Submission #136925

#	Time	Username	Problem	Language	Result	Execution time	Memory
136925		AlexPop28	Aliens (IOI16_aliens)	C++11	100 / 100	279 ms	6488 KiB

aliens

#include <bits/stdc++.h>
#include "aliens.h"
#define dbg(x) cerr << (#x) << ": " << (x) << "; "
#define endline cerr << endl

using namespace std;

struct Line {
  int photos;
  long long a, b;
  Line(long long a_ = 0LL, long long b_ = 0LL, int photos_ = 0) :
    photos(photos_), a(a_), b(b_) {}
  long long operator()(long long x) {
    return a * x + b;
  }
};

template<class T> long long Sqr(T x) {
  return 1LL * x * x;
}

struct CHT {
  int sz = 0;
  deque<Line> dq;
  bool IsUseless(Line old, Line nline, Line comp) {
    if ((comp.b - nline.b) * (old.a - comp.a) == (nline.a - comp.a) * (comp.b - old.b))
      return old.photos <= nline.photos;
    return (comp.b - nline.b) * (old.a - comp.a) <= (nline.a - comp.a) * (comp.b - old.b);
  }
  void Insert(Line nline) {
    while (sz >= 2 && IsUseless(dq[sz - 1], nline, dq[sz - 2])) {
      dq.pop_back();
      --sz;
    }
    dq.emplace_back(nline);
    ++sz;
  }
  long long Query(int x) {
    while (sz >= 2 && (dq[0](x) > dq[1](x) ||
                      (dq[0](x) == dq[1](x) && dq[0].photos >= dq[1].photos))) {
      dq.pop_front();
      --sz;
    }
    return dq[0](x);
  }
};

struct Solver { // 100 perhaps? ca cica asa se face
  int n, m, k;
  vector<pair<int, int>> points;
  Solver(int n_, int m_, int k_, vector<int> &r, vector<int> &c) :
    n(n_), m(m_), k(k_), points(n) {
    for (int i = 0; i < n; ++i) {
      if (r[i] > c[i])
        swap(r[i], c[i]);
      points[i] = {r[i], c[i]};
    }
    points = RemoveRedundant(points);
    n = points.size() - 1;
  }

  long long Solve() {
    auto Check = [&](long long cost) {
      CHT cht;
      cht.Insert(Line(-2 * points[1].first, Sqr(points[1].first), 0));
      for (int i = 1; i <= n; ++i) {
        int x = points[i].second + 1;
        long long dp = cht.Query(x) + Sqr(x) + cost;
        int photos = cht.dq.front().photos + 1;
        if (i == n)
          return make_pair(dp, photos);
        Line nline(-2 * points[i + 1].first,
                  dp + Sqr(points[i + 1].first) -
                    Sqr(max(0, points[i].second - points[i + 1].first + 1)),
                      photos);
        cht.Insert(nline);
      }
    };
    long long lo = 0, hi = (long long)1e18, ans = (long long)1e18;
    while (lo <= hi) {
      long long mid = lo + (hi - lo) / 2LL;
      auto ck = Check(mid);
      if (ck.second <= k) {
        ans = ck.first - k * mid;
        hi = mid - 1;
      } else
        lo = mid + 1;
    }
    return ans;
  }

  long long Solve60() {
    // points[i].first < points[i + 1].first
    // points[i].second < points[i + 1].second

    vector<CHT> cht(k + 1); // ar trebui sa mi pun semne de exclamare sa nu uit
    for (int i = 0; i <= k; ++i)
      cht[i].Insert(Line(-2 * points[1].first, Sqr(points[1].first)));
    for (int i = 1; i <= n; ++i) {
      for (int j = k; j >= 1; --j) {
        int x = points[i].second + 1; // queries increasing
        long long dp = cht[j - 1].Query(x) + Sqr(x);
        if (i == n) {
          return dp;
        }
        Line nline(-2 * points[i + 1].first, // slopes decreasing
                  dp + Sqr(points[i + 1].first) -
                    Sqr(max(0, points[i].second - points[i + 1].first + 1)));
        cht[j].Insert(nline);
      }
    }
  }

  vector<vector<long long>> Brute() {
    vector<vector<long long>> dp(n + 2, vector<long long>(k + 2, (long long)1e18));
    fill(dp[0].begin(), dp[0].end(), 0LL);
    for (int i = 1; i <= n; ++i) { 
      for (int j = 1; j <= k; ++j) {
        dp[i][j] = dp[i][k - 1];
        for (int p = 0; p <= i - 1; ++p) {
          dp[i][j] = min(dp[i][j],
            dp[p][j - 1] + Sqr(points[i].second - points[p + 1].first + 1) -
              Sqr(max(0, points[p].second - points[p + 1].first + 1))); // intersection
        }
      }
    }
    return dp;
  }

  vector<pair<int, int>> RemoveRedundant(vector<pair<int, int>> &v) {
    sort(v.begin(), v.end(), [](const pair<int, int> &a, const pair<int, int> &b) {
      if (a.first != b.first)
        return a.first < b.first;
      return a.second > b.second;
    });
    int max_rgt = -1;
    vector<pair<int, int>> ret;
    ret.emplace_back(-1, -1);
    for (int i = 0; i < (int)points.size(); ++i) {
      if (points[i].second > max_rgt) {
        max_rgt = points[i].second;
        ret.emplace_back(points[i]);
      }
    }
    return ret;
  }
};

long long take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
  Solver solver(n, m, k, r, c);
  return solver.Solve();
}

Compilation message (stderr)

aliens.cpp: In lambda function:
aliens.cpp:78:5: warning: control reaches end of non-void function [-Wreturn-type]
     };
     ^

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