Submission #330775

#	Time	Username	Problem	Language	Result	Execution time	Memory
330775		IgorI	Aliens (IOI16_aliens)	C++17	100 / 100	277 ms	14980 KiB

aliens

#include <bits/stdc++.h>

using namespace std;

const long long INFLL = 1e18;

pair<long long, long long> calc(int n, long long M, vector<int> l, vector<int> r)
{
    vector<long long> dp(n, INFLL);
    vector<long long> bl(n, INFLL);
    for (int i = 0; i < n; i++)
        dp[i] = M + 1ll * (r[i] - l[0] + 1) * (r[i] - l[0] + 1), bl[i] = 1;
    struct line{
        long long k, b, id;
    };
    vector<line> convex;
    int lj = 0;
    for (int i = 0; i < n; i++)
    {
        long long res = 1ll * r[i] * r[i];
        long long d = INFLL, used = 0;
        while (lj + 1 < convex.size())
        {
            line A = convex[lj];
            line B = convex[lj + 1];
            if (r[i] * (A.k - B.k) >= (B.b - A.b))
            {
                lj++;
            }
            else
            {
                break;
            }
        }
        //cout << endl;
        //cout << r[i] << " " << lj << endl;
        for (int io = max(0, lj - 1); io <= lj && io < convex.size(); io++)
        {
            line e = convex[io];
            if (e.b + e.k * r[i] < d)
            {
                d = e.b + e.k * r[i], used = INFLL;
            }
            if (e.b + e.k * r[i] == d && bl[e.id] < used)
            {
                used = bl[e.id];
            }
        }
        res += d;
        if (res < dp[i])
            dp[i] = res, bl[i] = used + 1;
        if (i + 1 < n)
        {
            long long b = dp[i] + 1ll * l[i + 1] * l[i + 1] + 1 - 2 * l[i + 1] + M - 1ll * max(0, r[i] - l[i + 1] + 1) * max(0, r[i] - l[i + 1] + 1);
            long long k = 2 * (1 - l[i + 1]);
            line L = {k, b, i};
            while (convex.size() >= 2)
            {
                line A = convex[convex.size() - 2];
                line B = convex[convex.size() - 1];
                if (1ll * (B.b - L.b) * (L.k - A.k) <= 1ll * (A.b - L.b) * (L.k - B.k))
                    convex.pop_back();
                else
                    break;
            }
            convex.push_back(L);
        }
    }
    //cout << M << " " << dp[n - 1] << " " << bl[n - 1] << endl;
    return {dp[n - 1], bl[n - 1]};
}

long long take_photos(int n, int m, int k, vector<int> l, vector<int> r)
{
    vector<int> cv(m);
    for (int i = 0; i < m; i++)
    {
        cv[i] = i + 1;
    }
    for (int i = 0; i < n; i++)
    {
        int x = min(l[i], r[i]);
        int y = max(l[i], r[i]);
        cv[y] = min(cv[y], x);
    }
    l.clear();
    r.clear();
    for (int i = 0; i < m; i++)
    {
        if (cv[i] <= i)
        {
            while (l.size() && l.back() >= cv[i])
                l.pop_back(), r.pop_back();
            l.push_back(cv[i]), r.push_back(i);
        }
    }
    n = l.size();
    //for (int i = 0; i < l.size(); i++)
    //    cout << l[i] << " " << r[i] << endl;
    long long L = 0, R = 1ll * m * m + 222;
    long long ans = INFLL;
    k = min(k, n);
    while (L + 1 < R)
    {
        long long M = (L + R) / 2;
        if (calc(n, M, l, r).second >= k)
            L = M;
        else
            R = M;
    }
    for (long long d = R - 1; d <= R; d++)
    {
        pair<long long, long long> res = calc(n, d, l, r);
        //cout << res.first << " " << res.second << " " << d << " " << k << endl;
        if (res.second <= k)
            ans = min(ans, res.first - 1ll * k * d);
    }
    return ans;
}

Compilation message (stderr)

aliens.cpp: In function 'std::pair<long long int, long long int> calc(int, long long int, std::vector<int>, std::vector<int>)':
aliens.cpp:22:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<calc(int, long long int, std::vector<int>, std::vector<int>)::line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   22 |         while (lj + 1 < convex.size())
      |                ~~~~~~~^~~~~~~~~~~~~~~
aliens.cpp:37:54: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<calc(int, long long int, std::vector<int>, std::vector<int>)::line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   37 |         for (int io = max(0, lj - 1); io <= lj && io < convex.size(); io++)
      |                                                   ~~~^~~~~~~~~~~~~~~

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40