Submission #837634

#	Time	Username	Problem	Language	Result	Execution time	Memory
837634		erdemkiraz	Aliens (IOI16_aliens)	C++17	4 / 100	2 ms	340 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
typedef pair<int, int> ii;
 
const int M = 1e6 + 5;
 
int n, m, k;
int at[M];

vector<int> ats;
vector<ll> a, b;

const ll is_query = -(1LL<<62);
struct Line {
    ll m, b;
    int cnt;
    mutable function<const Line*()> succ;
    bool operator<(const Line& rhs) const {
        if (rhs.b != is_query) return m < rhs.m;
        const Line* s = succ();
        if (!s) return 0;
        ll x = rhs.m;
        return b - s->b < (s->m - m) * x;
    }
};
struct HullDynamic : public multiset<Line> { // will maintain upper hull for maximum
    bool bad(iterator y) {
        auto z = next(y);
        if (y == begin()) {
            if (z == end()) return 0;
            return y->m == z->m && y->b <= z->b;
        }
        auto x = prev(y);
        if (z == end()) return y->m == x->m && y->b <= x->b;
        return (x->b - y->b)*(z->m - y->m) >= (y->b - z->b)*(y->m - x->m);
    }
    void insert_line(ll m, ll b, int cnt) {
      m *= -1;
      b *= -1;
        auto y = insert({ m, b, cnt });
        y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
        if (bad(y)) { erase(y); return; }
        while (next(y) != end() && bad(next(y))) erase(next(y));
        while (y != begin() && bad(prev(y))) erase(prev(y));
    }
    pair<ll, int> eval(ll x) {
        auto l = *lower_bound((Line) { x, is_query });
        return {-(l.m * x + l.b), l.cnt};
    }
};

vector<int> go;

tuple<ll, int, ll> get(ll discourage) {
  vector<ll> dp(m + 1, 1e18);

  dp[0] = 0;

  vector<ll> cost(m + 1);

  HullDynamic trick;

  for(int i = 1; i <= m; i++) {
    ll len = max(0LL, b[i - 1] - a[i]);
    cost[i] = dp[i - 1] + a[i] * a[i] - len * len;

    trick.insert_line(- 2 * a[i], cost[i], go[i - 1] + 1);

    auto [res, cnt] = trick.eval(b[i]);

    dp[i] = res + b[i] * b[i] + discourage;
    go[i] = cnt;
  }

  // printf("discourage = %.3lf cnt = %d dp = %.3lf real = %lll\n", discourage, cnt, dp[m], ans);

  ll ans = dp[m] - go[m] * discourage;

  return {dp[m], go[m], ans};
}
 
ll take_photos(int nn, int mm, int kk, vector<int> rr, vector<int> cc) {
  n = nn;
  m = mm;
  k = kk;
 
  for(int i = 0; i < n; i++) {
    if(rr[i] > cc[i]) {
      swap(rr[i], cc[i]);
    }
    at[rr[i] + 1] = max(at[rr[i] + 1], cc[i] + 2);
  }

  a.push_back(0);
  b.push_back(0);

  for(int i = 1; i <= m + 1; i++) {
    if(at[i]) {
      if(!ats.empty() and ats.back() >= at[i]) {
        continue;
      }
      ats.push_back(at[i]);

      a.push_back(i);
      b.push_back(at[i]);
    }
  }

  m = (int) a.size() - 1;

  k = min(k, m);

  if(k == 1 or m == 1) {
    return (b.back() - a[1]) * (b.back() - a[1]);
  }

  go.resize(m + 1);

  ll l = 0, r = 1e13;

  ll ans = 1e18;

  while(l < r) {
    ll m = (l + r) / 2;

    auto [_, used, res] = get(m);

    if(used > k) {
      l = m + 1;
    }
    else {
      ans = min(ans, res);
      r = m;
    }
  }

  auto [_, used, res] = get(l);

  ans = res;

  return ans;
}

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