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Submission #881809

# Submission time Handle Problem Language Result Execution time Memory
881809 2023-12-02T02:42:23 Z npmduyy Building Bridges (CEOI17_building) C++14
100 / 100
 38 ms 9676 KB 
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const int maxN = 1e5;

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

struct LineContainer : multiset<Line, less<>> {
    // (for doubles, use inf = 1/.0, div(a,b) = a/b)
    static const ll inf = LLONG_MAX;
    ll div(ll a, ll 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(ll k, ll 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));
    }
    ll query(ll x) {
        assert(!empty());
        auto l = *lower_bound(x);
        return l.k * x + l.m;
    }
};

int n;
ll h[maxN+1], w[maxN+1], dp[maxN+1];

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

    cin >> n;
    for (int i = 1; i <= n; ++i) {
        cin >> h[i];
    }
    for (int i = 1; i <= n; ++i) {
        cin >> w[i];
        w[i] += w[i-1];
    }

    LineContainer hull;
    hull.add(h[1]*2, - h[1]*h[1] + w[1]);
    for (int i = 2; i <= n; ++i) {
        dp[i] = w[i-1] + h[i]*h[i] - hull.query(h[i]);
        hull.add(h[i]*2, - h[i]*h[i] + w[i] - dp[i]);
    }
    cout << dp[n];
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2392 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 2652 KB Output is correct
2 Correct 29 ms 2652 KB Output is correct
3 Correct 29 ms 2648 KB Output is correct
4 Correct 26 ms 2652 KB Output is correct
5 Correct 26 ms 4864 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2392 KB Output is correct
6 Correct 30 ms 2652 KB Output is correct
7 Correct 29 ms 2652 KB Output is correct
8 Correct 29 ms 2648 KB Output is correct
9 Correct 26 ms 2652 KB Output is correct
10 Correct 26 ms 4864 KB Output is correct
11 Correct 29 ms 3920 KB Output is correct
12 Correct 34 ms 3924 KB Output is correct
13 Correct 28 ms 3900 KB Output is correct
14 Correct 31 ms 4024 KB Output is correct
15 Correct 38 ms 9676 KB Output is correct
16 Correct 25 ms 4696 KB Output is correct
17 Correct 16 ms 3640 KB Output is correct
18 Correct 20 ms 3676 KB Output is correct