Recursive function for calculating the height of the binary tree. >>> height(None) 0 >>> height(make_tree()) 3

Implementation of the hill climbling algorithm. We start with a given state, find all its neighbors, move towards the neighbor which prov

Generates random points uniformly distributed within an n-dimensional hypercube. Args: num_points: Number of points to generate.

Check if a system is in equilibrium. It takes two numpy.array objects. forces ==> [ [force1_x, force1_y],

Return the inorder traversal of the tree >>> t = BinarySearchTree() >>> [i.label for i in t.inorder_traversal()] []

insert a new value into the max heap >>> h = Heap() >>> h.insert(10) >>> h [10] >>> h = Heap()

>>> linked_list = DoublyLinkedList() >>> linked_list.insert_at_nth(-1, 666) Traceback (most recent call last): ..

Insert data at given index. >>> linked_list = LinkedList() >>> linked_list.insert_tail("first") >>> linked_list.inser

Calculate the intersection of this fuzzy set with another fuzzy set. Args: other: Another fuzzy set to intersect

Check if the Circular Linked List is empty. Returns: bool: True if the list is empty, False otherwise.

Checks if the tree is empty >>> t = BinarySearchTree() >>> t.is_empty() True >>> t.put(8) >>> t.is_e

>>> stack = LinkedStack() >>> stack.is_empty() True >>> stack.push(1) >>> stack.is_empty() Fals

Check if a list is monotonic. >>> is_monotonic([1, 2, 2, 3]) True >>> is_monotonic([6, 5, 4, 4]) True >>> is_monotonic([1, 3

Checks to see if a number is a prime in O(sqrt(n)). A number is prime if it has exactly two factors: 1 and itself. >>> is_prime(0)

Returns the index of left child Examples: >>> priority_queue_test = PriorityQueue() >>> priority_queue_test.left(0)

>>> make_matrix() [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]] >>> make_matrix(1) [[1]] >>> make_matrix(-2)

Compute the common substring of the prefix of the node and a word Args: word (str): word to compare Returns:

mean_squared_error: @param labels: a one-dimensional numpy array @param prediction: a floating point value return val

We merge 2 trees into one. Note: all left tree's values must be less than all right tree's

>>> minor([[1, 2], [3, 4]], 1, 1) [[1]]

Normalized Difference self.nir/self.red Normalized Difference Vegetation Index, Calibrated NDVI - CDVI https://www.indexdatab

Performs a nearest neighbor search in a KD-Tree for a given query point. Args: root (KDNode | None): The root node of the KD-Tree.

Helper function to normalize R/G/B value -> return 255 if value > 255

Returns the index of parent Examples: >>> priority_queue_test = PriorityQueue() >>> priority_queue_test.par(1)

Utility function to plot how the given body-system evolves over time. No doctest provided since this function does not have a return value.

Plots the Bezier curve using matplotlib plotting capabilities. step_size: defines the step(s) at which to evaluate the Bezier cur

Return the preorder traversal of the tree >>> t = BinarySearchTree() >>> [i.label for i in t.preorder_traversal()] [

Print pre-order traversal of the tree. >>> root = Node(1) >>> root.left = Node(2) >>> root.right = Node(3) >>> print_preorder(ro

Get range query value in log(N) time :param left: left element index :param right: right element index :return: eleme

Get range query value in log(N) time :param i: left element index :param j: right element index :return: element comb

>>> quick_select([2, 4, 5, 7, 899, 54, 32], 5) 54 >>> quick_select([2, 4, 5, 7, 899, 54, 32], 1) 4 >>> quick_select([5, 4, 3, 2],

Returns a pseudorandom value modulo ``modulus`` based on the input ``value`` and attempt-specific ``step`` size. >>> rand_fn

Remove label from this tree.

Removes and returns the given node from the list Returns None if node.prev or node.next is None

Retrace the path from parents to parents until start node

Retrace the path from parents to parents until start node

Reverses a portion of the list in place from index start to end. Parameters: start (int): Starting index of the portion to r

Schur complement of a symmetric matrix X given as a 2x2 block matrix consisting of matrices `A`, `B` and `C`. Matrix `A` must be quadrati

Calculate the score for a character pair based on whether they match or mismatch. Returns 1 if the characters match, -1 if they mismatch, and

This shortest path function returns a string, describing the result: 1.) No path is found. The string is a human readable message to

Also known as Logistic Function. 1 f(x) = ------- 1 + e⁻ˣ The sigmoid function approaches a value of 1

We split current tree into 2 trees with value: Left tree contains all values less than split value. Right tree contains all values great

Swaps array elements at indices i and j, update the pos{} Examples: >>> priority_queue_test = PriorityQueue() >>> pr

Converts the given string to little-endian in groups of 8 chars. Arguments: string_32 {[string]} -- [32-char string] Raises:

Union finds the roots of components for two nodes, compares the components in terms of size, and attaches the smaller one to the larger one to

Update an element in log(N) time :param p: position to be update :param v: new value >>> st = SegmentTree([3, 1, 2,

Calculate the volume of the spherical cap. >>> vol_spherical_cap(1, 2) 5.235987755982988 >>> vol_spherical_cap(1.6, 2.6) 16.6211

Check for available resources in line with each resource in the claim vector

A helper function that generates the triagrams and assigns each letter of the alphabet to its corresponding triagram and stores this in a d

Try to add 3 elements when the size is 5 >>> hm = HashMap(5) >>> hm._add_item(1, 10) >>> hm._add_item(2, 20)

Choose the second alpha using a heuristic algorithm Steps: 1: Choose alpha2 that maximizes the step size (|E1 - E2|).

Parameters --------- points: list or None, the hull of points from which to choose the next convex-hull point left: Point, t

Calculate the cross product of vectors OA and OB. Returns: > 0: Counter-clockwise turn (left turn) = 0: Collinear <

Constructs a polynomial regression design matrix for the given input data. For input data x = (x₁, x₂, ..., xₙ) and polynomial degree

:param data_set: train data or test data :param example_no: example number whose error has to be checked :return: error in example pointe

Extract the images into a 4D uint8 numpy array [index, y, x, depth]. Args: f: A file object that can be passed into a gzip reader. Ret

Extract the labels into a 1D uint8 numpy array [index]. Args: f: A file object that can be passed into a gzip reader. one_hot: Does o

Returns index of valid parent as per desired ordering among given index and both it's children

Fixes the heap in downward direction of given index

Calculates hypothesis function value for a given input :param data_input_tuple: Input tuple of a particular example :return: Value of hyp

Repair the coloring from inserting into a tree.

Returns True if input matrix is symmetric positive definite. Returns False otherwise. For a matrix to be SPD, all eigenvalues must be po

Check if a point lies on the line segment between p1 and p2.

Returns parent index of given index if exists else None

_set_value functions allows to update value at a particular hash Examples: 1. _set_value in HashTable of size 5 >>>

Performs changes required for swapping two elements in the heap

>>> _validate_list(["a"], "mock_name") >>> _validate_list("a", "mock_name") Traceback (most recent call last): ... ValueE

>>> _validate_nested_dict({"a":{"b": 0.5}}, "mock_name") >>> _validate_nested_dict("invalid", "mock_name") Traceback (most recent call la

Function using divide and conquer to calculate a^b. It only works for integer a,b. :param a: The base of the power operation, an integer

adds addend to digit array given in digits starting at index k

Destination vertex and weight.

Adds an entity, making sure the entity does not override another entity >>> wt = WaTor(WIDTH, HEIGHT) >>> wt.set_pla

Add a pointer to a vertex at neighbor's list.