while returning the intervals it intersected with
    std::vector<std::pair<T, T>> insert(std::pair<T, T> x) {
        std::set<std::pair<T, T>> bad;
        std::vector<std::pair<T, T>> ret;
        std::pair<T, T> use1 = {x.first, -INF}, use2 = {x.second, INF};
        auto it1 = le.lower_bound(use1);
        auto it2 = ri.lower_bound(use2);
        if (it2 != ri.end()) {
            T lo = (*it2).second, hi = (*it2).first;
            if (lo <= x.first && x.second <= hi) {
                ret.emplace_back(lo, hi);
                T mn = x.first, mx = x.second;
                for (auto b: ret) {
                    le.erase(b); ri.erase({b.second, b.first});
                    mn = std::min(mn, b.first); mx = std::max(mx, b.second);
                }
                le.emplace(mn, mx); ri.emplace(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.emplace(val.second, val.first);
                else break;
                if (it2 == ri.begin()) break;
                it2 = prev(it2);
            }
        }
        for (auto b: bad) ret.emplace_back(b);
        T mn = x.first, mx = x.second;
        for (auto b: ret) {
            le.erase(b); ri.erase({b.second, b.first});
            mn = std::min(mn, b.first); mx = std::max(mx, b.second);
        }
        le.emplace(mn, mx); ri.emplace(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<int> 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 2 ms 492 KB Output is correct
3 Correct 2 ms 492 KB Output is correct
4 Correct 1 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 1 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 1 ms 364 KB Output is correct
16 Correct 2 ms 492 KB Output is correct
17 Correct 1 ms 384 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 2 ms 492 KB Output is correct
3 Correct 2 ms 492 KB Output is correct
4 Correct 1 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 1 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 1 ms 364 KB Output is correct
16 Correct 2 ms 492 KB Output is correct
17 Correct 1 ms 384 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 8 ms 1004 KB Output is correct
25 Correct 6 ms 1004 KB Output is correct
26 Correct 6 ms 1024 KB Output is correct
27 Correct 6 ms 1004 KB Output is correct
28 Correct 7 ms 1004 KB Output is correct
29 Correct 6 ms 1004 KB Output is correct
30 Correct 7 ms 1020 KB Output is correct
31 Correct 7 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 1004 KB Output is correct
35 Correct 6 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 748 KB Output is correct
40 Correct 6 ms 1132 KB Output is correct
41 Correct 5 ms 792 KB Output is correct
42 Correct 8 ms 748 KB Output is correct
43 Correct 6 ms 1132 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 2 ms 492 KB Output is correct
3 Correct 2 ms 492 KB Output is correct
4 Correct 1 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 1 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 1 ms 364 KB Output is correct
16 Correct 2 ms 492 KB Output is correct
17 Correct 1 ms 384 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 8 ms 1004 KB Output is correct
25 Correct 6 ms 1004 KB Output is correct
26 Correct 6 ms 1024 KB Output is correct
27 Correct 6 ms 1004 KB Output is correct
28 Correct 7 ms 1004 KB Output is correct
29 Correct 6 ms 1004 KB Output is correct
30 Correct 7 ms 1020 KB Output is correct
31 Correct 7 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 1004 KB Output is correct
35 Correct 6 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 748 KB Output is correct
40 Correct 6 ms 1132 KB Output is correct
41 Correct 5 ms 792 KB Output is correct
42 Correct 8 ms 748 KB Output is correct
43 Correct 6 ms 1132 KB Output is correct
44 Correct 5 ms 748 KB Output is correct
45 Correct 1223 ms 69336 KB Output is correct
46 Correct 1237 ms 68364 KB Output is correct
47 Correct 1226 ms 68836 KB Output is correct
48 Correct 1247 ms 68664 KB Output is correct
49 Correct 1190 ms 67976 KB Output is correct
50 Correct 1214 ms 67568 KB Output is correct
51 Correct 1286 ms 68080 KB Output is correct
52 Correct 1246 ms 68960 KB Output is correct
53 Correct 1207 ms 68512 KB Output is correct
54 Correct 913 ms 81364 KB Output is correct
55 Correct 852 ms 65956 KB Output is correct
56 Correct 813 ms 61168 KB Output is correct
57 Correct 797 ms 57592 KB Output is correct
58 Correct 544 ms 28604 KB Output is correct
59 Correct 496 ms 28592 KB Output is correct
60 Correct 607 ms 91992 KB Output is correct
61 Correct 1014 ms 46044 KB Output is correct
62 Correct 937 ms 81136 KB Output is correct
63 Correct 951 ms 41220 KB Output is correct
64 Correct 936 ms 45040 KB Output is correct
65 Correct 931 ms 81060 KB Output is correct
66 Correct 1024 ms 40172 KB Output is correct