Submission #255443

#	Time	Username	Problem	Language	Result	Execution time	Memory
255443		rama_pang	Split the sequence (APIO14_sequence)	C++14	100 / 100	148 ms	6772 KiB

sequence

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

using lint = long long;
const int MAXN = 1e5 + 5;

struct Line {
  int id, cnt;
  lint a, b;
  Line() {}
  Line(int id, int cnt, lint a, lint b) : id(id), cnt(cnt), a(a), b(b) {}
  pair<lint, int> get(lint x) { return {a * x + b, cnt}; }
};

class ConvexHull {
 public:
  ConvexHull() {}

  int sz, ptr = 0;
  vector<Line> line;

  void Clear() {
    ptr = 0, line.clear();
  }

  bool Majorize(Line a, Line b, Line c) {
    return make_tuple((1.00 * (c.b - a.b) / (a.a - c.a)), -c.cnt, c.id) <
           make_tuple((1.00 * (b.b - a.b) / (a.a - b.a)), -b.cnt, b.id);
  } 

  void Insert(Line n) {
    sz = line.size();
    if (!line.empty() && line.back().a == n.a) {
      if (n.b < line.back().b) {
        n = line.back();
      }
      line.pop_back();
    }
    while (ptr + 1 < sz && Majorize(line[sz - 2], line[sz - 1], n)) {
      line.pop_back();
      sz--;
    }
    line.emplace_back(n);
  }

  tuple<lint, int, int> Query(lint x) {
    while (ptr + 1 < (int) line.size() && line[ptr].get(x) <= line[ptr + 1].get(x)) {
      ptr++;
    }
    return make_tuple(line[ptr].get(x).first, line[ptr].cnt, line[ptr].id);
  }
};

int N, K;
lint A[MAXN];
ConvexHull cht;
int prv[MAXN];
pair<lint, int> dp[MAXN];

void Trial(lint lambda, int sign) {
  cht.Clear();
  for (int i = 1; i <= N; i++) {
    cht.Insert(Line(i - 1, dp[i - 1].second, A[i - 1], dp[i - 1].first - A[i - 1] * A[i - 1]));
    lint x; int y, z;
    tie(x, y, z) = cht.Query(A[i]);
    dp[i] = make_pair(x - lambda, y + sign);
    prv[i] = z;
  }
}

vector<int> Trace(lint lambda, int sign) {
  Trial(lambda, sign);
  vector<int> res;
  for (int cur = N; cur > 0; cur = prv[cur]) {
    res.emplace_back(cur);
  }
  res.emplace_back(0);
  reverse(begin(res), end(res));
  return res;
}

void Answer(vector<int> res) {
  lint ans = 0;
  for (int i = 1; i < (int) res.size(); i++) {
    ans += (A[res[i]] - A[res[i - 1]]) * A[res[i - 1]];
  }
  cout << ans << "\n";
  for (int i = 1; i + 1 < (int) res.size(); i++) {
    if (i > 1) {
      cout << " ";
    }
    cout << res[i];
  }
  cout << "\n";
  exit(0);
}

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);

  cin >> N >> K; K++;
  for (int i = 1; i <= N; i++) {
    cin >> A[i];
    A[i] += A[i - 1];
  }

  lint lo = 0, hi = 1e17;
  while (lo < hi) {
    lint md = (lo + hi) / 2;
    Trial(md, -1);
    if (-dp[N].second <= K) {
      hi = md;
    } else {
      lo = md + 1;
    }
  }
  
  auto minim = Trace(lo, -1);
  auto maxim = Trace(lo, +1);
  if (minim.size() == K + 1) Answer(minim);
  if (maxim.size() == K + 1) Answer(maxim);
  for (int i = 1, j = 0; i < (int) maxim.size(); i++) {
    while (minim[j] <= maxim[i - 1]) {
      j++;
    }
    if (minim[j] >= maxim[i] && i + (int) minim.size() - j == K + 1) {
      vector<int> res;
      for (int k = 0; k < i; k++) {
        res.emplace_back(maxim[k]);
      }
      for (int k = j; k < (int) minim.size(); k++) {
        res.emplace_back(minim[k]);
      }
      Answer(res);
    }
  }
  return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:121:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if (minim.size() == K + 1) Answer(minim);
       ~~~~~~~~~~~~~^~~~~~~~
sequence.cpp:122:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if (maxim.size() == K + 1) Answer(maxim);
       ~~~~~~~~~~~~~^~~~~~~~

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