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Submission #641952

# Submission time Handle Problem Language Result Execution time Memory
641952 2022-09-18T01:22:09 Z SirCovidThe19th Building Bridges (CEOI17_building) C++17
100 / 100
 114 ms 9172 KB 
#include <bits/stdc++.h>
using namespace std;

template<class T> struct lichao{
    struct line{
        T m, b;
        T operator()(T x){ return m * x + b; }
    };
    lichao(){ extend(0); extend(0); }
    const T lim = 1e18; vector<line> seg; vector<int> lc, rc;
    
    int extend(int i){
        if (i) return i;
        seg.push_back({0, lim}); lc.push_back(0); rc.push_back(0);
        return seg.size() - 1;
    }
    void upd(line S, int l = -1e9, int r = 1e9, int i = 1){
        if (S.b == lim) return;
        if (l == r){ seg[i] = (S(l) < seg[i](l)) ? S : seg[i]; return; }
        if (seg[i].m > S.m) swap(seg[i], S); 

        int mid = (l + r) / 2 - (l + r < 0 and (l + r) % 2);
        if (S(mid) < seg[i](mid)){
            swap(S, seg[i]);
            upd(S, mid + 1, r, rc[i] = extend(rc[i]));
        }
        else upd(S, l, mid, lc[i] = extend(lc[i]));
    }
    T qry(int x, int l = -1e9, int r = 1e9, int i = 1){
        if (x < l or x > r or !i) return lim;
        if (l == r) return seg[i](l);
        int mid = (l + r) / 2 - (l + r < 0 and (l + r) % 2);
        return min({seg[i](x), qry(x, l, mid, lc[i]), qry(x, mid + 1, r, rc[i])});
    }
};

int n; long long H[100005], pref[100005], dp[100005]; lichao<long long> lc;

int main(){
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> H[i];
    for (int i = 1; i <= n; i++) cin >> pref[i], pref[i] += pref[i - 1];

    for (int i = 1; i <= n; i++){
        dp[i] = lc.qry(H[i]) + (H[i] * H[i] + pref[i - 1]);
        if (i == 1) dp[i] = 0;
        lc.upd({-2 * H[i], H[i] * H[i] + dp[i] - pref[i]});
    }
    cout<<dp[n]<<"\n";
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 316 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 312 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 97 ms 4128 KB Output is correct
2 Correct 101 ms 4160 KB Output is correct
3 Correct 110 ms 4172 KB Output is correct
4 Correct 89 ms 3752 KB Output is correct
5 Correct 83 ms 7072 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 316 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 312 KB Output is correct
6 Correct 97 ms 4128 KB Output is correct
7 Correct 101 ms 4160 KB Output is correct
8 Correct 110 ms 4172 KB Output is correct
9 Correct 89 ms 3752 KB Output is correct
10 Correct 83 ms 7072 KB Output is correct
11 Correct 108 ms 7176 KB Output is correct
12 Correct 104 ms 6932 KB Output is correct
13 Correct 99 ms 4788 KB Output is correct
14 Correct 114 ms 7208 KB Output is correct
15 Correct 99 ms 9172 KB Output is correct
16 Correct 85 ms 7136 KB Output is correct
17 Correct 59 ms 3624 KB Output is correct
18 Correct 61 ms 3716 KB Output is correct