Multidimensional Vectors in C++

Question

I just started learning C++. I was trying to grasp the syntax for multidimensional arrays and vectors when I started to get fairly confused. I get how to initialize multidimensional arrays. It seems straightforward: Rows followed by columns. However, vectors are a little more challenging. Do I have to initialize them in the same way or do I create a vector of vectors?

Solution 1

If you are able to use C++11, multidimensional arrays and vectors of vectors can be initialized in a similar manner.

int a1[3][3] = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9} };
std::vector<std::vector<int>> a2 = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9} };

However, there are differences that must be understood to access the elements without running into undefined behavior.

For a multidimensional array, memory for the elements of the array is required to be allocated contiguously. For a vector of vector, the memory for the elements is most likely going to be disjoint.

Memory for a1:

a1[0][0]    a1[1][0]    a1[2][0]
|           |           |
v           v           v
+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+---+

Memory for a2 (most likely):

a2[0][0]
|
v
+---+---+---+
|   |   |   |
+---+---+---+

a2[1][0]
|
v
+---+---+---+
|   |   |   |
+---+---+---+

a2[2][0]
|
v
+---+---+---+
|   |   |   |
+---+---+---+

Also, it is possible to defined a vector of vectors in which the number of columns is not same for each row.

std::vector<std::vector<int>> a2 = { {1, 2, 3}, {4, 5}, {6, 7, 8, 9} };

In a multidimensional array, the number of columns is guaranteed to be same for each row.

Given the above multidimensional array a1, a1[1][2] will be a valid element and a1[2][3] will be an invalid element. In the case of a vector of vectors, using the above line, a2[1][2] is not a valid element and a2[2][3] is a valid element.

Solution 2

declare a multidimensional vector:

vector<vector<int>> test(4,vector<int>(20));

This creates a 2D vector 4 X 20. Of course since they're vectors that can be changed as needed. The indexing is the same as an array test[3][19].

Solution 3

For interested readers, Boost has a MultiArray library designed specifically for this problem. It claims to be more efficient than std::vector<std::vector<...>> and its interface is C++ STL friendly.

#include "boost/multi_array.hpp"

int main () {
  // Create a 3D array that is 3 x 4 x 2
  boost::multi_array<double, 3>  A(boost::extents[3][4][2]);
 
  // Assignment
  A[0][0][0] = 1.0;

  // Dereference
  std::cout<<A[0][0][0];
  
return 0;
}

Read more here

Comments

[CrazyVideoGamer]

Is there a way to make multidimensional vectors (like 3d or more dimensions) more clearer and easier to read?

[R Sahu]

@CrazyVideoGamez, when you have a need for such arrays, it's best to encapsulate their usage behind a class. That will make it easier to use the class but the implementation of the class has to deal with the syntactic aspects of arrays. I don't think there's way to get around that.

[Sorush]

For vector, matrix and tensor calculation, checkout Eigen C++ library: eigen.tuxfamily.org