test/verify/yukicoder-705.test.cpp

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• Last update: 2024-04-24 02:34:04+09:00
• Problem: https://yukicoder.me/problems/no/705

Depends on

• Monotone Minima (dp/monotone-minima.hpp)
• Online Offline DP(オンライン・オフライン変換) (dp/online-offline-dp.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/705

#include "../../template/template.hpp"

#include "../../dp/online-offline-dp.hpp"

int main() {
  int n;
  cin >> n;
  vector< int > a(n), x(n), y(n);
  for(int i = 0; i < n; i++) cin >> a[i];
  for(int i = 0; i < n; i++) cin >> x[i];
  for(int i = 0; i < n; i++) cin >> y[i];
  function< int64_t(int, int) > dist = [&](int i, int j) {
    assert(0 <= i && i < j && j <= n);
    int s = abs(a[j - 1] - x[i]);
    int t = abs(y[i]);
    return 1LL * s * s * s + 1LL * t * t * t;
  };
  cout << online_offline_dp(n, dist).back() << endl;
}

#line 1 "test/verify/yukicoder-705.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/705

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};
 
template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/yukicoder-705.test.cpp"

#line 1 "dp/monotone-minima.hpp"
template< typename T, typename Compare = less< T > >
vector< pair< int, T > > monotone_minima(int H, int W, const function< T(int, int) > &f, const Compare &comp = Compare()) {
  vector< pair< int, T > > dp(H);
  function< void(int, int, int, int) > dfs = [&](int top, int bottom, int left, int right) {
    if(top > bottom) return;
    int line = (top + bottom) / 2;
    T ma;
    int mi = -1;
    for(int i = left; i <= right; i++) {
      T cst = f(line, i);
      if(mi == -1 || comp(cst, ma)) {
        ma = cst;
        mi = i;
      }
    }
    dp[line] = make_pair(mi, ma);
    dfs(top, line - 1, left, mi);
    dfs(line + 1, bottom, mi, right);
  };
  dfs(0, H - 1, 0, W - 1);
  return dp;
}
#line 2 "dp/online-offline-dp.hpp"

template< typename T, typename Compare = less< T > >
vector< T > online_offline_dp(int W, const function< T(int, int) > &f, const Compare &comp = Compare()) {
  vector< T > dp(W + 1);
  vector< int > isset(W + 1);
  int y_base = -1, x_base = -1;
  function< T(int, int) > get_cost = [&](int y, int x) { // return dp[0, x+x_base)+f[x+x_base, y+y_base)
    return dp[x + x_base] + f(x + x_base, y + y_base);
  };
  function< void(int, int, int) > induce = [&](int l, int m, int r) { // dp[l, m) -> dp[m, r)
    x_base = l, y_base = m;
    auto ret = monotone_minima(r - m, m - l, get_cost, comp);
    for(int i = 0; i < ret.size(); i++) {
      if(!isset[m + i] || comp(ret[i].second, dp[m + i])) {
        isset[m + i] = true;
        dp[m + i] = ret[i].second;
      }
    }
  };
  function< void(int, int) > dfs = [&](int l, int r) {
    if(l + 1 == r) {
      x_base = l, y_base = l;
      T cst = l ? get_cost(0, -1) : 0;
      if(!isset[l] || comp(cst, dp[l])) {
        isset[l] = true;
        dp[l] = cst;
      }
    } else {
      int mid = (l + r) / 2;
      dfs(l, mid);
      induce(l, mid, r);
      dfs(mid, r);
    }
  };
  dfs(0, W + 1);
  return dp;
};
#line 6 "test/verify/yukicoder-705.test.cpp"

int main() {
  int n;
  cin >> n;
  vector< int > a(n), x(n), y(n);
  for(int i = 0; i < n; i++) cin >> a[i];
  for(int i = 0; i < n; i++) cin >> x[i];
  for(int i = 0; i < n; i++) cin >> y[i];
  function< int64_t(int, int) > dist = [&](int i, int j) {
    assert(0 <= i && i < j && j <= n);
    int s = abs(a[j - 1] - x[i]);
    int t = abs(y[i]);
    return 1LL * s * s * s + 1LL * t * t * t;
  };
  cout << online_offline_dp(n, dist).back() << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample1.txt	AC	6 ms	4 MB
g++	00_sample2.txt	AC	6 ms	4 MB
g++	00_sample3.txt	AC	6 ms	4 MB
g++	00_sample4.txt	AC	6 ms	4 MB
g++	10_small_1.txt	AC	6 ms	4 MB
g++	10_small_10.txt	AC	6 ms	4 MB
g++	10_small_2.txt	AC	6 ms	4 MB
g++	10_small_3.txt	AC	7 ms	4 MB
g++	10_small_4.txt	AC	6 ms	4 MB
g++	10_small_5.txt	AC	6 ms	4 MB
g++	10_small_6.txt	AC	6 ms	4 MB
g++	10_small_7.txt	AC	6 ms	4 MB
g++	10_small_8.txt	AC	6 ms	4 MB
g++	10_small_9.txt	AC	6 ms	4 MB
g++	20_medium_1.txt	AC	7 ms	4 MB
g++	20_medium_10.txt	AC	7 ms	4 MB
g++	20_medium_2.txt	AC	7 ms	4 MB
g++	20_medium_3.txt	AC	7 ms	4 MB
g++	20_medium_4.txt	AC	7 ms	4 MB
g++	20_medium_5.txt	AC	6 ms	4 MB
g++	20_medium_6.txt	AC	6 ms	4 MB
g++	20_medium_7.txt	AC	7 ms	4 MB
g++	20_medium_8.txt	AC	7 ms	4 MB
g++	20_medium_9.txt	AC	7 ms	4 MB
g++	30_large_1.txt	AC	294 ms	13 MB
g++	30_large_2.txt	AC	294 ms	13 MB
g++	30_large_3.txt	AC	298 ms	13 MB
g++	30_large_4.txt	AC	297 ms	13 MB
g++	30_large_5.txt	AC	293 ms	13 MB
g++	30_large_6.txt	AC	295 ms	13 MB
g++	40_large_binary_1.txt	AC	337 ms	13 MB
g++	40_large_binary_2.txt	AC	304 ms	13 MB
g++	40_large_binary_3.txt	AC	297 ms	13 MB
g++	40_zero_000.txt	AC	283 ms	13 MB
g++	40_zero_001.txt	AC	284 ms	13 MB
g++	40_zero_010.txt	AC	289 ms	13 MB
g++	40_zero_011.txt	AC	296 ms	13 MB
g++	40_zero_100.txt	AC	289 ms	13 MB
g++	40_zero_101.txt	AC	296 ms	13 MB
g++	40_zero_110.txt	AC	336 ms	13 MB
g++	99_corner1.txt	AC	7 ms	4 MB
g++	99_corner2.txt	AC	6 ms	4 MB
g++	99_corner3.txt	AC	6 ms	4 MB
g++	99_corner4.txt	AC	301 ms	13 MB
clang++	00_sample1.txt	AC	7 ms	4 MB
clang++	00_sample2.txt	AC	6 ms	4 MB
clang++	00_sample3.txt	AC	6 ms	4 MB
clang++	00_sample4.txt	AC	6 ms	4 MB
clang++	10_small_1.txt	AC	6 ms	4 MB
clang++	10_small_10.txt	AC	7 ms	4 MB
clang++	10_small_2.txt	AC	6 ms	4 MB
clang++	10_small_3.txt	AC	6 ms	4 MB
clang++	10_small_4.txt	AC	6 ms	4 MB
clang++	10_small_5.txt	AC	6 ms	4 MB
clang++	10_small_6.txt	AC	6 ms	4 MB
clang++	10_small_7.txt	AC	6 ms	4 MB
clang++	10_small_8.txt	AC	7 ms	4 MB
clang++	10_small_9.txt	AC	7 ms	4 MB
clang++	20_medium_1.txt	AC	7 ms	4 MB
clang++	20_medium_10.txt	AC	7 ms	4 MB
clang++	20_medium_2.txt	AC	7 ms	4 MB
clang++	20_medium_3.txt	AC	7 ms	4 MB
clang++	20_medium_4.txt	AC	7 ms	4 MB
clang++	20_medium_5.txt	AC	6 ms	4 MB
clang++	20_medium_6.txt	AC	7 ms	4 MB
clang++	20_medium_7.txt	AC	7 ms	4 MB
clang++	20_medium_8.txt	AC	7 ms	4 MB
clang++	20_medium_9.txt	AC	6 ms	4 MB
clang++	30_large_1.txt	AC	295 ms	13 MB
clang++	30_large_2.txt	AC	293 ms	13 MB
clang++	30_large_3.txt	AC	293 ms	13 MB
clang++	30_large_4.txt	AC	293 ms	13 MB
clang++	30_large_5.txt	AC	293 ms	13 MB
clang++	30_large_6.txt	AC	293 ms	13 MB
clang++	40_large_binary_1.txt	AC	335 ms	13 MB
clang++	40_large_binary_2.txt	AC	301 ms	13 MB
clang++	40_large_binary_3.txt	AC	294 ms	13 MB
clang++	40_zero_000.txt	AC	280 ms	13 MB
clang++	40_zero_001.txt	AC	280 ms	13 MB
clang++	40_zero_010.txt	AC	285 ms	13 MB
clang++	40_zero_011.txt	AC	291 ms	13 MB
clang++	40_zero_100.txt	AC	286 ms	13 MB
clang++	40_zero_101.txt	AC	299 ms	13 MB
clang++	40_zero_110.txt	AC	339 ms	13 MB
clang++	99_corner1.txt	AC	7 ms	4 MB
clang++	99_corner2.txt	AC	6 ms	4 MB
clang++	99_corner3.txt	AC	6 ms	4 MB
clang++	99_corner4.txt	AC	302 ms	13 MB

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