Submission #751425

#	Time	Username	Problem	Language	Result	Execution time	Memory
751425		Desh03	Aliens (IOI16_aliens)	C++17	100 / 100	222 ms	8944 KiB

aliens

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

const long long INF = 9e18;

struct point {
    long long x, y;
    bool operator < (const point &p) const {
        return x == p.x ? y < p.y : x < p.x;
    }
};

struct line {
    long long m, c, s;
    line(long long m_, long long c_, long long s_) : m(m_), c(c_), s(s_), left(NULL), right(NULL) { };
    long long eval(long long x) {
        return m * x + c;
    }
    line *left, *right;
};

long long N, M;
vector<point> r;
vector<long long> dp;
vector<long long> cnt;

/*
struct lichaotree {
    line* root;
    lichaotree() : root(new line(0, INF, 0)) { };
    line* insert(line* v, long long l, long long r, long long m_, long long c_, long long s_) {
        if (v == NULL || l == r) return new line(m_, c_, s_);
        long long m = l + r >> 1;
        if (v->eval(m) > m_ * m + c_) swap(v->m, m_), swap(v->c, c_), swap(v->s, s_);
        if (v->eval(l) > m_ * l + c_)
            v->left = insert(v->left, l, m, m_, c_, s_);
        else
            v->right = insert(v->right, m + 1, r, m_, c_, s_);
        return v;
    }
    pair<long long, long long> qry(line* &v, long long l, long long r, long long x) {
        if (v == NULL) return {INF, 0};
        if (l == r) return {v->eval(x), v->s};
        long long m = l + r >> 1;
        if (x <= m) return min(make_pair(v->eval(x), v->s), qry(v->left, l, m, x));
        return min(make_pair(v->eval(x), v->s), qry(v->right, m + 1, r, x));
    }
    void insert(long long m, long long c, long long s) {
        insert(root, 0, M, m, c, s);
    }
    pair<long long, long long> qry(long long x) {
        return qry(root, 0, M, x);
    }
};
*/

struct Line {
  long long m = 0, c = 0;
  int cnt = 0;
  Line(long long _m, long long _c, int _cnt) : m(_m), c(_c), cnt(_cnt) { }
  long long get(long long x) { return m * x + c; }
  double intersection(Line o) { return (double) (o.c - c) / (double) (m - o.m); }
  bool good(Line l2, Line l3) { return __int128(l2.c - c) * (l2.m - l3.m) < __int128(l3.c - l2.c) * (m - l2.m); }
};

struct CHT {
  deque<Line> hull;
  void insert(Line l) {
    while (hull.size() > 1) {
      auto last = hull.end()[-1];
      auto p_last = hull.end()[-2];
      if (p_last.good(last, l)) break;
      hull.pop_back();
    }
    hull.push_back(l);
  }
  pair<long long, int> query(long long x) {
    while (hull.size() > 1 && hull[0].get(x) > hull[1].get(x)) {
      hull.pop_front();
    }
    return {hull[0].get(x), hull[0].cnt};
  }
};

long long sq(long long x) {
    return 1LL * x * x;
}

void aliens(long long lambda) {
   CHT cht;
   cht.insert(Line(-2 * r[0].x, sq(r[0].x) + 1 - 2 * r[0].x, 0));
   for (long long i = 0; i < N; i++) {
        auto [mn, cnt_] = cht.query(r[i].y);
        dp[i] = mn + sq(r[i].y) + 2 * r[i].y + lambda;
        cnt[i] = cnt_ + 1;
        if (i < N - 1) {
            cht.insert(Line(-2 * r[i + 1].x, dp[i] + sq(r[i + 1].x) - 2 * r[i + 1].x + 1 - sq(max(0LL, r[i].y - r[i + 1].x + 1)), cnt[i]));
        }
   }
}

long long take_photos(int n, int m, int K, vector<int> R, vector<int> C) {
    vector<point> f;
    r = vector<point> (), M = m;
    long long k = K;
    for (long long i = 0; i < n; i++) {
        if (R[i] > C[i]) swap(R[i], C[i]);
        f.push_back({R[i], C[i]});
    }
    sort(f.begin(), f.end());
    r.push_back(f[0]);
    for (long long i = 1; i < n; i++) {
        if (r.back().x == f[i].x) {
            r.pop_back();
            r.push_back(f[i]);
        } else if (f[i].y > r.back().y) {
            r.push_back(f[i]);
        }
    }
    N = r.size(), k = min(k, N);
    dp = vector<long long> (N), cnt = vector<long long> (N);
    long long l_ = 0, r_ = 1e17;
    while (l_ <= r_) {
        long long m_ = l_ + r_ >> 1;
        aliens(m_);
        if (l_ == r_) break;
        if (cnt[N - 1] > k) l_ = m_ + 1;
        else r_ = m_;
    }
    return dp[N - 1] - l_ * k;
}

Compilation message (stderr)

aliens.cpp: In function 'long long int take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:125:27: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  125 |         long long m_ = l_ + r_ >> 1;
      |                        ~~~^~~~

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