test/verify/yukicoder-952.test.cpp

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Last update: 2026-08-10 15:44:16+00:00
Problem: https://yukicoder.me/problems/no/952

Depends on

Convex Hull Trick Add Monotone (structure/convex-hull-trick/convex-hull-trick-add-monotone.hpp)

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/952

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <vector>

#include "../../structure/convex-hull-trick/convex-hull-trick-add-monotone.hpp"

using namespace std;

constexpr int64_t kInfinity = int64_t{1} << 60;

int main() {
  int N;
  cin >> N;
  vector<int> A(N);
  for (auto& a : A) cin >> a;
  vector<int64_t> S(N + 2);
  for (int i = 0; i < N; i++) {
    S[i + 1] = S[i] + A[i];
  }

  vector<vector<int64_t>> dp(N + 2, vector<int64_t>(N + 1, kInfinity));
  vector<vector<int64_t>> dp2(N + 2, vector<int64_t>(N + 1, kInfinity));
  dp[0][0] = 0;

  vector<ConvexHullTrickAddMonotone<int64_t, true>> chts(2 * N + 10);
  const int Shift = N + 5;

  for (int i = 0; i <= N + 1; i++) {
    if (i <= N) {
      for (int j = 0; j <= N; j++) {
        int Q = j - i + Shift;
        if (!chts[Q].empty())
          dp2[i + 1][j] =
              min(dp2[i + 1][j],
                  S[i] * S[i] + chts[Q].query_monotone_dec(-2 * S[i]));
      }
    }
    for (int j = 0; j <= N; j++) {
      if (i) dp[i][j] = min(dp[i - 1][j], dp2[i][j]);
      if (dp[i][j] != kInfinity)
        chts[j - i + Shift].add(S[i], dp[i][j] + S[i] * S[i]);
    }
  }

  for (int i = 1; i <= N; i++) {
    cout << dp[N + 1][i] << endl;
  }
}

#line 1 "test/verify/yukicoder-952.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/952

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <vector>

#line 2 "structure/convex-hull-trick/convex-hull-trick-add-monotone.hpp"

#include <cassert>
#include <cstdlib>
#include <deque>
#include <utility>

template <typename T, bool isMin>
struct ConvexHullTrickAddMonotone {
#define F first
#define S second
  using P = std::pair<T, T>;
  std::deque<P> H;

  ConvexHullTrickAddMonotone() = default;

  bool empty() const { return H.empty(); }

  void clear() { H.clear(); }

  static constexpr int sgn(T x) { return x == 0 ? 0 : (x < 0 ? -1 : 1); }

  static constexpr T floor_div(T n, T d) {
    return n / d - ((n ^ d) < 0 and n % d != 0);
  }

  static constexpr bool check(const P& a, const P& b, const P& c) {
    if (b.S == a.S || c.S == b.S)
      return sgn(b.F - a.F) * sgn(c.S - b.S) >= sgn(c.F - b.F) * sgn(b.S - a.S);
    // return (b.F-a.F)*(c.S-b.S) >= (b.S-a.S)*(c.F-b.F);
    if constexpr (std::is_integral<T>::value) {
      return floor_div(b.S - a.S, a.F - b.F) >= floor_div(c.S - b.S, b.F - c.F);
    } else {
      return (b.F - a.F) * sgn(c.S - b.S) / std::abs(b.S - a.S) >=
             (c.F - b.F) * sgn(b.S - a.S) / std::abs(c.S - b.S);
    }
  }

  void add(T a, T b) {
    if (!isMin) a *= -1, b *= -1;
    P line(a, b);
    if (empty()) {
      H.emplace_front(line);
      return;
    }
    if (H.front().F <= a) {
      if (H.front().F == a) {
        if (H.front().S <= b) return;
        H.pop_front();
      }
      while (H.size() >= 2 && check(line, H.front(), H[1])) H.pop_front();
      H.emplace_front(line);
    } else {
      assert(a <= H.back().F);
      if (H.back().F == a) {
        if (H.back().S <= b) return;
        H.pop_back();
      }
      while (H.size() >= 2 && check(H[H.size() - 2], H.back(), line))
        H.pop_back();
      H.emplace_back(line);
    }
  }

  static constexpr T get_y(const P& a, const T& x) { return a.F * x + a.S; }

  T query(T x) const {
    assert(!empty());
    int l = -1, r = H.size() - 1;
    while (l + 1 < r) {
      int m = (l + r) >> 1;
      if (get_y(H[m], x) >= get_y(H[m + 1], x))
        l = m;
      else
        r = m;
    }
    if (isMin) return get_y(H[r], x);
    return -get_y(H[r], x);
  }

  T query_monotone_inc(T x) {
    assert(!empty());
    while (H.size() >= 2 && get_y(H.front(), x) >= get_y(H[1], x))
      H.pop_front();
    if (isMin) return get_y(H.front(), x);
    return -get_y(H.front(), x);
  }

  T query_monotone_dec(T x) {
    assert(!empty());
    while (H.size() >= 2 && get_y(H.back(), x) >= get_y(H[H.size() - 2], x))
      H.pop_back();
    if (isMin) return get_y(H.back(), x);
    return -get_y(H.back(), x);
  }

#undef F
#undef S
};
#line 9 "test/verify/yukicoder-952.test.cpp"

using namespace std;

constexpr int64_t kInfinity = int64_t{1} << 60;

int main() {
  int N;
  cin >> N;
  vector<int> A(N);
  for (auto& a : A) cin >> a;
  vector<int64_t> S(N + 2);
  for (int i = 0; i < N; i++) {
    S[i + 1] = S[i] + A[i];
  }

  vector<vector<int64_t>> dp(N + 2, vector<int64_t>(N + 1, kInfinity));
  vector<vector<int64_t>> dp2(N + 2, vector<int64_t>(N + 1, kInfinity));
  dp[0][0] = 0;

  vector<ConvexHullTrickAddMonotone<int64_t, true>> chts(2 * N + 10);
  const int Shift = N + 5;

  for (int i = 0; i <= N + 1; i++) {
    if (i <= N) {
      for (int j = 0; j <= N; j++) {
        int Q = j - i + Shift;
        if (!chts[Q].empty())
          dp2[i + 1][j] =
              min(dp2[i + 1][j],
                  S[i] * S[i] + chts[Q].query_monotone_dec(-2 * S[i]));
      }
    }
    for (int j = 0; j <= N; j++) {
      if (i) dp[i][j] = min(dp[i - 1][j], dp2[i][j]);
      if (dp[i][j] != kInfinity)
        chts[j - i + Shift].add(S[i], dp[i][j] + S[i] * S[i]);
    }
  }

  for (int i = 1; i <= N; i++) {
    cout << dp[N + 1][i] << endl;
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	sample_1	AC	2 ms	4 MB
g++	sample_2	AC	2 ms	4 MB
g++	sample_3	AC	2 ms	4 MB
g++	testcase_1	AC	103 ms	100 MB
g++	testcase_10	AC	59 ms	59 MB
g++	testcase_11	AC	63 ms	62 MB
g++	testcase_12	AC	14 ms	17 MB
g++	testcase_13	AC	89 ms	89 MB
g++	testcase_14	AC	19 ms	22 MB
g++	testcase_15	AC	15 ms	17 MB
g++	testcase_16	AC	24 ms	28 MB
g++	testcase_17	AC	2 ms	4 MB
g++	testcase_18	AC	2 ms	4 MB
g++	testcase_19	AC	52 ms	54 MB
g++	testcase_2	AC	106 ms	98 MB
g++	testcase_20	AC	12 ms	14 MB
g++	testcase_3	AC	80 ms	80 MB
g++	testcase_4	AC	119 ms	119 MB
g++	testcase_5	AC	40 ms	43 MB
g++	testcase_6	AC	138 ms	134 MB
g++	testcase_7	AC	140 ms	136 MB
g++	testcase_8	AC	55 ms	56 MB
g++	testcase_9	AC	2 ms	4 MB
g++	testcase_tester_01	AC	2 ms	4 MB
g++	testcase_tester_02	AC	6 ms	8 MB
g++	testcase_tester_03	AC	155 ms	149 MB
clang++	sample_1	AC	2 ms	4 MB
clang++	sample_2	AC	2 ms	4 MB
clang++	sample_3	AC	2 ms	4 MB
clang++	testcase_1	AC	109 ms	100 MB
clang++	testcase_10	AC	62 ms	59 MB
clang++	testcase_11	AC	64 ms	62 MB
clang++	testcase_12	AC	15 ms	17 MB
clang++	testcase_13	AC	95 ms	89 MB
clang++	testcase_14	AC	20 ms	21 MB
clang++	testcase_15	AC	15 ms	17 MB
clang++	testcase_16	AC	26 ms	28 MB
clang++	testcase_17	AC	2 ms	4 MB
clang++	testcase_18	AC	2 ms	4 MB
clang++	testcase_19	AC	51 ms	54 MB
clang++	testcase_2	AC	108 ms	98 MB
clang++	testcase_20	AC	12 ms	14 MB
clang++	testcase_3	AC	91 ms	80 MB
clang++	testcase_4	AC	134 ms	119 MB
clang++	testcase_5	AC	43 ms	43 MB
clang++	testcase_6	AC	146 ms	134 MB
clang++	testcase_7	AC	153 ms	136 MB
clang++	testcase_8	AC	59 ms	56 MB
clang++	testcase_9	AC	2 ms	4 MB
clang++	testcase_tester_01	AC	2 ms	4 MB
clang++	testcase_tester_02	AC	6 ms	8 MB
clang++	testcase_tester_03	AC	166 ms	149 MB