K-Nearest Neighbors Classifier

K-nearest neighbors (KNN) classifies a new point by looking at the k training points closest to it and taking the most common label.

Compute the Euclidean distance from query to every point.
Sort the points by distance; if two distances are equal, the point with the smaller index comes first.
Take the first k points and count their labels.
Return the label with the most votes. If labels tie, return the tied label whose closest point comes first in the sorted order.

Implement knn_predict(points, labels, query, k).

Input

points: The training points, each a list of coordinates.

labels: The label of each point.

query: The point to classify.

k: How many neighbors vote.

Output

Return the predicted label.

Constraints

1 ≤ k ≤ number of points ≤ 1,000

1 ≤ dimensions ≤ 20

-1,000 ≤ each coordinate ≤ 1,000

Examples

Example 1

Input:
points = [
    [1.0, 1.0],
    [2.0, 2.0],
    [8.0, 8.0],
    [9.0, 9.0]
]
labels = ["A", "A", "B", "B"]
query = [3.0, 3.0]
k = 3

Expected output:
"A"

Explanation

Distances from (3, 3): (2, 2) ≈ 1.41, (1, 1) ≈ 2.83, (8, 8) ≈ 7.07. The 3 nearest labels are A, A and B, so the answer is A.

Example 2

Input:
points = [
    [0.0, 0.0],
    [4.0, 0.0],
    [0.0, 4.0],
    [4.0, 4.0]
]
labels = ["red", "blue", "blue", "red"]
query = [1.0, 1.0]
k = 2

Expected output:
"red"

Explanation

The nearest point is (0, 0) (red); the next two, (4, 0) and (0, 4), are at the same distance, so the smaller index (4, 0) (blue) wins the tie. Red and blue have one vote each, and red's point came first, so the answer is red.

References

scikit-learn, Nearest Neighbors

Run the sample tests to check your code without submitting.

Example 1 Not run

Input:

points = [
    [1.0, 1.0],
    [2.0, 2.0],
    [8.0, 8.0],
    [9.0, 9.0]
]
labels = ["A", "A", "B", "B"]
query = [3.0, 3.0]
k = 3

Expected output:

"A"

Your output

Example 2 Not run

Input:

points = [
    [0.0, 0.0],
    [4.0, 0.0],
    [0.0, 4.0],
    [4.0, 4.0]
]
labels = ["red", "blue", "blue", "red"]
query = [1.0, 1.0]
k = 2

Expected output:

"red"

Your output

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