Submission #492696

#	Time	Username	Problem	Language	Result	Execution time	Memory
492696		cuiaoxiang	Split the sequence (APIO14_sequence)	C++14	0 / 100	16 ms	8460 KiB

sequence

// #define LOCAL
#define _USE_MATH_DEFINES
#include <array>
#include <cassert>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <iomanip>
#include <string>
#include <sstream>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <complex>
#include <cmath>
#include <numeric>
#include <bitset>
#include <functional>
#include <random>
#include <ctime>

using namespace std;

template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
  out << "(" << a.first << "," << a.second << ")";
  return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
  out << "["; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
  return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
  out << "["; bool first = true;
  for (auto v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
  return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
  out << "{"; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
  return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const multiset<T, Cmp>& a) {
  out << "{"; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
  return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
  out << "{"; bool first = true;
  for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}";
  return out;
}
#ifdef LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 42
#endif
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}

template <class T> auto vect(const T& v, int n) { return vector<T>(n, v); }
template <class T, class... D> auto vect(const T& v, int n, D... m) {
  return vector<decltype(vect(v, m...))>(n, vect(v, m...));
}

using int64 = long long;
using int128 = __int128_t;
using ii = pair<int, int>;
#define SZ(x) (int)((x).size())
template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
const int MOD = 1e9 + 7;
// const int MOD = 998244353;
// mt19937 mrand(random_device{}());
// int rnd(int x) { return mrand() % x; }
mt19937_64 mrand(random_device{}());
int64 rnd(int64 x) { return mrand() % x; }
template <class T> void out(const vector<T>& a) { for (int i = 0; i < SZ(a); ++i) cout << a[i] << " \n"[i + 1 == SZ(a)]; }
template <class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template <class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
template <class T> void dedup(vector<T>& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); }
void add_mod(int& x, int y) { x += y; if (x >= MOD) x -= MOD; }
void sub_mod(int& x, int y) { x += MOD - y; if (x >= MOD) x -= MOD; }

struct fast_ios {
  fast_ios() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
  };
} fast_ios_;

struct Line {
  int64 m, b;
};

// maintain lower envolope (upper convex hull) for minimum
struct Envelop {
  vector<Line> a;
  int ptr = 0;
  bool bad(int x, int y, int z) {
    return (a[z].b - a[x].b) * (a[x].m - a[y].m) <
      (a[y].b - a[x].b) * (a[x].m - a[z].m);
  }
  void insert(int64 m, int64 b) {
    a.push_back(Line{m, b});
    while (a.size() >= 3 && bad(a.size() - 3, a.size() - 2, a.size() - 1)) {
      a.erase(a.end() - 2);
    }
  }
  int64 eval(int64 x) {
    ptr = min(ptr, (int)a.size() - 1);
    while (ptr < a.size() - 1 &&
           a[ptr + 1].m * x + a[ptr + 1].b < a[ptr].m * x + a[ptr].b) ++ptr;
    return a[ptr].m * x + a[ptr].b;
  }
};

int main() {
  int n, m;
  cin >> n >> m;
  vector<int> a(n);
  for (auto& x : a) cin >> x;
  vector<int64> pre(n + 1);
  for (int i = 0; i < n; ++i) pre[i + 1] = pre[i] + a[i];

  auto dp = vect<int64>(0, m + 1, n + 1);
  for (int i = 0; i < n; ++i) dp[0][i + 1] = pre[i + 1] * pre[i + 1];
  trace(dp[0]);

  for (int k = 1; k <= m; ++k) {
    Envelop E;
    for (int i = 1; i <= n; ++i) {
      E.insert(-2 * pre[i - 1], dp[k - 1][i - 1] + pre[i - 1] * pre[i - 1]);
      dp[k][i] = E.eval(pre[i]) + pre[i] * pre[i];
    }
    trace(k, dp[k]);
  }
  int64 ret = (pre[n] * pre[n] - dp[m][n]) / 2;
  cout << ret << '\n';

  auto sqr =
    [&](int64 x) {
      return x * x;
    };
  vector<int> rec;
  for (int t = n, nt, k = m; k > 0; t = nt, --k) {
    for (nt = t - 1; nt >= 0 && dp[k - 1][nt] + sqr(pre[t] - pre[nt]) != dp[k][t]; --nt);
    trace(k, t, nt);
    rec.push_back(nt);
  }
  reverse(rec.begin(), rec.end());
  out(rec);
  return 0;
}

Compilation message (stderr)

sequence.cpp: In member function 'int64 Envelop::eval(int64)':
sequence.cpp:132:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  132 |     while (ptr < a.size() - 1 &&
      |            ~~~~^~~~~~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:68:20: warning: statement has no effect [-Wunused-value]
   68 | #define trace(...) 42
      |                    ^~
sequence.cpp:148:3: note: in expansion of macro 'trace'
  148 |   trace(dp[0]);
      |   ^~~~~
sequence.cpp:68:20: warning: statement has no effect [-Wunused-value]
   68 | #define trace(...) 42
      |                    ^~
sequence.cpp:156:5: note: in expansion of macro 'trace'
  156 |     trace(k, dp[k]);
      |     ^~~~~
sequence.cpp:68:20: warning: statement has no effect [-Wunused-value]
   68 | #define trace(...) 42
      |                    ^~
sequence.cpp:168:5: note: in expansion of macro 'trace'
  168 |     trace(k, t, nt);
      |     ^~~~~

• Subtask 1: 0 / 11
• Subtask 2: 0 / 11
• Subtask 3: 0 / 11
• Subtask 4: 0 / 17
• Subtask 5: 0 / 21
• Subtask 6: 0 / 29