oj.uz

Submission #850388

# Submission time Handle Problem Language Result Execution time Memory
850388 2023-09-16T13:32:56 Z faruk Building Bridges (CEOI17_building) C++17
100 / 100
 72 ms 11224 KB 
#include <bits/stdc++.h>
#define mp make_pair
#define all(a) a.begin(), a.end()

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;

struct line {
    ll m, b;
    double x;
    bool is_searching;

    bool operator<(const line& b) const {
        if (is_searching || b.is_searching)
            return x < b.x;
        return m > b.m;
    }
};

typedef set<line>::iterator lineit;

set<line> hull;

bool has_prev(lineit a) {
    return a != hull.begin();
}

bool has_next(lineit b) {
    return next(b) != hull.end();
}

double intersection(lineit a, lineit b) {
    return ((double)a->b - (double)b->b) / ((double)b->m - (double)a->m);
}

void upd_x(lineit a) {
    if (has_prev(a)) {
        double point = intersection(a, prev(a));
        line copy = *a;
        copy.x = point;
        hull.erase(a);
        hull.insert(copy);
    }
}

bool bad(lineit a) {
    if (has_next(a) && next(a)->b <= a->b)
        return true;
    return (has_prev(a) && has_next(a) && intersection(prev(a), next(a)) <= intersection(prev(a), a));
}

void add_line(ll m, ll b) {
    auto it = hull.lower_bound({m, b, 0, 0});
    if (it != hull.end() && it->m == m) {
        if (it->b <= b)
            return;
        hull.erase(it);
    }
    it = hull.insert({m, b, 0, 0}).first;
    if (bad(it))
        hull.erase(it);
    else {
        while (has_prev(it) && bad(prev(it))) hull.erase(prev(it));
        while (has_next(it) && bad(next(it))) hull.erase(next(it));

        if (has_next(it)) upd_x(next(it));
        upd_x(it);
    }
}

ll query(ll val) {
    lineit l = prev(hull.upper_bound({0, 0, (double)val, 1}));
    return l->m * val + l->b;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;
    vector<ll> h(n);
    vector<ll> c(n);
    for (int i = 0; i<n; i++)
        cin >> h[i];
    for (int i = 0; i < n; i++)
        cin >> c[i];
    
    vector<ll> dp(n);
    dp[0] = -c[0];
    vector<ll> brute_dp(n, 1e18); brute_dp[0] = -c[0];
    for (int i = 1; i < n; i++) {
        /*for (int j = 0; j < i; j++)
            brute_dp[i] = min(brute_dp[i], brute_dp[j] + (h[i] - h[j]) * (h[i] - h[j]) - c[i]);*/
        add_line(-2*h[i - 1], h[i - 1]*h[i - 1] + dp[i - 1]);
        dp[i] = -c[i] + h[i] * h[i] + query(h[i]);
    }

    cout << accumulate(all(c), 0LL) + dp[n - 1] << "\n";
}

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 348 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 60 ms 3684 KB Output is correct
2 Correct 61 ms 3688 KB Output is correct
3 Correct 63 ms 3932 KB Output is correct
4 Correct 59 ms 3572 KB Output is correct
5 Correct 53 ms 5132 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 348 KB Output is correct
6 Correct 60 ms 3684 KB Output is correct
7 Correct 61 ms 3688 KB Output is correct
8 Correct 63 ms 3932 KB Output is correct
9 Correct 59 ms 3572 KB Output is correct
10 Correct 53 ms 5132 KB Output is correct
11 Correct 53 ms 3636 KB Output is correct
12 Correct 62 ms 3632 KB Output is correct
13 Correct 38 ms 3588 KB Output is correct
14 Correct 61 ms 3668 KB Output is correct
15 Correct 72 ms 11224 KB Output is correct
16 Correct 52 ms 5136 KB Output is correct
17 Correct 17 ms 3420 KB Output is correct
18 Correct 15 ms 3420 KB Output is correct