Submission #546946

#	Time	Username	Problem	Language	Result	Execution time	Memory
546946		Jomnoi	Building Bridges (CEOI17_building)	C++17	100 / 100	53 ms	9760 KiB

building

#include <bits/stdc++.h>
#define DEBUG 0
using namespace std;

const int MAX_N = 1e5 + 10;
const long long INF = LLONG_MAX;

long long H[MAX_N], W[MAX_N];
long long dp[MAX_N];

bool QueryMode;

long long divide(const long long &a, const long long &b) {
    return a / b - ((a ^ b) < 0 and a % b != 0);
}

class Line {
public :
    mutable long long m, c, p;
    Line(const long long &m_, const long long &c_) : m(m_), c(c_), p(0) {}
    Line(const long long &m_, const long long &c_, const long long &p_) : m(m_), c(c_), p(p_) {}

    bool operator<(const Line &o) const {
        if(QueryMode == true) {
            return p < o.p;
        }
        return m < o.m;
    }
};

class LineContainer : multiset <Line> {
public :
    bool intersect(iterator now, iterator nxt) {
        if(nxt == end()) {
            now->p = INF;
            return false;
        }

        if(now->m == nxt->m) {
            now->p = INF;
            if(now->c < nxt->c) {
                now->p = -INF;
            }
        }
        else {
            now->p = divide(nxt->c - now->c, now->m - nxt->m);
        }
        return now->p >= nxt->p;
    }

    void addline(const Line &f) {
        auto nxt = insert(f), now = nxt++, prv = now;
        while(intersect(now, nxt) == true) {
            nxt = erase(nxt);
        }
        if(prv != begin() and intersect(--prv, now) == true) {
            intersect(prv, now = erase(now));
        }
        while((now = prv) != begin() and (--prv)->p >= now->p) {
            intersect(prv, erase(now));
        }
    }

    long long query(const long long &x) {
        QueryMode = true;
        auto it = *lower_bound(Line(-INF, -INF, x));
        QueryMode = false;

        return it.m * x + it.c;
    }
}cht;

int main() {
    cin.tie(0)->sync_with_stdio(0);
    int N;
    cin >> N;
    for(int i = 1; i <= N; i++) {
        cin >> H[i];
    }
    long long sum_w = 0;
    for(int i = 1; i <= N; i++) {
        cin >> W[i];
        sum_w += W[i];
    }

    dp[1] = -W[1];
    cht.addline(Line(2 * H[1], -H[1] * H[1] - dp[1]));
    for(int i = 2; i <= N; i++) {
        dp[i] = -cht.query(H[i]) + H[i] * H[i] - W[i];
        cht.addline(Line(2 * H[i], -H[i] * H[i] - dp[i]));
    }
    cout << sum_w + dp[N];
    return 0;
}

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