Submission #819460

#	Time	Username	Problem	Language	Result	Execution time	Memory
819460		borisAngelov	Building Bridges (CEOI17_building)	C++17	100 / 100	76 ms	67176 KiB

building

#include <bits/stdc++.h>

using namespace std;

const int maxn = 100005;
const int max_size = 1000000;
const long long inf = (1LL << 62);

int n;

long long h[maxn];
long long w[maxn];
long long pref[maxn];
long long dp[maxn];

struct line
{
    long long a;
    long long b;

    line()
    {
        a = 0;
        b = inf;
    }

    line(long long _a, long long _b)
    {
        a = _a;
        b = _b;
    }

    long long calc(long long x)
    {
        return a * x + b;
    }
};

struct li_chao_tree
{
    line tree[4 * max_size + 20];

    void update(int node, int l, int r, line new_line)
    {
        if (tree[node].calc(l) < new_line.calc(l) && tree[node].calc(r) < new_line.calc(r))
        {
            return;
        }

        int mid = (l + r) / 2;

        if (tree[node].calc(mid) > new_line.calc(mid))
        {
            swap(tree[node], new_line);
        }

        if (tree[node].calc(l) > new_line.calc(l))
        {
            update(2 * node, l, mid, new_line);
        }

        if (tree[node].calc(r) > new_line.calc(r))
        {
            update(2 * node + 1, mid + 1, r, new_line);
        }
    }

    long long query(int node, int l, int r, int pos)
    {
        if (l == r)
        {
            return tree[node].calc(pos);
        }

        int mid = (l + r) / 2;

        if (pos <= mid)
        {
            return min(tree[node].calc(pos), query(2 * node, l, mid, pos));
        }

        return min(tree[node].calc(pos), query(2 * node + 1, mid + 1, r, pos));
    }

    void update(const line& new_line)
    {
        update(1, 0, max_size, new_line);
    }

    long long query(int pos)
    {
        return query(1, 0, max_size, pos);
    }
};

li_chao_tree tree;

void fastIO()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
}

int main()
{
    fastIO();

    cin >> n;

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

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

    dp[1] = 0;

    line curr = line(-(2 * h[1]), h[1] * h[1] - pref[1]);
    tree.update(curr);

    for (int i = 2; i <= n; ++i)
    {
        dp[i] = h[i] * h[i] + pref[i - 1] + tree.query(h[i]);

        curr = line(-(2 * h[i]), dp[i] + h[i] * h[i] - pref[i]);
        tree.update(curr);
    }

    cout << dp[n] << endl;

    return 0;
}

/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40