oj.uz

Submission #880154

# Submission time Handle Problem Language Result Execution time Memory
880154 2023-11-28T21:46:46 Z DylanSmith Building Bridges (CEOI17_building) C++17
100 / 100
 38 ms 8276 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

#define pb push_back
#define sz(x) (int)x.size()
#define all(x) begin(x),end(x)
#define lb(x,y) lower_bound(all(x),y)-begin(x)

mt19937 rng;

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;
    }
};

void solve() {
    int N; cin >> N;
    vector<int> h(N), w(N);
    for (int i = 0; i < sz(h); i++) cin >> h[i];
    for (int i = 0; i < sz(w); i++) cin >> w[i];
    ll sub = 0;
    for (int i : w) sub += i;
    LineContainer lc;
    lc.add(2 * h[0], w[0] - (ll)h[0] * h[0]);
    for (int i = 1; i < N; i++) {
        ll n = -lc.query(h[i]) + (ll)h[i] * h[i] - w[i];
        if (i == N - 1) cout << (n + sub) << "\n";
        lc.add(2 * h[i], -n - (ll)h[i] * h[i]);
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    rng = mt19937(chrono::steady_clock::now().time_since_epoch().count());

    solve();

    return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 600 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 2140 KB Output is correct
2 Correct 33 ms 2140 KB Output is correct
3 Correct 31 ms 2136 KB Output is correct
4 Correct 27 ms 2016 KB Output is correct
5 Correct 25 ms 3152 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 600 KB Output is correct
6 Correct 30 ms 2140 KB Output is correct
7 Correct 33 ms 2140 KB Output is correct
8 Correct 31 ms 2136 KB Output is correct
9 Correct 27 ms 2016 KB Output is correct
10 Correct 25 ms 3152 KB Output is correct
11 Correct 34 ms 2652 KB Output is correct
12 Correct 30 ms 2136 KB Output is correct
13 Correct 24 ms 2136 KB Output is correct
14 Correct 29 ms 2396 KB Output is correct
15 Correct 38 ms 8276 KB Output is correct
16 Correct 31 ms 3208 KB Output is correct
17 Correct 16 ms 2140 KB Output is correct
18 Correct 15 ms 2136 KB Output is correct