Submission #731582

#	Time	Username	Problem	Language	Result	Execution time	Memory
731582		danikoynov	Aliens (IOI16_aliens)	C++14	12 / 100	10 ms	5844 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int maxn = 1e5 + 10;

struct interval
{
    ll left, right;

    interval(ll _left = 0, ll _right = 0)
    {
        left = _left;
        right = _right;
    }
};

bool cmp(const interval &it1, const interval &it2)
{
    if (it1.left == it2.left)
        return it1.right > it2.right;
    return it1.left < it2.left;
}

const ll inf = 1e18;

interval h[maxn];
ll dp[1010][1010];

ll area(ll left, ll right)
{
    if (left > right)
        return 0;
    return (right - left + 1) * (right - left + 1);
}

struct line
{
    ll k, m;

    line(ll _k, ll _m)
    {
        k = _k;
        m = _m;
    }

    double do_math(ll x)
    {
        return k * x + m;
    }
};

double intersect(const line &l1, const line &l2) /// when does the second line become better
{
    if (l1.k == l2.k)
    {
        if (l1.m < l2.m)
            return -inf;
        else
            return inf;
    }
    /**
    l1.k * x + l1.m = l2.k * x + l2.m
    (l1.k - l2.k) * x = l2.m - l1.m
    */
    return (double)(l2.m - l1.m) / (double)(l1.k - l2.k);
}

struct convex_hull_trick
{
    vector < line > cht;

    void add_line(ll k, ll m)
    {
        line l(k, m);

        while(cht.size() > 1 && intersect(cht[cht.size() - 2], cht.back()) > intersect(cht.back(), l))
            cht.pop_back();

        cht.push_back(l);
    }

    ll query(ll x)
    {
        int lf = 0, rf = (int)(cht.size()) - 2;
        while(lf <= rf)
        {
            int mf = (lf + rf) / 2;
            if (intersect(cht[mf], cht[mf + 1]) < (double)(x))
                lf = mf + 1;
            else
                rf = mf - 1;
        }
        return cht[lf].do_math(x);
    }
};

ll take_photos(int n, int m, int k, vector<int> r, vector<int> c)
{
    vector < interval > vec;
    for (int i = 0; i < n; i ++)
    {
        if (r[i] > c[i])
            swap(r[i], c[i]);
        interval cur(r[i], c[i]);
        vec.push_back(cur);
    }

    sort(vec.begin(), vec.end(), cmp);
    n = 0;
    int to = -1;
    for (int i = 0; i < vec.size(); i ++)
    {
        if (vec[i].right > to)
        {
            to = vec[i].right;
            h[++ n] = vec[i];
        }
    }

    ///for (int i = 1; i <= n; i ++)
    /// cout << h[i].left << " : " << h[i].right << endl;

    for (int i = 0; i <= n; i ++)
        for (int j = 0; j <= k; j ++)
            dp[i][j] = inf;

    k = min(k, n);
    dp[0][0] = 0;
    h[0] = interval(-1, -1);
    for (int j = 1; j <= k; j ++)
    {
        convex_hull_trick cht;
        cht.add_line(- 2 * (h[1].left - 1), (h[1].left - 1) * (h[1].left - 1) + dp[0][j - 1] - area(h[1].left, h[0].right));
        for (int i = 1; i <= n; i ++)
        {
            dp[i][j] = cht.query(h[i].right) + h[i].right * h[i].right;
            cht.add_line(- 2 * (h[i + 1].left - 1), (h[i + 1].left - 1) * (h[i + 1].left - 1) + dp[i][j - 1] - area(h[i + 1].left, h[i].left));
        }
        /**for (int p = 1; p <= i; p ++)
        {
            dp[i][j] = min(dp[i][j], dp[p - 1][j - 1] + area(h[p].left, h[i].right) - area(h[p].left, h[p - 1].right));
        }*/


    }
    /**for (int i = 1; i <= n; i ++, cout << endl)
        for (int j = 1; j <= k; j ++)
        cout << dp[i][j] << " ";*/
    return dp[n][k];
}

Compilation message (stderr)

aliens.cpp: In function 'll take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:114:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<interval>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  114 |     for (int i = 0; i < vec.size(); i ++)
      |                     ~~^~~~~~~~~~~~

• Subtask 1: 0 / 4
• Subtask 2: 12 / 12
• Subtask 3: 0 / 9
• Subtask 4: 0 / 16
• Subtask 5: 0 / 19
• Subtask 6: 0 / 40