Question

I am using a datatype of std::vector<std::vector<T> > to store a 2D matrix/array. I would like to determine the unique rows of this matrix. I am looking for any advice or pointers on how to go about doing this operation.

I have tried two methods.

Method 1: slightly convoluted. I keep an index for each row with 0/1 indicating whether the row is a duplicate value, and work through the matrix, storing the index of each unique row in a deque. I want to store the results in a <vector<vector<T> >, and so from this deque of indices, I pre-allocate and then assign the rows from the matrix into the return value.

Method 2: Is easier to read, and in many cases faster than method 1. I keep a deque of the unique rows that have been found, and just loop through the rows and compare each row to all the entries in this deque.

I am comparing both of these methods to matlab, and these C++ routines are orders of magnitude slower. Does anyone have any clever ideas on how I might speed this operation up? I am looking to do this operation on matrices that potentially have millions of rows.

I am storing the unique rows in a deque during the loop to avoid the cost of resizing a vector, and then copying the deque to the vector<vector<T> > for the results. I’ve benchmarked this operation closely, and it is not anywhere near slowing operation down, it accounts for less than .5% of the runtime on a matrix with 100,000 rows for example.

Thanks,

Bob

Here is the code. If anyone is interested in a more complete example showing the usage, drop me a comment and I can put something together.

Method 1:

  template <typename T>
      void uniqueRows( const std::vector<std::vector<T> > &A,
                       std::vector<std::vector<T> > &ret) {
    // Go through a vector<vector<T> > and find the unique rows
    // have a value ind for each row that is 1/0 indicating if a value
    // has been previously searched.

    // cur : current item being compared to every item
    // num : number of values searched for.  Once all the values in the
    //  matrix have been searched, terminate.

    size_t N = A.size();
    size_t num=1,cur=0,it=1;
    std::vector<unsigned char> ind(N,0);
    std::deque<size_t> ulist;  // create a deque to store the unique inds

    ind[cur] = 1;
    ulist.push_back(0); // ret.push_back(A[0]);

    while(num < N ) {

      if(it >= N ) {
        ++cur;   // find next non-duplicate value, push back
        while(ind[cur])
          ++cur;

        ulist.push_back(cur); //ret.push_back(A[cur]);
        ++num;
        it = cur+1; // start search for duplicates at the next row

        if(it >= N && num == N)
          break;
      }

      if(!ind[it] && A[cur]==A[it]) {        
        ind[it] = 1; // mark as duplicate
        ++num;
      }
      ++it;
    } // ~while num

    // loop over the deque and .push_back the unique vectors    
    std::deque<size_t>::iterator iter;
    const std::deque<size_t>::iterator end = ulist.end();
    ret.reserve(ulist.size());

    for(iter= ulist.begin(); iter != end; ++iter) {
      ret.push_back(A[*iter]);
    }
  }

Here is the code for method 2:

  template <typename T>
      inline bool isInList(const std::deque< std::vector<T> > &A,
                    const std::vector<T> &b) {
    typename std::deque<std::vector<T> >::const_iterator it;
    const typename std::deque<std::vector<T> >::const_iterator end = A.end();

    for(it = A.begin(); it != end; ++it) {
      if(*it == b)
        return true;
    }
    return false;
  }

  template <typename T>
  void uniqueRows1(const::std::vector<std::vector<T> > &A,
                   std::vector<std::vector<T> > &ret) {    
    typename std::deque<std::vector<T> > ulist;
    typename std::vector<std::vector<T> >::const_iterator it = A.begin();
    const typename std::vector<std::vector<T> >::const_iterator end = A.end();

    ulist.push_back(*it);

    for(++it; it != end; ++it) {
      if(!isInList(ulist,*it)) {
        ulist.push_back(*it);
      }
    }
    ret.reserve(ulist.size());

    for(size_t i = 0; i != ulist.size(); ++i) {
      ret.push_back(ulist[i]);
    }
  }

Answer 1

You should also consider using hashing, it preserves row ordering and could be faster (amortized O(m*n) if alteration of the original is permitted, O(2*m*n) if a copy is required) than sort/unique — especially noticeable for large matrices (on small matrices you are probably better off with Billy’s solution since his requires no additional memory allocation to keep track of the hashes.)

Anyway, taking advantage of Boost.Unordered, here’s what you can do:

#include <vector>
#include <boost/foreach.hpp>
#include <boost/ref.hpp>
#include <boost/typeof/typeof.hpp>
#include <boost/unordered_set.hpp>

namespace boost {
  template< typename T >
  size_t hash_value(const boost::reference_wrapper< T >& v) {
    return boost::hash_value(v.get());
  }
  template< typename T >
  bool operator==(const boost::reference_wrapper< T >& lhs, const boost::reference_wrapper< T >& rhs) {
    return lhs.get() == rhs.get();
  }
}

// destructive, but fast if the original copy is no longer required
template <typename T>
void uniqueRows_inplace(std::vector<std::vector<T> >& A)
{
  boost::unordered_set< boost::reference_wrapper< std::vector< T > const > > unique(A.size());
  for (BOOST_AUTO(it, A.begin()); it != A.end(); ) {
    if (unique.insert(boost::cref(*it)).second) {
      ++it;
    } else {
      A.erase(it);
    }
  }
}

// returning a copy (extra copying cost)
template <typename T>
void uniqueRows_copy(const std::vector<std::vector<T> > &A,
                 std::vector< std::vector< T > > &ret)
{
  ret.reserve(A.size());
  boost::unordered_set< boost::reference_wrapper< std::vector< T > const > > unique;
  BOOST_FOREACH(const std::vector< T >& row, A) {
    if (unique.insert(boost::cref(row)).second) {
      ret.push_back(row);
    }
  }
}