Submission #879447

#	Time	Username	Problem	Language	Result	Execution time	Memory
879447		kh0i	Discharging (NOI20_discharging)	C++17	100 / 100	143 ms	36580 KiB

Discharging

#include "bits/stdc++.h"
using namespace std;

#ifdef LOCAL
#include "debug.h"
#else
#define debug(...)
#endif

using ll = long long;
using pii = pair<int, int>;

#define F first
#define S second
#define sz(x) (int)((x).size())
#define all(x) (x).begin(), (x).end()

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll get_rand(ll l, ll r) {
    assert(l <= r);
    return uniform_int_distribution<ll> (l, r)(rng);
}

const int N = 1e6 + 3;

#pragma once

struct Node{
    ll val;

    const Node operator + (const Node &other){
        Node res;
        res.val = max(val, other.val);
        return res;
    }
};

struct ST{
    int n;
    vector<Node> st;

    Node def = Node(); // default value

    void init(int _n){
        n = _n;
        st.resize(4 * n + 6, def);
    }

    void _update(int id, int l, int r, int pos, ll val){
        if(l == r){
            st[id].val = val;
            return;
        }

        int m = (l + r) / 2;
        if(l <= pos and pos <= m)
            _update(2 * id, l, m, pos, val);
        else
            _update(2 * id + 1, m + 1, r, pos, val);

        st[id] = st[2 * id] + st[2 * id + 1];
    }

    Node _query(int id, int l, int r, int tl, int tr){
        if(l > tr or tl > r)
            return def;
        if(tl <= l and r <= tr)
            return st[id];
        int m = (l + r) / 2;

        return _query(2 * id,  l, m, tl, tr) + _query(2 * id + 1, m + 1, r, tl, tr);
    }

    Node query(int l, int r){
        return _query(1, 1, n, l, r);
    }

    void update(int pos, ll val){
        _update(1, 1, n, pos, val);
    }
};

int n;
ll a[N], f[N];

namespace Sub14{
    bool valid_input(){
        return n <= 1500;
    }

    void solve(){
        ST dak;
        dak.init(n);
        for(int i = 1; i <= n; ++i)
            dak.update(i, a[i]);

        memset(f, 0x3f3f3f, sizeof(f));
        f[0] = 0;

        for(int i = 1; i <= n; ++i)
            for(int j = 1; j <= i; ++j)
                f[i] = min(f[i], f[j - 1] + 1ll * (n - j + 1) * dak.query(j, i).val);

        cout << f[n];
    }
}

struct Line {
    mutable ll k, m, p;
    bool operator<(const Line& o) const { return k < o.k; }
    bool operator<(ll x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
    // (for doubles, use inf = 1/.0, div(a,b) = a/b)
    static const ll inf = LLONG_MAX;
    ll div(ll a, ll b) { // floored division
        return a / b - ((a ^ b) < 0 && a % b); }
    bool isect(iterator x, iterator y) {
        if (y == end()) return x->p = inf, 0;
        if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
        else x->p = div(y->m - x->m, x->k - y->k);
        return x->p >= y->p;
    }
    void add(ll k, ll m) {
        auto z = insert({k, m, 0}), y = z++, x = y;
        while (isect(y, z)) z = erase(z);
        if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
        while ((y = x) != begin() && (--x)->p >= y->p)
            isect(x, erase(y));
    }
    ll query(ll x) {
        assert(!empty());
        auto l = *lower_bound(x);
        return l.k * x + l.m;
    }
};

namespace Sub2{
    bool valid_input(){
        bool ok = 1;
        for(int i = 2; i <= n; ++i)
            ok &= (a[i] >= a[i - 1]);
        return ok;
    }

    LineContainer cht;

    ll f[N];

    void solve(){
        f[0] = 1;
        cht.add(-n, 0);
        for(int i = 1; i <= n; ++i){
            f[i] = -cht.query(a[i]);
            cht.add(-(n - i), -f[i]);
        }

        cout << f[n];
    }
}

namespace Sub3{
    bool valid_input(){
        bool ok = 1;
        for(int i = n - 1; i >= 1; --i)
            ok &= (a[i] >= a[i + 1]);
        return ok;
    }

    ll pref[N];

    void solve(){
        f[0] = 0;
        pref[1] = f[0] + 1ll * n * a[1];
        for(int i = 1; i <= n; ++i){
            f[i] = pref[i];
            pref[i + 1] = min(pref[i], f[i] + 1ll * (n - i) * a[i + 1]);
        }
        cout << f[n];
    }
}

namespace Sub5{
    int r[N];
    ll mx[N];
    LineContainer cht;

    void solve(){
        int cur = 0;
        for(int i = 1; i <= n; ++i){
            if(a[cur] < a[i]){
                while(cur < i){
                    cht.add(-(n - cur), -f[cur]);
                    ++cur;
                }
            }
            f[i] = -cht.query(a[cur]);
        }
        cout << f[n];
    }
}

void solve(){
    cin >> n;
    for(int i = 1; i <= n; ++i)
        cin >> a[i];
    if(Sub14::valid_input())
        Sub14::solve();
    else if(Sub2::valid_input())
        Sub2::solve();
    else if(Sub3::valid_input())
        Sub3::solve();
    else
        Sub5::solve();
}

int32_t main() {
    cin.tie(nullptr)->sync_with_stdio(0);
    #define task "troll"
    if(fopen(task".inp", "r")){
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }
    int test = 1;
//    cin >> test;
    for(int i = 1; i <= test; ++i){
//        cout << "Case #" << i << ": ";
        solve();
    }
    #ifdef LOCAL
        cerr << "\n[Time]: " << 1000.0 * clock() / CLOCKS_PER_SEC << " ms.\n";
    #endif
    return 0;
}

Compilation message (stderr)

Discharging.cpp:26:9: warning: #pragma once in main file
   26 | #pragma once
      |         ^~~~
Discharging.cpp: In function 'int32_t main()':
Discharging.cpp:222:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  222 |         freopen(task".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
Discharging.cpp:223:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  223 |         freopen(task".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 9 / 9
• Subtask 2: 13 / 13
• Subtask 3: 25 / 25
• Subtask 4: 11 / 11
• Subtask 5: 14 / 14
• Subtask 6: 28 / 28