Submission #716196

#	Time	Username	Problem	Language	Result	Execution time	Memory
716196		arush_agu	Split the sequence (APIO14_sequence)	C++17	100 / 100	1525 ms	83276 KiB

sequence

#include <algorithm>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>

#ifdef DEBUG
#include <time.h>
#endif

#define all(a) (a).begin(), (a).end()
#define rev(a) (a).rbegin(), (a).rend()
#define F first
#define S second
int recur_depth = 0;
#ifdef DEBUG
#define dbg(x)                                                                 \
  {                                                                            \
    ++recur_depth;                                                             \
    auto x_ = x;                                                               \
    --recur_depth;                                                             \
    cerr << string(recur_depth, '\t') << "\e[91m" << __func__ << ":"           \
         << __LINE__ << "\t" << #x << " = " << x_ << "\e[39m" << endl;         \
  }
#else
#define dbg(x)
#endif

using namespace std;
using namespace __gnu_pbds;

typedef pair<int, int> ii;

typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> llll;

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<pair<int, int>> vii;
typedef vector<vii> vvii;

typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<pair<ll, ll>> vll;
typedef vector<vll> vvll;

typedef vector<bool> vb;

template <class type1>
using ordered_set = tree<type1, null_type, less<type1>, rb_tree_tag,
                         tree_order_statistics_node_update>;

template <typename A, typename B>
ostream &operator<<(ostream &os, const pair<A, B> &p) {
  return os << '(' << p.first << ", " << p.second << ')';
}
template <typename T_container, typename T = typename enable_if<
                                    !is_same<T_container, string>::value,
                                    typename T_container::value_type>::type>
ostream &operator<<(ostream &os, const T_container &v) {
  os << '{';
  string sep;
  for (const T &x : v)
    os << sep << x, sep = ", ";
  return os << '}';
}

const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
const ll INF = 2e18;
const ld EPS = 1e-9;

void solve() {
  int n, k; cin >> n >> k;
  vl a(n); for (ll &x : a) cin >> x;

  vl p(n); partial_sum(all(a), p.begin());
  // cerr << p << "\n";

  // vvl dp(k + 1, vl(n, -1)), split_at(k + 1, vl(n, -1));
  // function<ll(int, int)> f = [&](int i, int no_sub) -> ll {
  //   if (i < no_sub) return -INF;
  //   if (no_sub == 0) return 0;
  //
  //   ll &x = dp[no_sub][i];
  //   if (x != -1) return x;
  //
  //   // cerr << i << " " << no_sub << "\n";
  //
  //   x = -INF;
  //   for (int split=i - 1; split>=0; split--) {
  //     ll split_score = f(split, no_sub - 1);
  //     // cerr << "Split: " << split << "\n";
  //     // cerr << "\t" << split_score << "\n";
  //     // cerr << "\t" << p[split] * (p[i] - p[split]) << "\n";
  //     if (split_score >= 0) {
  //       ll curr = p[split] * (p[i] - p[split]) + split_score;
  //       if (x < curr) {
  //         x = curr;
  //         split_at[no_sub][i] = split;
  //       }
  //     }
  //   }
  //
  //   return x;
  // };
  //
  // // cerr << f(2, 1) << "\n";
  //
  // cout << f(n - 1, k) << "\n";
  // int idx = n - 1;
  // vl sa;
  // for (int kk=k; kk>0; kk--) {
  //   sa.push_back(split_at[kk][idx]);
  //   idx = sa.back();
  // }
  // reverse(all(sa));
  // for (ll &x : sa) cout << x + 1 << " ";
  // cout << "\n";
  

  vl dp_before(n), dp_after(n);
  vvi split_at(k + 1, vi(n));
  function<void(int, int, int, int, int)> f = [&](int l, int r, int sl, int sr, int kk) {
    if (l > r) return;

    int mid = (l + r) / 2;
    llll best = {-INF, sl};
    for (int ss=sl; ss<min(mid, sr + 1); ss++) if (dp_before[ss] >= 0) {
      ll curr_cost = p[ss] * (p[mid] - p[ss]) + dp_before[ss];
      best = max(best, {curr_cost, ss});
    }

    dp_after[mid] = best.first;
    split_at[kk][mid] = best.second;

    f(l, mid - 1, sl, best.second, kk);
    f(mid + 1, r, best.second, sr, kk);
  };

  for (int i=1; i<=k; i++) {
    f(0, n - 1, 0, n - 1, i);
    swap(dp_before, dp_after);
  }
  cout << dp_before[n - 1] << "\n";
  int idx = n - 1;
  vl sa;
  for (int kk=k; kk>0; kk--) {
    sa.push_back(split_at[kk][idx]);
    idx = sa.back();
  }
  reverse(all(sa));
  for (ll &x : sa) cout << x + 1 << " ";
  cout << "\n";
}

int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);

  clock_t start = clock();

  int test_cases = 1;
  /* cin >> test_cases; */

  while (test_cases--)
    solve();

#ifdef DEBUG
  cerr << fixed << setprecision(10)
       << "\nTime Taken: " << (double)(clock() - start) / CLOCKS_PER_SEC
       << "s\n";
#endif
  return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:179:11: warning: unused variable 'start' [-Wunused-variable]
  179 |   clock_t start = clock();
      |           ^~~~~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29