test/dp/d_and_c.test.cpp

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• Last update: 2024-11-09 00:49:07+00:00
• Problem: https://www.hackerrank.com/contests/ioi-2014-practice-contest-2/challenges/guardians-lunatics-ioi14

Depends on

• dp/d_and_c.hpp
• prelude.hpp

Code

// competitive-verifier: PROBLEM https://www.hackerrank.com/contests/ioi-2014-practice-contest-2/challenges/guardians-lunatics-ioi14

#include "dp/d_and_c.hpp"

int n, k, a[8000];
ll sum[8001];

int main() {
  scanf("%d%d", &n, &k);
  rep(i, n) scanf("%d", a+i);
  rep(i, n) sum[i+1] = sum[i] + a[i];
  auto cost = [](int l, int r) {
    return (sum[r] - sum[l]) * (r - l);
  };
  auto dp = d_and_c_dp(k, n, cost);
  printf("%lld", dp[n]);
}

#line 1 "test/dp/d_and_c.test.cpp"
// competitive-verifier: PROBLEM https://www.hackerrank.com/contests/ioi-2014-practice-contest-2/challenges/guardians-lunatics-ioi14

#line 2 "prelude.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vc = vector<char>;
#define rep2(i, m, n) for (auto i = (m); i < (n); i++)
#define rep(i, n) rep2(i, 0, n)
#define repr2(i, m, n) for (auto i = (n); i-- > (m);)
#define repr(i, n) repr2(i, 0, n)
#define all(x) begin(x), end(x)
auto ndvec(int n, auto e) { return vector(n, e); }
auto ndvec(int n, auto ...e) { return vector(n, ndvec(e...)); }
auto comp_key(auto&& f) { return [&](auto&& a, auto&& b) { return f(a) < f(b); }; }
auto& max(const auto& a, const auto& b) { return a < b ? b : a; }
auto& min(const auto& a, const auto& b) { return b < a ? b : a; }
#if __cpp_lib_ranges
namespace R = std::ranges;
namespace V = std::views;
#endif
#line 3 "dp/d_and_c.hpp"

// O(k n log(n))
// Minimizes cost of k-partitions of [0, n) with k <= max_k
// (k == max_k if cost(i,i) == inf).
// Requires cost(a,c) + cost(b,d) <= cost(a,d) + cost(b,c)
// for a < b < c < d (wider is worse).
template <class F>
auto d_and_c_dp(int max_k, int n, F cost) {
  using T = decltype(cost(0, 0));
  vector<T> dp(n + 1), nxt(n + 1);
  rep(i, n + 1) dp[i] = cost(0, i);
  auto rec = [&](auto&& f, int l, int r, int optl, int optr) -> void {
    if (l == r) return;
    int m = (l + r) / 2;
    T best = numeric_limits<T>::max() / 2;
    int opt = -1;
    rep2(j, optl, min(m, optr) + 1) {
      if (best > dp[j] + cost(j, m)) best = dp[j] + cost(j, m), opt = j;
    }
    nxt[m] = best;
    f(f, l, m, optl, opt);
    f(f, m + 1, r, opt, optr);
  };
  rep2(k, 1, max_k) rec(rec, 0, n + 1, 0, n - 1), swap(dp, nxt);
  return dp;
}
#line 4 "test/dp/d_and_c.test.cpp"

int n, k, a[8000];
ll sum[8001];

int main() {
  scanf("%d%d", &n, &k);
  rep(i, n) scanf("%d", a+i);
  rep(i, n) sum[i+1] = sum[i] + a[i];
  auto cost = [](int l, int r) {
    return (sum[r] - sum[l]) * (r - l);
  };
  auto dp = d_and_c_dp(k, n, cost);
  printf("%lld", dp[n]);
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-12	00	AC	12 ms	8 MB
g++-12	01	AC	684 ms	8 MB
g++-12	02	AC	679 ms	8 MB
g++-12	03	AC	13 ms	8 MB
g++-12	04	AC	69 ms	8 MB
g++-12	05	AC	159 ms	8 MB
g++-12	06	AC	450 ms	8 MB
g++-12	07	AC	378 ms	8 MB
g++-12	08	AC	73 ms	8 MB
g++-12	09	AC	657 ms	8 MB
g++-12	10	AC	659 ms	8 MB
g++-12	11	AC	106 ms	8 MB
g++-12	12	AC	567 ms	8 MB
g++-12	13	AC	493 ms	8 MB
g++-12	14	AC	38 ms	8 MB
g++-12	15	AC	17 ms	8 MB
g++-12	16	AC	683 ms	8 MB
g++-12	17	AC	675 ms	8 MB
g++-12	18	AC	175 ms	8 MB
g++-12	19	AC	668 ms	8 MB
g++-12	20	AC	26 ms	8 MB
g++-12	21	AC	320 ms	8 MB
g++-12	22	AC	287 ms	8 MB
g++-12	23	AC	13 ms	8 MB
g++-12	24	AC	129 ms	8 MB
g++-12	25	AC	100 ms	8 MB
g++-12	26	AC	658 ms	8 MB
g++-12	27	AC	652 ms	8 MB
g++-12	28	AC	113 ms	8 MB
g++-12	29	AC	308 ms	8 MB
g++-12	30	AC	196 ms	8 MB
g++-12	31	AC	38 ms	8 MB
g++-12	32	AC	683 ms	8 MB
g++-12	33	AC	684 ms	8 MB
g++-12	34	AC	119 ms	8 MB
g++-12	35	AC	138 ms	8 MB
g++-12	36	AC	601 ms	8 MB
g++-12	37	AC	146 ms	8 MB
g++-12	38	AC	152 ms	8 MB
g++-12	39	AC	84 ms	8 MB
g++-12	40	AC	664 ms	8 MB
g++-12	41	AC	376 ms	8 MB
g++-12	42	AC	657 ms	8 MB
g++-12	43	AC	140 ms	8 MB
g++-12	44	AC	390 ms	8 MB
g++-12	45	AC	591 ms	8 MB
g++-12	46	AC	199 ms	8 MB
g++-12	47	AC	655 ms	8 MB
g++-12	48	AC	632 ms	8 MB
g++-12	49	AC	388 ms	8 MB
g++-12	50	AC	29 ms	8 MB
g++-12	51	AC	656 ms	8 MB
g++-12	52	AC	665 ms	8 MB
g++-12	53	AC	113 ms	8 MB
g++-12	54	AC	615 ms	8 MB
g++-12	55	AC	628 ms	8 MB
g++-12	56	AC	72 ms	8 MB
g++-12	57	AC	640 ms	8 MB
g++-12	58	AC	654 ms	8 MB
g++-12	59	AC	148 ms	8 MB
g++-12	60	AC	645 ms	8 MB
g++-12	61	AC	642 ms	8 MB
g++-12	62	AC	45 ms	8 MB
g++-12	63	AC	616 ms	8 MB
g++-12	64	AC	311 ms	8 MB
g++-12	65	AC	617 ms	8 MB

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