Submission #1356246

#TimeUsernameProblemLanguageResultExecution timeMemory
1356246satoulogaritDischarging (NOI20_discharging)C++20
47 / 100
954 ms1114112 KiB
//LongvnXD
#include <bits/stdc++.h>

#define i128 __int128_t
#define ll long long 
#define pll pair<ll, ll>
#define ii pair<int, int> 
#define fi first
#define se second
#define x first
#define y second
#define all(v) v.begin(), v.end()

using namespace std;

const int N = 1e6 + 6;
const i128 oo = (i128)1000000000000000000LL * (i128)10000000000LL + 25;

void print(i128 a) {
    if(a == 0) return cout << 0, void();
    if(a < 0) { cout << '-'; a = -a; }
    stack<int> s;
    while(a > 0) {
        s.push((int)(a % 10));
        a /= 10;
    }
    while(!s.empty()) {
        cout << s.top();
        s.pop();
    }
}

struct Line { 
    ll a; i128 b; 
    i128 get(ll x) { return (i128)a * x + b; }
};

struct History {
    int node;
    Line old_line;
    bool had_line;
};

Line tree[N << 2];
bool has_line[N << 2];
vector<History> history_stack;

void add_line(int i, int l, int r, Line newline) {
    int mid = (l + r) >> 1;
    history_stack.push_back({i, tree[i], has_line[i]});

    if(!has_line[i]) {
        tree[i] = newline;
        has_line[i] = 1;
        return;
    }

    bool better_l = newline.get(l) < tree[i].get(l);
    bool better_m = newline.get(mid) < tree[i].get(mid);

    if(better_m) swap(tree[i], newline);
    if(l == r) return;

    if(better_l != better_m) add_line(i << 1, l, mid, newline);
    else add_line(i << 1 | 1, mid + 1, r, newline);
}

i128 query_lichao(int i, int l, int r, ll x) {
    if(!has_line[i]) return oo;
    i128 res = tree[i].get(x);
    if(l == r) return res;
    int mid = (l + r) >> 1;
    if(x <= mid) res = min(res, query_lichao(i << 1, l, mid, x));
    else res = min(res, query_lichao(i << 1 | 1, mid + 1, r, x));
    return res;
}

void rollback(int target_size) {
    while((int)history_stack.size() > target_size) {
        History h = history_stack.back();
        history_stack.pop_back();
        tree[h.node] = h.old_line;
        has_line[h.node] = h.had_line;
    }
}

struct segMunToRi {
    i128 st[N << 2];
    void init(int n) {
        for(int i = 0; i <= (n << 2); ++i) st[i] = oo;
    }
    void update(int i, int l, int r, int x, i128 val) {
        if(l == r) { st[i] = val; return; }
        int mid = (l + r) >> 1;
        if(x <= mid) update(i << 1, l, mid, x, val);
        else update(i << 1 | 1, mid + 1, r, x, val);
        st[i] = min(st[i << 1], st[i << 1 | 1]);
    }
    i128 get(int i, int l, int r, int x, int y) {
        if(l > y || r < x) return oo;
        if(l >= x && r <= y) return st[i];
        int mid = (l + r) >> 1;
        return min(get(i << 1, l, mid, x, y), get(i << 1 | 1, mid + 1, r, x, y));
    }
} it;

int n, a[N];
i128 d[N];

int main() {
    ios::sync_with_stdio(0); cin.tie(0);

    if(!(cin >> n)) return 0;
    for(int i = 1; i <= n; ++i) cin >> a[i];

    it.init(n + 1);
    d[n + 1] = 0;
    a[n + 1] = 2e9;
    it.update(1, 1, n + 1, n + 1, 0);

    stack<int> st;
    stack<int> h_ptr; 
    st.push(n + 1);

    for(int i = n; i >= 1; --i) {
        while(!st.empty() && a[st.top()] <= a[i]) {
            st.pop();
            if(!h_ptr.empty()) {
                rollback(h_ptr.top());
                h_ptr.pop();
            }
        }
        
        int j = st.top();
        st.push(i);

        i128 val_min = it.get(1, 1, n + 1, i + 1, j);
        
        h_ptr.push((int)history_stack.size());
        add_line(1, 1, n, {a[i], val_min});

        d[i] = query_lichao(1, 1, n, n - i + 1);
        
        it.update(1, 1, n + 1, i, d[i]);
    }

    i128 ok = d[1];
    print(ok);
    cout << "\n";

    return 0;
}
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