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Submission #1085227

# Submission time Handle Problem Language Result Execution time Memory
1085227 2024-09-07T17:37:56 Z vladilius Meetings (IOI18_meetings) C++17
60 / 100
 5500 ms 503004 KB 
#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pll = pair<ll, ll>;
#define pb push_back
#define ff first
#define ss second
#define ins insert
#define arr3 array<int, 3>
const ll inf = 1e18;
const int N = 7.5e5;

struct DS{
    struct line{
        int k; ll b;
        ll operator ()(int x){
            return 1LL * k * x + b;
        }
        line(int ks, ll bs){
            k = ks; b = bs;
        }
    };
    pair<int, ll> t[4 * N];
    pll p[4 * N];
    int n;
    DS(int ns){
        n = ns;
        for (int i = 0; i < 4 * n; i++){
            t[i] = {0, inf};
            p[i] = {0, 0};
        }
    }
    void apply(int v, pll x){
        t[v].ff += x.ff; t[v].ss += x.ss;
        p[v].ff += x.ff; p[v].ss += x.ss;
    }
    void push1(int& v, int& tl, int& tr){
        int vv = 2 * v;
        apply(vv, p[v]); apply(vv + 1, p[v]);
        p[v] = {0, 0};
    }
    void push2(int& v, int& tl, int& tr){
        int vv = 2 * v, tm = (tl + tr) / 2;
        insert(vv, tl, tm, t[v]);
        insert(vv + 1, tm + 1, tr, t[v]);
        t[v] = {0, inf};
    }
    void insert(int v, int tl, int tr, pil f){
        if (tl == tr){
            if ((1LL * t[v].ff * tl + t[v].ss) > (1LL * f.ff * tl + f.ss)) t[v] = f;
            return;
        }
        int tm = (tl + tr) / 2, vv = 2 * v;
        push1(v, tl, tr);
        if (t[v].ff > f.ff) swap(t[v], f);
        if ((1LL * f.ff * tm + f.ss) <= (1LL * t[v].ff * tm + t[v].ss)){
            swap(t[v], f);
            insert(vv + 1, tm + 1, tr, f);
        }
        else {
            insert(vv, tl, tm, f);
        }
    }
    void chmin(int v, int tl, int tr, int& l, int& r, pil& f){
        if (l > tr || r < tl) return;
        if (l <= tl && tr <= r){
            insert(v, tl, tr, f);
            return;
        }
        int tm = (tl + tr) / 2, vv = 2 * v;
        push1(v, tl, tr);
        chmin(vv, tl, tm, l, r, f);
        chmin(vv + 1, tm + 1, tr, l, r, f);
    }
    void chmin(int l, int r, int k, ll b){
        pil f = {k, b};
        chmin(1, 1, n, l, r, f);
    }
    void add(int v, int tl, int tr, int& l, int& r, pil& f){
        if (l > tr || r < tl) return;
        if (l <= tl && tr <= r){
            apply(v, {f.ff, f.ss});
            return;
        }
        int tm = (tl + tr) / 2, vv = 2 * v;
        push1(v, tl, tr);
        push2(v, tl, tr);
        add(vv, tl, tm, l, r, f);
        add(vv + 1, tm + 1, tr, l, r, f);
    }
    void add(int l, int r, int k, ll b){
        pil f = {k, b};
        add(1, 1, n, l, r, f);
    }
    ll get(int v, int tl, int tr, int& x){
        if (tl == tr) return (1LL * t[v].ff * x + t[v].ss);
        int tm = (tl + tr) / 2, vv = 2 * v;
        push1(v, tl, tr);
        if (x <= tm){
            return min((1LL * t[v].ff * x + t[v].ss), get(vv, tl, tm, x));
        }
        return min((1LL * t[v].ff * x + t[v].ss), get(vv + 1, tm + 1, tr, x));
    }
    ll get(int x){
        return get(1, 1, n, x);
    }
};

vector<ll> minimum_costs(vector<int> H, vector<int> L, vector<int> R){
    const int A = 1e9;

    int n = (int) H.size(), q = (int) L.size();
    vector<int> h(n + 1), aa;
    for (int i = 1; i <= n; i++){
        h[i] = H[i - 1];
        aa.pb(h[i]);
    }
    
    sort(aa.begin(), aa.end());
    vector<int> vv;
    int i = 0;
    while (i < n){
        int j = i;
        while (j < n && aa[i] == aa[j]){
            j++;
        }
        vv.pb(aa[i]);
        i = j;
    }
    
    vector<int> :: iterator it;
    auto pos = [&](int x){
        it = lower_bound(vv.begin(), vv.end(), x);
        int j = (int) (it - vv.begin());
        return j;
    };
    
    vector<int> d[(int) vv.size()];
    for (int i = 1; i <= n; i++){
        d[pos(h[i])].pb(i);
    }
    
    vector<int> log(n + 1);
    for (int i = 2; i <= n; i++) log[i] = log[i / 2] + 1;
    const int lg = log[n];
    vector<vector<int>> pw(n + 1, vector<int>(lg + 1)), pw1(n + 1, vector<int>(lg + 1, A));
    for (int i = 1; i <= n; i++) pw[i][0] = pw1[i][0] = h[i];
    for (int j = 1; j <= lg; j++){
        for (int i = 1; i + (1 << j) <= n + 1; i++){
            pw[i][j] = max(pw[i][j - 1], pw[i + (1 << (j - 1))][j - 1]);
            pw1[i][j] = min(pw1[i][j - 1], pw1[i + (1 << (j - 1))][j - 1]);
        }
    }
    
    auto get = [&](int l, int r){
        int k = log[r - l + 1];
        return max(pw[l][k], pw[r - (1 << k) + 1][k]);
    };
    
    auto getm = [&](int l, int r){
        int k = log[r - l + 1];
        return min(pw1[l][k], pw1[r - (1 << k) + 1][k]);
    };
    
    vector<int> f;
    auto pp = [&](int x, int l, int r){
        f.clear();
        int X = pos(x);
        it = lower_bound(d[X].begin(), d[X].end(), l);
        while (it != d[X].end() && (*it) <= r){
            f.pb((*it));
            it++;
        }
    };
    
    vector<pii> all1;
    auto gp = [&](int x, int l, int r){
        pp(x, l, r);
        all1.clear();
        int pre = l;
        for (int i: f){
            if (pre < i){
                all1.pb({pre, i - 1});
            }
            pre = i + 1;
        }
        if (pre <= r) all1.pb({pre, r});
    };
    
    vector<pii> mp[(int) vv.size()];
    function<void(int, int)> build1 = [&](int l, int r){
        int m = get(l, r);
        mp[pos(m)].pb({l, r});
        
        gp(m, l, r);
        vector<pii> all = all1;
        
        for (auto [l1, r1]: all){
            build1(l1, r1);
        }
    };
    build1(1, n);
    
    vector<ll> out(q + 1);
    map<pii, vector<arr3>> qs;
    for (int i = 1; i <= q; i++){
        int l, r;
        l = L[i - 1]; r = R[i - 1];
        l++; r++;
        
        if (get(l, r) == getm(l, r)){
            out[i] = 1LL * h[l] * (r - l + 1);
            continue;
        }
        int k = pos(get(l, r)), l1 = 0, r1 = (int) mp[k].size() - 1;
        while (l1 + 1 < r1){
            int m = (l1 + r1) / 2;
            if (mp[k][m].ff <= l){
                l1 = m;
            }
            else {
                r1 = m - 1;
            }
        }
        if (mp[k][r1].ff <= l) l1 = r1;
        
        qs[mp[k][l1]].pb({l, r, i});
    }

    DS T1(n), T2(n);
    vector<int> :: iterator it1, it2;
    function<void(int, int)> build = [&](int l, int r){
        int m = get(l, r);
        
        gp(m, l, r);
        vector<pii> all = all1;
        
        for (auto [l1, r1]: all) build(l1, r1);
        
        if (all.empty()){
            T1.add(l, r, m, -1LL * m * (l - 1));
            T2.add(l, r, -m, 1LL * m * (r + 1));
        }
                
        for (auto [l1, r1]: all){
            int m1 = get(l1, r1);
            gp(m1, l1, r1);
            ll mn = inf;
            for (auto [l2, r2]: all1){
                // f(l1, i) = min(mn + m1 * (i - l1), f(l2, i) + m1 * (l2 - l1));
                ll F = T1.get(r2);
                T1.add(l2, r2, 0, 1LL * m1 * (l2 - l1));

                if (mn != inf) T1.chmin(l2, r2, m1, mn - 1LL * m1 * l1);
                
                mn = min(mn, F - 1LL * m1 * (r2 - l2));
            }
            
            reverse(all1.begin(), all1.end());
            mn = inf;
            for (auto [l2, r2]: all1){
                // f(i, r1) = min(mn + m1 * (r1 - i), f(i, r2) + m1 * (r1 - r2));
                ll F = T2.get(l2);
                T2.add(l2, r2, 0, 1LL * m1 * (r1 - r2));
                
                if (mn != inf) T2.chmin(l2, r2, -m1, mn + 1LL * m1 * r1);
                
                mn = min(mn, F - 1LL * m1 * (r2 - l2));
            }
            
            pp(m1, l1, r1);
            for (int i: f){
                T1.add(i, i, 0, -T1.get(i));
                ll mn = 1LL * m1 * (i - l1 + 1);
                if (i != l1) mn = min(mn, T1.get(i - 1) + m1);
                T1.add(i, i, 0, mn);
            }
            reverse(f.begin(), f.end());
            for (int i: f){
                T2.add(i, i, 0, -T2.get(i));
                ll mn = 1LL * m1 * (r1 - i + 1);
                if (i != r1) mn = min(mn, T2.get(i + 1) + m1);
                T2.add(i, i, 0, mn);
            }
        }
        
        if (all.empty()) return;
        
        vector<int> x1, y1;
        for (auto [l1, r1]: all){
            x1.pb(l1); y1.pb(r1);
        }
        int N = (int) all.size(), LG = log2(N);
        vector<vector<ll>> sp(N + 1, vector<ll>(LG + 1, inf));
        for (int i = 1; i <= N; i++) sp[i][0] = (T1.get(all[i - 1].ss) - 1LL * m * (all[i - 1].ss - all[i - 1].ff));
        for (int j = 1; j <= LG; j++){
            for (int i = 1; i + (1 << j) <= N + 1; i++){
                sp[i][j] = min(sp[i][j - 1], sp[i + (1 << (j - 1))][j - 1]);
            }
        }
        
        auto gets = [&](int l, int r){
            if (l > r) return inf;
            int k = log[r - l + 1];
            return min(sp[l][k], sp[r - (1 << k) + 1][k]);
        };
        
        for (auto [ql, qr, i]: qs[{l, r}]){
            it1 = lower_bound(x1.begin(), x1.end(), ql);
            it2 = upper_bound(y1.begin(), y1.end(), qr); it2--;
            
            int i1 = (int) (it1 - x1.begin()), i2 = (int) (it2 - y1.begin());
            out[i] = gets(i1 + 1, i2 + 1);
            if (out[i] != inf) out[i] += 1LL * m * (qr - ql);
            
            if (i1 > 0){
                i1--;
                if (all[i1].ss >= ql){
                    out[i] = min(out[i], T2.get(ql) + 1LL * m * (qr - all[i1].ss));
                }
            }
            if (it2 != prev(y1.end())){
                i2++;
                if (all[i2].ff <= qr){
                    out[i] = min(out[i], T1.get(qr) + 1LL * m * (all[i2].ff - ql));
                }
            }
        }
    };
    build(1, n);

    vector<ll> ret;
    for (int i = 1; i <= q; i++) ret.pb(out[i]);
    return ret;
}

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 89 ms 188076 KB Output is correct
2 Correct 117 ms 189164 KB Output is correct
3 Correct 128 ms 189344 KB Output is correct
4 Correct 123 ms 189152 KB Output is correct
5 Correct 114 ms 189224 KB Output is correct
6 Correct 106 ms 189012 KB Output is correct
7 Correct 126 ms 189296 KB Output is correct
8 Correct 103 ms 188752 KB Output is correct
9 Correct 108 ms 188632 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 89 ms 188076 KB Output is correct
2 Correct 117 ms 189164 KB Output is correct
3 Correct 128 ms 189344 KB Output is correct
4 Correct 123 ms 189152 KB Output is correct
5 Correct 114 ms 189224 KB Output is correct
6 Correct 106 ms 189012 KB Output is correct
7 Correct 126 ms 189296 KB Output is correct
8 Correct 103 ms 188752 KB Output is correct
9 Correct 108 ms 188632 KB Output is correct
10 Correct 146 ms 190292 KB Output is correct
11 Correct 135 ms 190288 KB Output is correct
12 Correct 138 ms 190372 KB Output is correct
13 Correct 134 ms 190324 KB Output is correct
14 Correct 128 ms 190372 KB Output is correct
15 Correct 135 ms 189648 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 120 ms 188240 KB Output is correct
2 Correct 140 ms 192344 KB Output is correct
3 Correct 638 ms 219192 KB Output is correct
4 Correct 881 ms 216204 KB Output is correct
5 Correct 657 ms 218028 KB Output is correct
6 Correct 515 ms 215636 KB Output is correct
7 Correct 504 ms 215772 KB Output is correct

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 120 ms 188240 KB Output is correct
2 Correct 140 ms 192344 KB Output is correct
3 Correct 638 ms 219192 KB Output is correct
4 Correct 881 ms 216204 KB Output is correct
5 Correct 657 ms 218028 KB Output is correct
6 Correct 515 ms 215636 KB Output is correct
7 Correct 504 ms 215772 KB Output is correct
8 Correct 1307 ms 221240 KB Output is correct
9 Correct 1319 ms 221208 KB Output is correct
10 Correct 1336 ms 221248 KB Output is correct
11 Correct 1380 ms 221124 KB Output is correct
12 Correct 1344 ms 221088 KB Output is correct
13 Correct 1370 ms 221248 KB Output is correct
14 Correct 714 ms 224744 KB Output is correct
15 Correct 1472 ms 220996 KB Output is correct
16 Correct 856 ms 216612 KB Output is correct

Subtask #5
0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 89 ms 188076 KB Output is correct
2 Correct 117 ms 189164 KB Output is correct
3 Correct 128 ms 189344 KB Output is correct
4 Correct 123 ms 189152 KB Output is correct
5 Correct 114 ms 189224 KB Output is correct
6 Correct 106 ms 189012 KB Output is correct
7 Correct 126 ms 189296 KB Output is correct
8 Correct 103 ms 188752 KB Output is correct
9 Correct 108 ms 188632 KB Output is correct
10 Correct 146 ms 190292 KB Output is correct
11 Correct 135 ms 190288 KB Output is correct
12 Correct 138 ms 190372 KB Output is correct
13 Correct 134 ms 190324 KB Output is correct
14 Correct 128 ms 190372 KB Output is correct
15 Correct 135 ms 189648 KB Output is correct
16 Correct 120 ms 188240 KB Output is correct
17 Correct 140 ms 192344 KB Output is correct
18 Correct 638 ms 219192 KB Output is correct
19 Correct 881 ms 216204 KB Output is correct
20 Correct 657 ms 218028 KB Output is correct
21 Correct 515 ms 215636 KB Output is correct
22 Correct 504 ms 215772 KB Output is correct
23 Correct 1307 ms 221240 KB Output is correct
24 Correct 1319 ms 221208 KB Output is correct
25 Correct 1336 ms 221248 KB Output is correct
26 Correct 1380 ms 221124 KB Output is correct
27 Correct 1344 ms 221088 KB Output is correct
28 Correct 1370 ms 221248 KB Output is correct
29 Correct 714 ms 224744 KB Output is correct
30 Correct 1472 ms 220996 KB Output is correct
31 Correct 856 ms 216612 KB Output is correct
32 Execution timed out 5529 ms 503004 KB Time limit exceeded
33 Halted 0 ms 0 KB -