test/dp/knuth_partition.test.cpp

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• Last update: 2024-11-09 00:49:07+00:00
• Problem: https://www.hackerrank.com/contests/world-codesprint-5/challenges/mining/problem

Depends on

• dp/knuth_partition.hpp
• prelude.hpp

Code

// competitive-verifier: PROBLEM https://www.hackerrank.com/contests/world-codesprint-5/challenges/mining/problem

#include "dp/knuth_partition.hpp"

int k, n, w[1000000], x[1000000];
ll cost[5001][5001];

int main() {
  scanf("%d%d", &n, &k);
  rep(i, n) scanf("%d%d", &x[i], &w[i]);
  rep(l, n) {
    int k = l;
    ll wl = w[l], wr = 0;
    ll c = cost[l][l + 1] = 0;
    rep2(r, l + 1, n) {
      wr += w[r], c += 1LL * (x[r] - x[k]) * w[r];
      while (k < r && wl < wr) {
        c = c + (wl - wr) * (x[k + 1] - x[k]);
        k++;
        wl += w[k], wr -= w[k];
      }
      cost[l][r + 1] = c;
    }
  }
  auto dp = knuth_partition_dp(k, n, [](int l, int r) { return cost[l][r]; });
  printf("%lld", dp[n]);
}

#line 1 "test/dp/knuth_partition.test.cpp"
// competitive-verifier: PROBLEM https://www.hackerrank.com/contests/world-codesprint-5/challenges/mining/problem

#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/knuth_partition.hpp"

// O(kn + n^2)
// 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 knuth_partition_dp(int max_k, int n, F cost) {
  using T = decltype(cost(0, 0));
  vector<T> dp(n + 1), dp2(n + 1);
  vector<int> opt(n + 2), opt2(n + 2);
  rep(i, n + 1) dp[i] = cost(0, i);
  rep2(k, 1, max_k) {
    fill(all(dp2), numeric_limits<T>::max() / 2);
    opt2[n+1] = n;
    repr(i, n + 1) rep2(j, opt[i], min(i, opt2[i + 1]) + 1) {
      if (dp2[i] > dp[j] + cost(j, i)) dp2[i] = dp[j] + cost(j, i), opt2[i] = j;
    }
    swap(dp, dp2);
    swap(opt, opt2);
  }
  return dp;
}
#line 4 "test/dp/knuth_partition.test.cpp"

int k, n, w[1000000], x[1000000];
ll cost[5001][5001];

int main() {
  scanf("%d%d", &n, &k);
  rep(i, n) scanf("%d%d", &x[i], &w[i]);
  rep(l, n) {
    int k = l;
    ll wl = w[l], wr = 0;
    ll c = cost[l][l + 1] = 0;
    rep2(r, l + 1, n) {
      wr += w[r], c += 1LL * (x[r] - x[k]) * w[r];
      while (k < r && wl < wr) {
        c = c + (wl - wr) * (x[k + 1] - x[k]);
        k++;
        wl += w[k], wr -= w[k];
      }
      cost[l][r + 1] = c;
    }
  }
  auto dp = knuth_partition_dp(k, n, [](int l, int r) { return cost[l][r]; });
  printf("%lld", dp[n]);
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-12	00	AC	30 ms	12 MB
g++-12	01	AC	29 ms	12 MB
g++-12	02	AC	30 ms	12 MB
g++-12	03	AC	29 ms	12 MB
g++-12	04	AC	30 ms	12 MB
g++-12	05	AC	29 ms	14 MB
g++-12	06	AC	29 ms	14 MB
g++-12	07	AC	29 ms	12 MB
g++-12	08	AC	30 ms	12 MB
g++-12	09	AC	30 ms	12 MB
g++-12	10	AC	30 ms	12 MB
g++-12	11	AC	32 ms	18 MB
g++-12	12	AC	37 ms	28 MB
g++-12	13	AC	58 ms	45 MB
g++-12	14	AC	45 ms	39 MB
g++-12	15	AC	38 ms	29 MB
g++-12	16	AC	36 ms	30 MB
g++-12	17	AC	55 ms	45 MB
g++-12	18	AC	42 ms	37 MB
g++-12	19	AC	108 ms	70 MB
g++-12	20	AC	76 ms	63 MB
g++-12	21	AC	171 ms	102 MB
g++-12	22	AC	199 ms	129 MB
g++-12	23	AC	71 ms	55 MB
g++-12	24	AC	117 ms	86 MB
g++-12	25	AC	925 ms	189 MB
g++-12	26	AC	321 ms	149 MB
g++-12	27	AC	954 ms	206 MB
g++-12	28	AC	1160 ms	207 MB
g++-12	29	AC	1031 ms	207 MB
g++-12	30	AC	1041 ms	207 MB
g++-12	31	AC	1099 ms	207 MB
g++-12	32	AC	1110 ms	205 MB
g++-12	33	AC	730 ms	206 MB
g++-12	34	AC	907 ms	206 MB
g++-12	35	AC	1212 ms	207 MB
g++-12	36	AC	1171 ms	205 MB
g++-12	37	AC	1193 ms	206 MB
g++-12	38	AC	1166 ms	206 MB
g++-12	39	AC	49 ms	51 MB

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