Sparse Matrix Transposition

Sparse matrix is very useful in some scientific computing, such as calculating the similarity between two web pages or clustering multiple web pages. The vector representation tends to be sparse.

There are many ways to represent sparse matrix, one of them is called COO, coordinate list which is list of tuples storing row index, column index and its value; See wiki page for COO: https://en.wikipedia.org/wiki/Sparse_matrix#Coordinate_list_.28COO.29

Now we need to transpose a sparse matrix with COO list to another COO list. Below is the code with comments containing the detailed explanation of the algorithm.