Implement sparse vector dot product

Q: Implement sparse vector dot product

This question evaluates understanding of sparse data representation, memory-efficient data structures, and algorithmic complexity for computing operations like dot products on large but sparsely populated vectors.

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Question

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.

Implement sparse vector dot product

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