Submission #1266983

#	Time	Username	Problem	Language	Result	Execution time	Memory
1266983		canhnam357	Building Bridges (CEOI17_building)	C++20	100 / 100	42 ms	9796 KiB

building

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

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

struct LineContainer : multiset<Line, less<>> {
    // (for doubles, use inf = 1/.0, div(a,b) = a/b)
    static const long long inf = LLONG_MAX;
    long long div(long long a, long long 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(long long k, long long 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));
    }
    long long query(long long x) {
        assert(!empty());
        auto l = *lower_bound(x);
        return l.k * x + l.m;
    }
};
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int n;
    cin >> n;
    vector<long long> h(n + 1), w(n + 1);
    for (int i = 1; i <= n; i++) {
        cin >> h[i];
    }   
    for (int i = 1; i <= n; i++) {
        cin >> w[i];
    }
    auto pre = w;
    for (int i = 1; i <= n; i++) {
        pre[i] = pre[i - 1] + w[i];
    }
    // dp[r] = dp[l] + pre[r - 1] - pre[l] + h[l] * h[l] - 2 * h[l] * h[r] + h[r] * h[r]
    // -2 * h[l], dp[l] - pre[l] + h[l] * h[l]
    LineContainer lc;
    vector<long long> dp(n + 1, LLONG_MAX);
    dp[1] = 0;
    lc.add(2 * h[1], -dp[1] + pre[1] - h[1] * h[1]);
    for (int i = 2; i <= n; i++) {
        dp[i] = -lc.query(h[i]) + h[i] * h[i] + pre[i - 1];
        lc.add(2 * h[i], -dp[i] + pre[i] - h[i] * h[i]);
    }
    cout << dp[n];
    return 0;
}

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