Problem p01347 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; --i)
#define srep(i, s, t) for (int i = (int)(s); i < (int)(t); ++i)
#define each(a, b) for (auto &(a) : (b))
#define all(v) (v).begin(), (v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)), v.erase(unique(all(v)), v.end())
#define cmx(x, y) x = max(x, y)
#define cmn(x, y) x = min(x, y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout << #x << " = " << (x) << endl
#define spair(p) cout << #p << ": " << p.fi << " " << p.se << endl
#define sar(a, n)                                                              \\
  cout << #a << ":";                                                           \\
  rep(pachico, n) cout << " " << a[pachico];                                   \\
  cout << endl
#define svec(v)                                                                \\
  cout << #v << ":";                                                           \\
  rep(pachico, v.size()) cout << " " << v[pachico];                            \\
  cout << endl
#define svecp(v)                                                               \\
  cout << #v << ":";                                                           \\
  each(pachico, v) cout << " {" << pachico.first << ":" << pachico.second      \\
                        << "}";                                                \\
  cout << endl
#define sset(s)                                                                \\
  cout << #s << ":";                                                           \\
  each(pachico, s) cout << " " << pachico;                                     \\
  cout << endl
#define smap(m)                                                                \\
  cout << #m << ":";                                                           \\
  each(pachico, m) cout << " {" << pachico.first << ":" << pachico.second      \\
                        << "}";                                                \\
  cout << endl

using namespace std;

typedef pair<int, int> P;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 101;

struct edge {
  int to, cost;
};

vector<edge> G[MAX_N];
int d[MAX_N];

// max c * x s.t. A*x <= b, x >= 0
class Simplex {
private:
  using Arr = vector<double>;
  using Mat = vector<vector<double>>;
  int *index;
  double **a;
  int row, column, L;

  void Set(const Mat &A, const Arr &b, const Arr &c) {
    infinity = none = false;
    row = A.size(), column = A[0].size() + 1;
    index = new int[row + column];
    int i, j;
    for (i = 0; i < row + column; i++) {
      index[i] = i;
    }
    L = row;
    a = new double *[row + 2];
    for (i = 0; i < row + 2; i++) {
      a[i] = new double[column + 4];
    }
    for (i = 0; i < row; i++) {
      for (j = 0; j < column - 1; j++) {
        a[i][j] = -A[i][j];
      }
      a[i][column - 1] = 1;
      a[i][column] = b[i];
      if (a[L][column] > a[i][column])
        L = i;
    }
    for (j = 0; j < column - 1; j++) {
      a[row][j] = c[j];
    }
    a[row + 1][column - 1] = -1;
  }

  void solve() {
    int E, i, j;
    for (E = column - 1;;) {
      if (L < row) {
        swap(index[E], index[L + column]);
        a[L][E] = 1 / a[L][E];
        for (j = 0; j < column + 1; j++) {
          if (j != E)
            a[L][j] *= -a[L][E];
        }
        for (i = 0; i < row + 2; i++) {
          if (abs(a[i][E]) < EPS || i == L)
            continue;
          for (j = 0; j < column + 1; j += 4) {
            if (j != E)
              a[i][j] += a[i][E] * a[L][j];
            if (j + 1 != E)
              a[i][j + 1] += a[i][E] * a[L][j + 1];
            if (j + 2 != E)
              a[i][j + 2] += a[i][E] * a[L][j + 2];
            if (j + 3 != E)
              a[i][j + 3] += a[i][E] * a[L][j + 3];
          }
          a[i][E] = a[i][E] * a[L][E];
        }
      }
      E = -1;
      // int pre = EPS;
      for (j = 0; j < column; j++) {
        if (E < 0 || index[E] > index[j]) {
          if (a[row + 1][j] > EPS)
            E = j;
          else if (abs(a[row + 1][j]) < EPS && a[row][j] > EPS)
            E = j;
        }
      }
      if (E < 0)
        break;
      L = -1;
      for (i = 0; i < row; i++) {
        if (a[i][E] < -EPS) {
          if (L < 0 || a[L][column] / a[L][E] - a[i][column] / a[i][E] < EPS)
            L = i;
        }
      }
      if (L < 0) {
        infinity = true;
        return;
      }
    }
    if (a[row + 1][column] < -EPS) {
      none = true;
      return;
    }
    x.assign(column - 1, 0);
    for (i = 0; i < row; i++) {
      if (index[column + i] < column - 1)
        x[index[column + i]] = a[i][column];
    }
    ans = a[row][column];
  }

public:
  bool infinity, none;
  double ans;
  Arr x;
  Simplex(const Mat &A, const Arr &b, const Arr &c) {
    Set(A, b, c);
    solve();
  }
};

struct eda {
  int from, to, cost;
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  vector<eda> es(m);
  rep(i, m) {
    int x, y, s;
    cin >> x >> y >> s;
    G[x].pb((edge){y, s});
    es[i] = (eda){x, y, s};
  }
  rrep(i, n) {
    each(e, G[i]) { cmx(d[i], d[e.to] + e.cost); }
  }
  int mx = d[0];
  vd b(m + 1, 0.0), c(n + m, 0.0);
  rep(i, m) { c[n + i] = 1.0; }
  vector<vd> A(m + 1, vd(n + m, 0.0));
  rep(i, m) {
    A[i][es[i].from] = 1, A[i][es[i].to] = -1, A[i][n + i] = 1;
    b[i] = -es[i].cost;
  }
  A[m][n - 1] = 1, b[m] = mx;
  Simplex sp(A, b, c);
  int ans = round(sp.ans);
  cout << ans << "\\n";
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; --i)
#define srep(i, s, t) for (int i = (int)(s); i < (int)(t); ++i)
#define each(a, b) for (auto &(a) : (b))
#define all(v) (v).begin(), (v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)), v.erase(unique(all(v)), v.end())
#define cmx(x, y) x = max(x, y)
#define cmn(x, y) x = min(x, y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout << #x << " = " << (x) << endl
#define spair(p) cout << #p << ": " << p.fi << " " << p.se << endl
#define sar(a, n)                                                              \\
  cout << #a << ":";                                                           \\
  rep(pachico, n) cout << " " << a[pachico];                                   \\
  cout << endl
#define svec(v)                                                                \\
  cout << #v << ":";                                                           \\
  rep(pachico, v.size()) cout << " " << v[pachico];                            \\
  cout << endl
#define svecp(v)                                                               \\
  cout << #v << ":";                                                           \\
  each(pachico, v) cout << " {" << pachico.first << ":" << pachico.second      \\
                        << "}";                                                \\
  cout << endl
#define sset(s)                                                                \\
  cout << #s << ":";                                                           \\
  each(pachico, s) cout << " " << pachico;                                     \\
  cout << endl
#define smap(m)                                                                \\
  cout << #m << ":";                                                           \\
  each(pachico, m) cout << " {" << pachico.first << ":" << pachico.second      \\
                        << "}";                                                \\
  cout << endl

using namespace std;

typedef pair<int, int> P;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 101;

struct edge {
  int to, cost;
};

vector<edge> G[MAX_N];
int d[MAX_N];

// max c * x s.t. A*x <= b, x >= 0
class Simplex {
private:
  using Arr = vector<double>;
  using Mat = vector<vector<double>>;
  int *index;
  double **a;
  int row, column, L;

  void Set(const Mat &A, const Arr &b, const Arr &c) {
    infinity = none = false;
    row = A.size(), column = A[0].size() + 1;
    index = new int[row + column];
    int i, j;
    for (i = 0; i < row + column; i++) {
      index[i] = i;
    }
    L = row;
    a = new double *[row + 2];
    for (i = 0; i < row + 2; i++) {
      a[i] = new double[column + 4];
    }
    for (i = 0; i < row; i++) {
      for (j = 0; j < column - 1; j++) {
        a[i][j] = -A[i][j];
      }
      a[i][column - 1] = 1;
      a[i][column] = b[i];
      if (a[L][column] > a[i][column])
        L = i;
    }
    for (j = 0; j < column - 1; j++) {
      a[row][j] = c[j];
    }
    a[row + 1][column - 1] = -1;
  }

  void solve() {
    int E, i, j;
    for (E = column - 1;;) {
      if (L < row) {
        swap(index[E], index[L + column]);
        a[L][E] = 1 / a[L][E];
        for (j = 0; j < column + 1; j++) {
          if (j != E)
            a[L][j] *= -a[L][E];
        }
        for (i = 0; i < row + 2; i++) {
          if (abs(a[i][E]) < EPS || i == L)
            continue;
          for (j = 0; j < column + 1; j += 4) {
            if (j != E)
              a[i][j] += a[i][E] * a[L][j];
            if (j + 1 != E)
              a[i][j + 1] += a[i][E] * a[L][j + 1];
            if (j + 2 != E)
              a[i][j + 2] += a[i][E] * a[L][j + 2];
            if (j + 3 != E)
              a[i][j + 3] += a[i][E] * a[L][j + 3];
          }
          a[i][E] = a[i][E] * a[L][E];
        }
      }
      E = -1;
      int pre = EPS;
      for (j = 0; j < column; j++) {
        if (E < 0 || index[E] > index[j]) {
          if (a[row + 1][j] > EPS)
            E = j;
          else if (abs(a[row + 1][j]) < EPS && a[row][j] > pre)
            E = j, pre = a[row][j];
        }
      }
      if (E < 0)
        break;
      L = -1;
      for (i = 0; i < row; i++) {
        if (a[i][E] < -EPS) {
          if (L < 0 || a[L][column] / a[L][E] - a[i][column] / a[i][E] < EPS)
            L = i;
        }
      }
      if (L < 0) {
        infinity = true;
        return;
      }
    }
    if (a[row + 1][column] < -EPS) {
      none = true;
      return;
    }
    x.assign(column - 1, 0);
    for (i = 0; i < row; i++) {
      if (index[column + i] < column - 1)
        x[index[column + i]] = a[i][column];
    }
    ans = a[row][column];
  }

public:
  bool infinity, none;
  double ans;
  Arr x;
  Simplex(const Mat &A, const Arr &b, const Arr &c) {
    Set(A, b, c);
    solve();
  }
};

struct eda {
  int from, to, cost;
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  vector<eda> es(m);
  rep(i, m) {
    int x, y, s;
    cin >> x >> y >> s;
    G[x].pb((edge){y, s});
    es[i] = (eda){x, y, s};
  }
  rrep(i, n) {
    each(e, G[i]) { cmx(d[i], d[e.to] + e.cost); }
  }
  int mx = d[0];
  vd b(m + 1, 0.0), c(n + m, 0.0);
  rep(i, m) { c[n + i] = 1.0; }
  vector<vd> A(m + 1, vd(n + m, 0.0));
  rep(i, m) {
    A[i][es[i].from] = 1, A[i][es[i].to] = -1, A[i][n + i] = 1;
    b[i] = -es[i].cost;
  }
  A[m][n - 1] = 1, b[m] = mx;
  Simplex sp(A, b, c);
  int ans = round(sp.ans);
  cout << ans << "\\n";
  return 0;
}