Sparse Vector Dot Product

class SparseVector:
    """
    Represents a sparse vector and performs dot product.

    Time Complexity:
    ----------------
    O(min(n1, n2))
    - n1, n2: number of non-zero elements in both vectors.

    Space Complexity:
    -----------------
    O(n1 + n2)
    - n1, n2: space for storing non-zero elements of both vectors.
    """

    def __init__(self, nums: List[int]):
        # Store the non-zero values and their indices
        self.dense_index_num_pairs = [(i, num) for i, num in enumerate(nums) if num > 0]
        self.size = len(self.dense_index_num_pairs)

    """
    The O(n) time complexity occurs during the initialization of the SparseVector object, not during each
    computation. This means we pay the cost once, and if you perform many dot product operations with the same
    vector, the initial O(n) cost is amortized over all these operations, making each operation more efficient.
    """
    def solve(self, vec: "SparseVector") -> int:
        answer = 0
        min_size = min(self.size, vec.size)

        # Determine which vector is smaller
        running_vector = self.dense_index_num_pairs if min_size == self.size else vec.dense_index_num_pairs
        other_vector_map = dict(vec.dense_index_num_pairs) \
            if min_size == self.size else dict(self.dense_index_num_pairs)

        # Compute dot product by multiplying matching indices
        for my_index, my_num in running_vector:
            if my_index in other_vector_map:
                answer += my_num * other_vector_map[my_index]

        return answer