Problem p02709 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

using namespace std;

#define SZ(x) (int)(x.size())

using ll = long long;
using ld = long double;
const ld eps = 1e-9;
const ll MOD = 1000000007;
const int INF = 1000000000;
const ll LINF = 1ll << 50;

template <typename T1, typename T2> void chmax(T1 &a, const T2 &b) {
  if (a < b)
    a = b;
}

template <typename T1, typename T2> void chmin(T1 &a, const T2 &b) {
  if (a > b)
    a = b;
}

template <typename T> void printv(const vector<T> &s) {
  for (int i = 0; i < (int)(s.size()); ++i) {
    cout << s[i];
    if (i == (int)(s.size()) - 1)
      cout << endl;
    else
      cout << " ";
  }
}

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

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(10);

  int n;
  cin >> n;
  vector<pair<ll, ll>> v(n);
  for (int i = 0; i < n; ++i) {
    cin >> v[i].first;
    v[i].second = i;
  }
  sort(v.rbegin(), v.rend());

  vector<vector<ll>> dp(n, vector<ll>(n + 1, -LINF));
  dp[0][0] = v[0].first * abs(n - 1 - v[0].second);
  dp[0][1] = v[0].first * v[0].second;

  for (int i = 1; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (dp[i - 1][j] == -LINF)
        continue;
      chmax(dp[i][j + 1], dp[i - 1][j] + v[i].first * abs(v[i].second - j));
      chmax(dp[i][j],
            dp[i - 1][j] + v[i].first * abs(n - 1 - (i - j) - v[i].second));
    }
  }

  ll ans = 0;
  for (int i = 0; i < n; ++i) {
    chmax(ans, dp[n - 1][i]);
  }
  cout << ans << endl;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

#define SZ(x) (int)(x.size())

using ll = long long;
using ld = long double;
const ld eps = 1e-9;
const ll MOD = 1000000007;
const int INF = 1000000000;
const ll LINF = 1ll << 50;

template <typename T1, typename T2> void chmax(T1 &a, const T2 &b) {
  if (a < b)
    a = b;
}

template <typename T1, typename T2> void chmin(T1 &a, const T2 &b) {
  if (a > b)
    a = b;
}

template <typename T> void printv(const vector<T> &s) {
  for (int i = 0; i < (int)(s.size()); ++i) {
    cout << s[i];
    if (i == (int)(s.size()) - 1)
      cout << endl;
    else
      cout << " ";
  }
}

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

template <typename flow_t, typename cost_t> struct PrimalDual {
  const cost_t INF;

  struct edge {
    int to;
    flow_t cap;
    cost_t cost;
    int rev;
    bool isrev;
  };
  vector<vector<edge>> graph;
  vector<cost_t> potential, min_cost;
  vector<int> prevv, preve;

  PrimalDual(int V) : graph(V), INF(numeric_limits<cost_t>::max()) {}

  void add_edge(int from, int to, flow_t cap, cost_t cost) {
    graph[from].emplace_back(
        (edge){to, cap, cost, (int)graph[to].size(), false});
    graph[to].emplace_back(
        (edge){from, 0, -cost, (int)graph[from].size() - 1, true});
  }

  cost_t min_cost_flow(int s, int t, flow_t f) {
    int V = (int)graph.size();
    cost_t ret = 0;
    using Pi = pair<cost_t, int>;
    priority_queue<Pi, vector<Pi>, greater<Pi>> que;
    potential.assign(V, 0);
    preve.assign(V, -1);
    prevv.assign(V, -1);

    while (f > 0) {
      min_cost.assign(V, INF);
      que.emplace(0, s);
      min_cost[s] = 0;
      while (!que.empty()) {
        Pi p = que.top();
        que.pop();
        if (min_cost[p.second] < p.first)
          continue;
        for (int i = 0; i < graph[p.second].size(); i++) {
          edge &e = graph[p.second][i];
          cost_t nextCost = min_cost[p.second] + e.cost + potential[p.second] -
                            potential[e.to];
          if (e.cap > 0 && min_cost[e.to] > nextCost) {
            min_cost[e.to] = nextCost;
            prevv[e.to] = p.second, preve[e.to] = i;
            que.emplace(min_cost[e.to], e.to);
          }
        }
      }
      if (min_cost[t] == INF)
        return -1;
      for (int v = 0; v < V; v++)
        potential[v] += min_cost[v];
      flow_t addflow = f;
      for (int v = t; v != s; v = prevv[v]) {
        addflow = min(addflow, graph[prevv[v]][preve[v]].cap);
      }
      f -= addflow;
      ret += addflow * potential[t];
      for (int v = t; v != s; v = prevv[v]) {
        edge &e = graph[prevv[v]][preve[v]];
        e.cap -= addflow;
        graph[v][e.rev].cap += addflow;
      }
    }
    return ret;
  }

  void output() {
    for (int i = 0; i < graph.size(); i++) {
      for (auto &e : graph[i]) {
        if (e.isrev)
          continue;
        auto &rev_e = graph[e.to][e.rev];
        cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/"
             << rev_e.cap + e.cap << ")" << endl;
      }
    }
  }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(10);

  int n;
  cin >> n;
  vector<ll> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }

  PrimalDual<ll, ll> flow(2 * n + 2);
  for (int i = 0; i < n; ++i) {
    flow.add_edge(0, i + 1, 1, 0);
    flow.add_edge(2 * n - i, 2 * n + 1, 1, 0);
  }

  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      flow.add_edge(i + 1, n + 1 + j, 1, INF - a[i] * abs(i - j));
    }
  }

  ll tmp = flow.min_cost_flow(0, 2 * n + 1, n);
  cout << (ll)n * INF - tmp << endl;
}