A sparse vector is a vector whose entries are almost all zero, like [1, 0, 0, 0, 0, 0, 3, 0, 0, 0]. Storing all those zeros in a list wastes memory, so programmers often use dictionaries instead to keep track of just the nonzero entries. For example, the vector shown earlier would be represented as {0:1, 6:3}, because the vector it is meant to represent has the value 1 at index 0 and the value 3 at index 6. a. The sum of two vectors is just the element-wise sum of their elements. For example, the sum of [1, 2, 3] and [4, 5, 6] is [5, 7, 9]. Write a function called sparse_add that takes two sparse vectors stored as dictionaries and returns a new dictionary representing their sum. b. The dot product of two vectors is the sum of the products of corresponding elements. For example, the dot product of [1, 2, 3] and [4, 5, 6] is 4+10+18, or 32. Write another function called sparse_dot that calculates the dot product of two sparse vectors.

Question

A sparse vector is a vector whose entries are almost all zero, like [1, 0, 0, 0, 0, 0, 3, 0, 0, 0]. Storing all those zeros in a list wastes memory, so programmers often use dictionaries instead to keep track of just the nonzero
entries. For example, the vector shown earlier would be represented as {0:1, 6:3}, because the vector it is meant to represent has the value 1 at index 0 and the value 3 at index 6.

a. The sum of two vectors is just the element-wise sum of their elements.
For example, the sum of [1, 2, 3] and [4, 5, 6] is [5, 7, 9]. Write a function called sparse_add that takes two sparse vectors stored as dictionaries and returns a new dictionary representing their sum.
b. The dot product of two vectors is the sum of the products of corresponding elements. For example, the dot product of [1, 2, 3] and [4, 5, 6] is 4+10+18, or 32. Write another function called sparse_dot that calculates
the dot product of two sparse vectors.