Solution: Dot Product of Two Sparse Vectors

Statement

We must calculate the dot product of two given sparse vectors, nums1 and nums2.

Create a SparseVector class:

• Constructor(): Initializes the object with the vector.

• DotProduct(): Computes the dot product between the current instance of the vector and the other.

Note: A sparse vector is a vector that contains mostly zero values. Therefore, we should store the sparse vectors and calculate the dot product accordingly.

Constraints:

• $n ==$ nums1.length $==$ nums2.length

• $1 <= n <= 10^3$

• $0 <=$ nums1[i], nums2[i] $<= 100$

Solution

This solution involves handling sparse vectors, which mostly contain zeroes. Instead of storing all elements, it only keeps track of nonzero values and their positions. When finding the dot product of two such vectors, it only looks at positions where both vectors have nonzero values. Focusing only on the nonzero values speeds up the process and uses less memory.

Now, let’s walk through the steps of the solution.

• Create hash maps to store the nonzero elements of the sparse vectors and their indexes.

• Initialize a variable, sum, with zero.

• Iterate through the nonzero elements of the first vector.

• For each non-zero element in the hash map of the first vector, check if the corresponding index in the hash map of the second vector is also nonzero.

  • If both have non-zero elements at the same corresponding index, multiply these elements and add the result to the sum.

• Return the sum as the final dot product value.

Let’s look at the following illustration to get a better understanding of the solution: