Implement 1-Nearest-Neighbor (1NN) and a Simple Neural Network in NumPy, then Modify to Use L1 Distance (Follow-up)

Problem: Implement 1NN and a Simple Neural Network in NumPy, then Modify to Use L1 Distance (Follow-up) Given training features X_train with labels y_train, and test features X_test: Implement a 1-Nearest-Neighbor (1NN) predictor in NumPy: For each test sample in X_test, find the single closest sample in X_train. Predict the label of that nearest training sample. The initial version uses L2 (Euclidean) distance. Implement a simple feed-forward neural network in NumPy: Build a small MLP from scratch using NumPy (e.g., linear layers + non-linear activations) for forward inference. (If required) implement training, or at least the forward pass that produces outputs. Follow-up: change the 1NN distance metric to L1 (Manhattan) distance: Replace the distance function with L1: [ d(x, z) = \sum_i |x_i - z_i| ] Explain/implement how to compute pairwise L1 distances between X_test and X_train efficiently in NumPy and produce predictions. I/O Convention (typical interview form) Input: X_train has shape (N, D), y_train has shape (N,), X_test has shape (M, D). Output: return y_pred with shape (M,). Constraints (typical interview focus) Must be implemented in NumPy; prefer vectorization (minimize Python loops). Be careful with broadcasting and shapes. Test Cases Below are 5 test cases to validate 1NN (for the L2 version; the L1 version only changes the metric): Case 1 Input: X_train = [[0,0],[1,1],[2,2]] y_train = [0,1,1] X_test = [[1.1,1.1],[0.2,0.1]] Expected output: [1,0] Case 2 Input: X_train = [[-1,0],[0,0],[3,0]] y_train = [5,6,7] X_test = [[2,0],[-0.6,0]] Expected output: [7,5] Case 3 Input: X_train = [[1,2,3],[4,5,6],[7,8,9]] y_train = [10,11,12] X_test = [[6,7,8]] Expected output: [12] Case 4 (duplicate points) Input: X_train = [[0,0],[0,0],[1,0]] y_train = [1,2,3] X_test = [[0,0]] Expected output: [1] Case 5 Input: X_train = [[0,1],[1,0],[1,1]] y_train = [0,1,2] X_test = [[0,0],[2,2]] Expected output: [0,2] Example Input X_train=[[0,0],[1,1],[2,2]] y_train=[0,1,1] X_test=[[1.1,1.1],[0.2,0.1]] Output [1, 0]