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Submission #938342

# Submission time Handle Problem Language Result Execution time Memory
938342 2024-03-05T04:56:17 Z WendidIask0303 Building Bridges (CEOI17_building) C++17
100 / 100
 60 ms 9676 KB 
#include <iostream>
#include <set>

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 = 1000000000000000001;
    long long div(long long a, long long b){
        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) {
        auto l = *lower_bound(x);
        return l.k * x + l.m;
    }
};
 
long long h[100001];
long long w[100001];
long long dp[100001];
 
int main() {
    int n;
    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, -1*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, -1*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 2392 KB Output is correct
4 Correct 1 ms 2392 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 55 ms 3860 KB Output is correct
2 Correct 55 ms 3848 KB Output is correct
3 Correct 59 ms 3732 KB Output is correct
4 Correct 51 ms 3480 KB Output is correct
5 Correct 48 ms 4692 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 2392 KB Output is correct
4 Correct 1 ms 2392 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 55 ms 3860 KB Output is correct
7 Correct 55 ms 3848 KB Output is correct
8 Correct 59 ms 3732 KB Output is correct
9 Correct 51 ms 3480 KB Output is correct
10 Correct 48 ms 4692 KB Output is correct
11 Correct 56 ms 3872 KB Output is correct
12 Correct 54 ms 3668 KB Output is correct
13 Correct 56 ms 3852 KB Output is correct
14 Correct 58 ms 3920 KB Output is correct
15 Correct 60 ms 9676 KB Output is correct
16 Correct 49 ms 4692 KB Output is correct
17 Correct 43 ms 3668 KB Output is correct
18 Correct 43 ms 3676 KB Output is correct