Submission #684085

#	Time	Username	Problem	Language	Result	Execution time	Memory
684085		jhwest2	Aliens (IOI16_aliens)	C++17	100 / 100	162 ms	11864 KiB

aliens

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

typedef long long ll;

const int N = 101010;
const int M = 1010101;

int n, m, k; pair<int, int> a[M];
vector<pair<int, int>> v;

struct cht {
    vector<array<ll, 3>> cht;
    int p = 0;

    void init() {
        p = 0;
        vector<array<ll, 3>>().swap(cht);
    }
    // min-cht, decreasing s
    void insert(ll s, ll t, int i) {
        while (cht.size() >= 2) {
            auto [ps, pt, _] = cht[cht.size() - 2];
            auto [qs, qt, __] = cht.back();

            if ((t - pt) * (ps - qs) <= (ps - s) * (qt - pt))
                cht.pop_back();
            else
                break;
        }
        cht.push_back({s, t, i});
    }
    // increasing x
    pair<ll, int> query(ll x) {
        while (p + 1 < cht.size()) {
            auto [ps, pt, _] = cht[p];
            auto [qs, qt, __] = cht[p + 1];

            if (x * (ps - qs) >= (qt - pt))
                ++p;
            else
                break;
        }
        return {x * cht[p][0] + cht[p][1], cht[p][2]};
    }
} t1;

ll dp[N], bt[N];

pair<ll, ll> run(ll x) {
    t1.init();
    t1.insert(-4 * v[0].first, 2ll * v[0].first * v[0].first, 0);

    for (int i = 1; i <= n; i++) {
        auto [val, b] = t1.query(v[i - 1].second + 1);

        dp[i] = val + 2ll * (v[i - 1].second + 1) * (v[i - 1].second + 1) + x;
        bt[i] = b;

        if (i != n) {
            ll val = 2ll * v[i].first * v[i].first + dp[i];;
            if (v[i - 1].second >= v[i].first)
                val -= 2ll * (v[i - 1].second - v[i].first + 1) * (v[i - 1].second - v[i].first + 1);
            
            t1.insert(-4 * v[i].first, val, i);
        }
    }

    int cnt = 0;
    for (int i = n; i != 0; i = bt[i])
        ++cnt;

    return {dp[n], cnt};
}
ll take_photos(int _n, int _m, int _k, vector<int> _r, vector<int> _c) {
    n = _m; m = _n; k = _k;
    for (int i = 0; i < m; i++) {
        if (_r[i] > _c[i])
            swap(_r[i], _c[i]);

        a[i] = {_r[i], _c[i]};
    }

    sort(a, a + m);
    v.push_back(a[0]);
    for (int i = 1; i < m; i++) {
        if (v.back().second < a[i].second) {
            if (v.back().first == a[i].first)
                v.pop_back();
            v.push_back(a[i]);
        }
    }
    n = v.size();

    // aliens trick
    ll L = 0, R = 1e12 + 10;
    while (L < R) { 
        ll M = (L + R) / 2;
        
        if (run(2 * M + 1).second <= k)
            R = M;
        else
            L = M + 1;
    }
    auto [x, y] = run(2 * L + 1);
    return (x - (2 * L + 1) * y - 2 * L * (min(n, k) - y)) / 2;
}

Compilation message (stderr)

aliens.cpp: In member function 'std::pair<long long int, int> cht::query(ll)':
aliens.cpp:36:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::array<long long int, 3> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   36 |         while (p + 1 < cht.size()) {
      |                ~~~~~~^~~~~~~~~~~~

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