Implement local maxima, bagging, and k-means

Solve the following programming tasks.

1) Find all “local maxima” in a streaming temperature array

You are cleaning sensor data for temperature-fluctuation anomaly modeling.

You are given:

• An integer array rawData of length n .
• An integer localArea >= 0 .

Index i is a local maximum if:

• Looking left from i , the sequence rawData[i], rawData[i-1], rawData[i-2], ... is strictly decreasing for L = min(localArea, i) steps, i.e.
  • rawData[i] > rawData[i-1] > rawData[i-2] > ... > rawData[i-L] .
• Looking right from i , the sequence rawData[i], rawData[i+1], rawData[i+2], ... is strictly decreasing for R = min(localArea, n-1-i) steps, i.e.
  • rawData[i] > rawData[i+1] > rawData[i+2] > ... > rawData[i+R] .

If there are fewer than localArea elements to the left or right, use all available elements on that side.

Task: Return all indices i (0-based) that are local maxima, in increasing order.

Constraints (typical for OA): Aim for better than $O(n\cdot localArea)$ when n is large.

2) Implement Bagging classification from scratch (code skeleton)

Implement missing functions in a provided code skeleton (you may not change existing code besides filling in the ellipses).

You are given:

• x_train : 2D array of floats with shape (n_train, d) .
• y_train : 1D array of integer class labels with shape (n_train,) .
• x_test : 2D array of floats with shape (n_test, d) .
• base_classifiers : an array/list of length n_estimators , where each classifier supports:
  • fit(X, y)
  • predict(X) returning integer labels.

Task: Build a Bagging classifier that:

1. Creates a bootstrap sample (sample n_train rows with replacement ) for each base classifier.
2. Fits each base classifier on its bootstrap sample.
3. Predicts labels for x_test by majority vote across estimators.

Output: Return a 1D array of predicted integer labels of length n_test.

(If there is a voting tie, use the smallest class label as the tie-breaker unless the skeleton specifies otherwise.)

3) Implement k-means clustering from scratch (code skeleton)

Implement missing functions in a provided k-means skeleton.

You are given:

• data : 2D array of floats with shape (n, d) .
• k : number of clusters.
• centroids : initial centroids, 2D array of floats with shape (k, d) .
• iterations : number of update steps to perform.

k-means loop:

1. Compute distances from each point to each centroid (typically Euclidean).
2. Assign each point to the nearest centroid.
3. Update each centroid to the mean of points assigned to it.
4. Repeat for iterations iterations.

Output: Return a 1D integer array of length n with the predicted cluster index for each point.

(If a cluster gets zero points in an iteration, keep its centroid unchanged unless the skeleton specifies another rule.)