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Submission #624724

# Submission time Handle Problem Language Result Execution time Memory
624724 2022-08-08T16:08:47 Z Jomnoi Building Bridges (CEOI17_building) C++17
100 / 100
 67 ms 9688 KB 
#include <bits/stdc++.h>
using namespace std;

const int MAX_N = 1e5 + 5;
const long long INF = 1e18 + 7;

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

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

struct Line {
    mutable long long m, c, p;

    Line() {}
    Line(long long m_, long long c_) : m(m_), c(c_), p(0) {}
    Line(long long m_, long long c_, 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;
    }
};

struct LineContainer : multiset <Line> {
    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(now->c - nxt->c, nxt->m - now->m);
        }
        return now->p >= nxt->p;
    }

    void addLine(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(long long x) {
        queryMode = true;
        auto it = lower_bound({-INF, -INF, x});
        queryMode = false;

        return it->m * x + it->c;
    }
};

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);

    int N;
    cin >> N;

    long long sumW = 0;
    for(int i = 1; i <= N; i++) {
        cin >> H[i];
    }
    for(int i = 1; i <= N; i++) {
        cin >> W[i];

        sumW += W[i];
    }

    LineContainer cht;
    dp[1] = -W[1];
    cht.addLine({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({2 * H[i], -H[i] * H[i] - dp[i]});
    }
    cout << sumW + dp[N];
    return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 0 ms 324 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 39 ms 3684 KB Output is correct
2 Correct 49 ms 3644 KB Output is correct
3 Correct 39 ms 3648 KB Output is correct
4 Correct 34 ms 3568 KB Output is correct
5 Correct 36 ms 4732 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 0 ms 324 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 39 ms 3684 KB Output is correct
7 Correct 49 ms 3644 KB Output is correct
8 Correct 39 ms 3648 KB Output is correct
9 Correct 34 ms 3568 KB Output is correct
10 Correct 36 ms 4732 KB Output is correct
11 Correct 36 ms 3884 KB Output is correct
12 Correct 37 ms 3668 KB Output is correct
13 Correct 31 ms 3728 KB Output is correct
14 Correct 39 ms 3884 KB Output is correct
15 Correct 67 ms 9688 KB Output is correct
16 Correct 35 ms 4772 KB Output is correct
17 Correct 20 ms 3668 KB Output is correct
18 Correct 22 ms 3700 KB Output is correct