Problems

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Implement Dot Product

Linear Algebra

Easy

The dot product of two equal-length 1-D arrays $x$ and $y$ of length $n$ is defined algebraically as:

x \cdot y = \sum_{i=1}^{n} x_i y_i = x_1 y_1 + x_2 y_2 + \cdots + x_n y_n

and geometrically as:

x \cdot y = \|x\| \cdot \|y\| \cdot \cos(\theta)

where $\|x\|$ and $\|y\|$ are the magnitudes of $x$ and $y$ , and $\theta$ is the angle between them.

Return the dot product as a scalar float.

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Examples

Input: x = [1,2,3], y = [4,5,6]

Output: 32.0

1×4 + 2×5 + 3×6 = 4 + 10 + 18 = 32

Input: x = [1,0], y = [0,1]

Output: 0.0

Orthogonal vectors (perpendicular)

Input: x = [-1,2], y = [3,-1]

Output: -5.0

(-1)×3 + 2×(-1) = -3 + (-2) = -5

Hint 1

Convert inputs to NumPy arrays first, then use vectorized operations.

Hint 2

NumPy has a built-in function for this: $\texttt{np.dot(x, y)}$ .

Requirements

Must work for lists or NumPy arrays
Must return a float
Must be vectorized (no Python element loops)
Must handle 1D arrays only
Must raise ValueError for mismatched lengths

Constraints

Time limit: 200 ms, Memory: 64 MB
NumPy only (no sklearn, scipy)

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