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

#include <algorithm>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;
using lint = long long int;
long long int INF = 1001001001001001LL;
int inf = 1000000007;
long long int MOD = 1000000007LL;
double PI = 3.1415926535897932;

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

#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()

/* do your best */

int main() {

  int n;
  cin >> n;
  vector<lint> a(n);
  vector<pair<lint, lint>> dat(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    dat[i] = {a[i], i + 1};
  }

  sort(RALL(dat));
  vector<vector<lint>> dp(n + 1, vector<lint>(n + 1, 0));
  for (int i = 1; i <= n; i++) {
    lint score;
    lint x;
    tie(score, x) = dat[i - 1];

    // すでに i - 1 個埋まってる
    for (int l = 0; l < i; l++) {
      // r は (i - 1) - l 個埋まってる
      int r = (i - 1) - l;

      // 左に埋める
      {
        int y = l + 1;
        dp[l + 1][r] = max(dp[l + 1][r], dp[l][r] + (lint)abs(x - y) * score);
      }

      // 右に埋める
      {
        int y = n - r;
        dp[l][r + 1] = max(dp[l][r + 1], dp[l][r] + (lint)abs(x - y) * score);
      }
    }
  }

  lint ans = 0;
  // 合計が n になるやつを探す
  for (int l = 0; l <= n; l++) {
    int r = n - l;
    ans = max(ans, dp[l][r]);
  }

  cout << ans << endl;
  return 0;
}


Error: TLE

Fixed submission:

#pragma GCC optimize("Ofast")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;
using lint = long long int;
long long int INF = 1001001001001001LL;
int inf = 1000000007;
long long int MOD = 1000000007LL;
double PI = 3.1415926535897932;

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

#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()

// 最小費用流
// O(F E log V)
// 与えられるもの
// 有向グラフ G = (V, E)
// 各辺 e に対して, 容量 u(e) >= 0
// 各辺 e に対して, 費用 c(e) (負でも ok)

// 使い方
// PrimalDual(V) (コンストラクタ)
// add_edge(int from, int to, flow_t cap, cost_t cost)
// cost に関する負の閉路が存在する場合,だめ
// veryfied :
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_6_B&lang=jp
// 流れなかったら -1 を返す

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() {

  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n;
  cin >> n;
  vector<lint> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }

  int V = 2 * n + 2;
  PrimalDual<int, lint> dc(V);

  int source = 2 * n;
  int sink = 2 * n + 1;

  for (int i = 0; i < n; i++) {
    dc.add_edge(source, i, 1, 0);
    dc.add_edge(i + n, sink, 1, 0);
  }

  for (int from = 0; from < n; from++) {
    for (int to = 0; to < n; to++) {
      lint cost = (lint)abs(from - to) * a[from];
      dc.add_edge(from, to + n, 1, -cost);
    }
  }

  cout << -dc.min_cost_flow(source, sink, n) << endl;

  return 0;
}