Implement sparse vector dot product

You need to implement a data structure for a sparse vector of integers and support efficient computation of the dot product between two such vectors. - The length `n` of the vector can be large (e.g., up to 10^5), but only a small number of positions contain non-zero values. - You are initially given each vector as a dense integer array `nums` of length `n`. Design a `SparseVector` class with: - A constructor `SparseVector(int[] nums)` that stores the vector in a space-efficient way. - A method `int dotProduct(SparseVector other)` that returns the dot product of the current vector with another sparse vector. The dot product of two vectors `a` and `b` of length `n` is defined as: `a · b = a[0]*b[0] + a[1]*b[1] + ... + a[n-1]*b[n-1]`. Specify your data representation, and analyze the time and space complexity of: - Constructing the sparse vector. - Computing the dot product. You do not need to provide actual code, but your algorithm must be clearly described.