Submission #856318

#	Time	Username	Problem	Language	Result	Execution time	Memory
856318		Cyanmond	Building Bridges (CEOI17_building)	C++17	100 / 100	57 ms	10700 KiB

building

#include <bits/stdc++.h>

using namespace std;

#define rep(i, l, r) for (int i = (l); i < (r); ++i)
#define per(i, l, r) for (int i = (r - 1); i >= l; --i)
#define ALL(x) (x).begin(), (x).end()

using i64 = long long;

struct CHT {
    // naive
    struct Line {
        i64 a, b;
        i64 eval(i64 x) {
            return a * x + b;
        }
    };

    int n, siz, lg;
    vector<i64> xs;
    vector<Line> data;

    CHT(vector<i64> xs_) {
        xs = xs_;
        n = (int)xs.size();
        lg = 0;
        while ((1 << lg) < n) ++lg;
        siz = 1 << lg;
        while ((int)xs.size() < siz) xs.push_back(1ll << 30);
        n = siz;
        data.assign(2 * siz, {1ll << 30, 1ll << 60});
    }

    void add(int i, int l, int r, Line ln) {
        const int m = (l + r) / 2;
        const int lx = xs[l], mx = xs[m];
        if (data[i].eval(mx) > ln.eval(mx)) {
            swap(data[i], ln);
        }
        if (r - l == 1) return;
        if (data[i].eval(lx) > ln.eval(lx)) {
            add(2 * i, l, m, ln);
        } else {
            add(2 * i + 1, m, r, ln);
        }
    }

    void add(i64 x, i64 y) {
        Line ln = {x, y};
        add(1, 0, siz, ln);
    }

    i64 calcMin(int i) {
        i64 x = xs[i];
        i += siz;
        i64 ret = 1ll << 60;
        while (i != 0) {
            ret = min(ret, data[i].eval(x));
            i /= 2;
        }
        return ret;
    }
};

void main_() {
    int N;
    cin >> N;
    vector<i64> H(N), W(N);
    for (auto &e : H) cin >> e;
    for (auto &e : W) cin >> e;

    vector<i64> dp(N, 1ll << 60);
    dp[0] = 0;

    auto xs = H;
    sort(ALL(xs));

    CHT cht(xs);

    cht.add(-2 * H[0], -W[0] + dp[0] + H[0] * H[0]);
    i64 sumW = W[0];
    rep(i, 1, N) {
        const int p = (int)(lower_bound(ALL(xs), H[i]) - xs.begin());
        const auto mn = cht.calcMin(p);
        dp[i] = mn + H[i] * H[i] + sumW;
        sumW += W[i];
        cht.add(-2 * H[i], -sumW + dp[i] + H[i] * H[i]);
    }

    cout << dp[N - 1] << endl;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    main_();
}

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40