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def evaltree(root,xTe):
    """Evaluates xTe using decision tree root.
    
    Input:
        root: TreeNode decision tree
        xTe:  n x d matrix of data points
    
    Output:
        pred: n-dimensional vector of predictions
    """

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def all_same(items):
    
    if len(items) > 0:
        return np.all(items == items[0])
    elif len(items) is 0:
        return False
      
      
# This funciton basically checks majority of labels in the list
def majority_vote(y):

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def cart(xTr,yTr):
    """Builds a CART tree.
    
    The maximum tree depth is defined by "maxdepth" (maxdepth=2 means one split).
    Each example can be weighted with "weights".

    Args:
        xTr:      n x d matrix of data
        yTr:      n-dimensional vector

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# this is TreeNode class
class TreeNode(object):
    """Tree class.
    (You don't need to add any methods or fields here but feel
    free to if you like. The tests will only reference the fields
    defined in the constructor below, so be sure to set these
    correctly.)
    """
    
    def __init__(self, left, right, feature, cut, prediction):

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def sqsplit(xTr, yTr):
    """Finds the best feature, cut value, and loss value.
    
    Input:
        xTr:     n x d matrix of data points
        yTr:     n-dimensional vector of labels
    
    Output:
        feature:  index of the best cut's feature
        cut:      cut-value of the best cut

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def sqimpurity(yTr):
    """Computes the weighted variance of the labels
    
    Input:
        yTr:     n-dimensional vector of labels
    
    Output:
        impurity: weighted variance / squared loss impurity of this data set
    """

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def knnclassifier(xTr,yTr,xTe,k):
    """
    function preds=knnclassifier(xTr,yTr,xTe,k);
    
    k-nn classifier 
    
    Input:
    xTr = nxd input matrix with n row-vectors of dimensionality d
    xTe = mxd input matrix with m row-vectors of dimensionality d
    k = number of nearest neighbors to be found

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def accuracy(truth,preds):
    """
    function output=accuracy(truth,preds)         
    Analyzes the accuracy of a prediction against the ground truth
    
    Input:
    truth = n-dimensional vector of true class labels
    preds = n-dimensional vector of predictions
    
    Output:

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def findknn(xTr,xTe,k):
    """
    function [indices,dists]=findknn(xTr,xTe,k);
    
    Finds the k nearest neighbors of xTe in xTr.
    
    Input:
    xTr = nxd input matrix with n row-vectors of dimensionality d
    xTe = mxd input matrix with m row-vectors of dimensionality d
    k = number of nearest neighbors to be found

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def calculatedistance(X,Z=None):
    # Input:
    # X: nxd data matrix with n vectors (rows) of dimensionality d
    # Z: mxd data matrix with m vectors (rows) of dimensionality d
    #
    # Output:
    # Matrix D of size nxm
    # D(i,j) is the Euclidean distance of X(i,:) and Z(j,:)
    
    if Z is None: