Submission #962494

#	Time	Username	Problem	Language	Result	Execution time	Memory
962494		RaresFelix	Aliens (IOI16_aliens)	C++17	100 / 100	437 ms	11384 KiB

aliens

#include <bits/stdc++.h>
#include "aliens.h"
#pragma GCC optimize("O3")
#pragma GCC target("avx,avx2,fma")

#define sz(x) int((x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()

using namespace std;
using ll = long long;
using ld = long double;  // or double, if TL is tight
using str = string;
using ii = pair<int, int>;
using pl = pair<ll, ll>;
using vi = vector<int>;
using vll = vector<ll>;

const ll INF = 1e16;

struct CHT {
    int p = 0;
    vector<pair<ll, ll>> V;
    void insert(ll a, ll b) { /// add ax + b
        while(V.size() > 1) {
            auto [a1, b1] = V.end()[-2];
            auto [a2, b2] = V.end()[-1];
            if((b1 - b2) * (a - a2) >= (b2 - b) * (a2 - a1)) {
                V.pop_back();
            } else break;
        }
        V.push_back({a, b});
    }
    ll query(ll x) {
        if(V.empty()) return 1e18;
        auto eval = [&](pair<ll, ll> f) {
            return f.first * x + f.second;
        };
        while(p + 1 < V.size() && eval(V[p]) >= eval(V[p + 1])) ++p;
        return eval(V[p]);
    }
};

ll take_photos(int n0, int m, int k, vi r, vi c) {
    vector<ii> SegInit;
    for(int i = 0; i < n0; ++i) {
        SegInit.push_back({min(r[i], c[i]), max(r[i], c[i]) + 1});
    }
    sort(all(SegInit), [&](auto a, auto b) {
        if(a.first != b.first) return a < b;
        return a > b;
    });
    vector<ii> Seg;
    int cur_dr = -1;
    for(auto [st, dr] : SegInit) {
        if(dr <= cur_dr) continue;
        else {
            Seg.push_back({st, dr});
            cur_dr = dr;
        }
    }
    int n = Seg.size();
    vll st(n, 0), dr(n, 0), sb(n, 0);
    for(int i = 0; i < n; ++i) {
        st[i] = Seg[i].first; dr[i] = Seg[i].second;
        sb[i] = (dr[i] - st[i]) * (dr[i] - st[i]);
        if(i) {
            if(dr[i - 1] > st[i]) 
                sb[i] -= (dr[i - 1] - st[i]) * (dr[i - 1] - st[i]);
            sb[i] += sb[i - 1];
        }
    }
    auto cost = [&](int i, int j) {
        return (dr[j] - st[i]) * (dr[j] - st[i]) - (dr[i] - st[i]) * (dr[i] - st[i])
            - sb[j] + sb[i];
        return (dr[j] * dr[j] - sb[j]) 
            + (2 * st[i] * dr[i] - dr[i] * dr[i] + sb[i]) 
            - 2 * st[i] * dr[j];
    };
    ll re0 = sb.back();

    auto t = [&](ll lambda) {
        ll re = - lambda * k;
        CHT Sol;
        vector<ll> DP(n, 0.);
        for(int i = 0; i < n; ++i) {
            ll dpant = 0.;
            if(i) dpant = DP[i - 1];
            Sol.insert(- 2 * st[i], 
                        (dpant + (2 * st[i] * dr[i] - dr[i] * dr[i] + sb[i])));

            DP[i] = lambda + (ll)cost(0, i);
            ll v = lambda + (Sol.query(dr[i]) + dr[i] * dr[i] - sb[i]);
            DP[i] = min(DP[i], v);
        }
        re += DP.back();
        return re;
    };
    ll re = 0;

    ll s = 0, d = 1e14, mij;
    ll vm = 0;
    for(int i = 0; i < 100; ++i) {
        ll m1 = (2 * s + d) / 3, v1 = t(m1);
        ll m2 = (s + 2 * d) / 3, v2 = t(m2);
        vm = max(vm, v1);
        vm = max(vm, v2);
        if(s == d) break;
        if(v1 < v2) s = m1;
        else d = m2;
    }
    re = ll(round(vm) + 1e-8);
    re += re0;
    return re;
}

Compilation message (stderr)

aliens.cpp: In member function 'll CHT::query(ll)':
aliens.cpp:39:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   39 |         while(p + 1 < V.size() && eval(V[p]) >= eval(V[p + 1])) ++p;
      |               ~~~~~~^~~~~~~~~~
aliens.cpp: In function 'll take_photos(int, int, int, vi, vi)':
aliens.cpp:101:25: warning: unused variable 'mij' [-Wunused-variable]
  101 |     ll s = 0, d = 1e14, mij;
      |                         ^~~

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