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

#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using P = pair<lint, lint>;

lint dp[2123][2123];

template <class T> void chmax(T &a, T b) { a = max(a, b); }

int main() {
  lint n;
  cin >> n;

  vector<P> a(n);
  for (lint i = 0; i < n; i++) {
    lint x;
    cin >> x;
    a.emplace_back(x, i);
  }
  sort(a.rbegin(), a.rend());

  fill(&dp[0][0], &dp[2123][0], -1e18);
  dp[0][0] = 0;
  for (lint all = 0; all < n; all++) {
    auto [x, i] = a[all];
    for (lint mn = 0; mn <= all; mn++) {
      chmax(dp[all + 1][mn], dp[all][mn] + x * abs(n - 1 - all + mn - i));
      chmax(dp[all + 1][mn + 1], dp[all][mn] + x * abs(mn - i));
    }
  }

  cout << *max_element(begin(dp[n]), end(dp[n])) << endl;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
using lint = long long int;

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() {
  lint n;
  cin >> n;

  vector<lint> a(n);
  for (auto &elem : a)
    cin >> elem;

  PrimalDual<lint, lint> g(n + n + 2);

  lint s = n + n;
  lint t = n + n + 1;
  for (lint i = 0; i < n; i++) {
    g.add_edge(s, i, 1, 0);
    g.add_edge(i + n, t, 1, 0);
  }

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

  cout << -g.min_cost_flow(s, t, n) << endl;
}