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Submission #1034396

# Submission time Handle Problem Language Result Execution time Memory
1034396 2024-07-25T13:16:07 Z Blagoj Building Bridges (CEOI17_building) C++17
100 / 100
 95 ms 129904 KB 
#include <bits/stdc++.h>

using namespace std;

#define endl '\n'
#define ll long long
#define all(x) x.begin(), x.end()

const int mxn = 1e5 + 100;

vector<ll> h(mxn), val(mxn), prf(mxn);

ll sum(int l, int r) {
    return prf[r] - (l == 0 ? 0 : prf[l - 1]);
}

struct Node {
    ll m = 0, b = 1e16;
};

ll f(Node a, ll x) {
    return -a.m * x + a.b;
}

struct LiChao {
    vector<Node> sgt;

    LiChao(int sz) {
        sgt.resize(4 * sz);
    }

    void update(int k, int l, int r, Node nv) {
        int mid = (l + r) / 2;
        bool f1 = f(nv, l) < f(sgt[k], l);
        bool f2 = f(nv, mid) < f(sgt[k], mid);
        if (f2) swap(nv, sgt[k]);
        if (l == r) return;
        if (f1 != f2) update(k * 2, l, mid, nv);
        else update(k * 2 + 1, mid + 1, r, nv);
    }

    ll get(int k, int l, int r, ll x) {
        if (l > x || r < x) return 1e16;
        ll ans = f(sgt[k], x);
        if (l == r) return ans;
        int mid = (l + r) / 2;
        return min({ans, get(k * 2, l, mid, x), get(k * 2 + 1, mid + 1, r, x)});
    }
};

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int n;
    cin >> n;
    for (int i = 0; i < n; i++) cin >> h[i];
    for (int i = 0; i < n; i++) cin >> val[i];
    prf[0] = val[0];
    for (int i = 1; i < n; i++) prf[i] = prf[i - 1] + val[i];
    LiChao lc(2e6 + 100);
    lc.update(1, 0, 2e6, {2 * h[0], h[0] * h[0] - val[0]});
    ll ans[n];
    for (int i = 1; i < n; i++) {
        ll best = lc.get(1, 0, 2e6, h[i]) - val[i] + h[i] * h[i];
        ans[i] = best;
        lc.update(1, 0, 2e6, {2 * h[i], best + h[i] * h[i]});
    }
    cout << ans[n - 1] + sum(0, n - 1);
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 45 ms 127824 KB Output is correct
2 Correct 46 ms 127824 KB Output is correct
3 Correct 45 ms 127828 KB Output is correct
4 Correct 47 ms 127824 KB Output is correct
5 Correct 45 ms 127824 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 79 ms 129796 KB Output is correct
2 Correct 78 ms 129656 KB Output is correct
3 Correct 78 ms 129616 KB Output is correct
4 Correct 83 ms 129652 KB Output is correct
5 Correct 75 ms 129736 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 45 ms 127824 KB Output is correct
2 Correct 46 ms 127824 KB Output is correct
3 Correct 45 ms 127828 KB Output is correct
4 Correct 47 ms 127824 KB Output is correct
5 Correct 45 ms 127824 KB Output is correct
6 Correct 79 ms 129796 KB Output is correct
7 Correct 78 ms 129656 KB Output is correct
8 Correct 78 ms 129616 KB Output is correct
9 Correct 83 ms 129652 KB Output is correct
10 Correct 75 ms 129736 KB Output is correct
11 Correct 88 ms 129868 KB Output is correct
12 Correct 82 ms 129616 KB Output is correct
13 Correct 95 ms 129876 KB Output is correct
14 Correct 85 ms 129904 KB Output is correct
15 Correct 77 ms 129648 KB Output is correct
16 Correct 75 ms 129764 KB Output is correct
17 Correct 73 ms 129772 KB Output is correct
18 Correct 71 ms 129872 KB Output is correct