Hungarian algorithm

pair<long long, vector<int>> hungarianAlgorithm(vector<vector<long long>> a)
{
  int n = a.size() - 1;
  int m = a[0].size() - 1;

  vector<int> pl(n + 1, 0), pr(n + 1, 0), mt(n + 1, 0), way(n + 1, 0);
  for (int row = 1; row <= n; row++) 
  {
    mt[0] = row;
    vector<int> minv(n + 1, INT_MAX);
    vector<bool> used(n + 1, false);
    int col = 0;
    do 
    {
      used[col] = true;
      int v = mt[col], delta = INT_MAX, nextcol;
      for (int i = 1; i <= n; i++) 
      {
        if (used[i])
          continue;
        int x = a[v][i] - pl[v] - pr[i];
        if (x < minv[i])
          minv[i] = x, way[i] = col;
        if (minv[i] < delta)
          delta = minv[i], nextcol = i;
      }
      for (int i = 0; i <= n; i++) 
      {
        if (used[i])
          pl[mt[i]] += delta, pr[i] -= delta;
        else
          minv[i] -= delta;
      }
      col = nextcol;
    } while (mt[col] != 0);

    do 
    {
      int nextcol = way[col];
      mt[col] = mt[nextcol];
      col = nextcol;
    } while (col);
  }

  vector<int> res(n+1);
  for (int i = 1; i <= m; i++)
    res[mt[i]] = i;

  return { -pr[0],res };

}