What is a Sparse Vector
A vector is a one-dimensional array of elements. So in a programming language, an implementation of a vector is as a one-dimensional array. A vector is said to be sparse when many elements of a have zero values. And when we write programs it will not be a good idea from storage perspective to store all these zero values in the array.
So the best way of representation of a sparse vector will be by just specifying the location and value.