Return a decimal number in its simplest fraction form >>> decimal_to_fraction(2) (2, 1) >>> decimal_to_fraction(89.) (89, 1)

Calculate Greatest Common Divisor (GCD). >>> greatest_common_divisor(24, 40) 8 >>> greatest_common_divisor(1, 1) 1 >>> greate

If the binary search tree is empty, make a new node and declare it as root. >>> node_a = BinaryTreeNode(12345) >>> node_b = insert(node_a

predict: @param x: a floating point value to predict the label of the prediction function works by recursively calling the pr

The Rabin-Karp Algorithm for finding a pattern within a piece of text with complexity O(nm), most efficient when it is used with multiple pat

Rotate the subtree rooted at this node to the right and returns the new root to this subtree. Performing one rotation can be done in

Set the coefficients for the IIR filter. These should both be of size `order` + 1. :math:`a_0` may be left out, and it will u

Times the execution of a function with parameters

Find the absolute value of a number. >>> abs_val(-5.1) 5.1 >>> abs_val(-5) == abs_val(5) True >>> abs_val(0) 0

Add an edge between two vertices. :param from_vertex: The source vertex. :param to_vertex: The destination vertex.

adding the edge between two vertices >>> g = Graph() >>> g.print_graph() >>> g.add_edge(0, 1) >>> g.print_gra

Determines the outcome of comparing self hand with other hand. Returns the output as 'Win', 'Loss', 'Tie' according to the rules of

Calculate the cross product of vectors (self -> point_a) and (point_a -> point_b). Returns: - Positive value: counte

returns the euclidean length of the vector >>> Vector([2, 3, 4]).euclidean_length() 5.385164807134504 >>> Vector([1]

Checks if a node exists in the tree >>> t = BinarySearchTree() >>> t.put(8) >>> t.put(10) >>> t.exists(8)

>>> from math import isclose >>> isclose(expectation([1, 2], [0.7, 0.3]), 1.3) True

Returns if the word is on the tree Args: word (str): word to check Returns: bool: True if the word appears o

Return the parent of x

Fits the SVC with a set of observations. Args: observations (list[ndarray]): list of observations classes (n

Below method is more memory efficient because it does not create additional stack frames for recursive functions calls (as done in the above

Find the midpoint of two points >>> get_mid((0, 0), (2, 2)) (1.0, 1.0) >>> get_mid((-3, -3), (3, 3)) (0.0, 0.0) >>> get_mid(

Generates hash for the given key value Examples: Creating HashTable with size 5 >>> ht = HashTable(5) >>> h

Checks if the deque is empty. Time complexity: O(1) >>> our_deque = Deque([1, 2, 3]) >>> our_deque.is_empty()

The Knuth-Morris-Pratt Algorithm for finding a pattern within a piece of text with complexity O(n + m) 1) Preprocess pattern to identify

>>> left_shift("0123456789") '1234567890'

Return the lowest common ancestor between u and v >>> level = [-1, 0, 1, 1, 2, 2, 2] >>> parent = [[0, 0, 1, 1, 2, 2, 3],[0, 0, 0, 0, 1,

Resolves force along rectangular components. (force, angle) => (force_x, force_y) >>> import math >>> force = polar_force(10, 45)

Looks for a page in the cache store and adds reference to the set. Remove the least recently used key if the store is full. U

Removes the edge between the two vertices. If any given vertex doesn't exist or the edge does not exist, a ValueError will be thrown.

Removes the edge between the two vertices. If any given vertex doesn't exist or the edge does not exist, a ValueError will be thrown.

Rotate the subtree rooted at this node to the left and returns the new root to this subtree. Performing one rotation can be done in

Searches for a pattern in the suffix tree. Args: pattern (str): The pattern to search for. Returns:

Applies sigmoid activation function. return normalized values >>> sigmoid(np.array(([1, 0, 2], [1, 0, 0]), dtype=np.float64)) array

Provides the derivative value of the sigmoid function. returns derivative of the sigmoid value >>> sigmoid_derivative(np.array(([1, 0,

>>> data = [-1, 2, -5, 0] >>> bucket_sort(data) == sorted(data) True >>> data = [9, 8, 7, 6, -12] >>> bucket_sort(data) == sorted

Cross product of elements in A and elements in B. >>> cross('AB', '12') ['A1', 'A2', 'B1', 'B2'] >>> cross('ABC', '123') ['A1',

Convert a Decimal Number to an Octal Number. >>> all(decimal_to_octal(i) == oct(i) for i ... in (0, 2, 8, 64, 65, 216, 255, 256, 512))

Delete and return the data of the node at the nth pos in Circular Linked List. Args: index (int): The index of the node t

Returns True if the tree does not have any element(s). False if the tree has element(s). >>> BinarySearchTree().empty()

>>> equation(5) -15 >>> equation(0) 10 >>> equation(-5) -15 >>> equation(0.1) 9.99 >>> equation(-0.1) 9.99

>>> queue = LinkedQueue() >>> queue.get() Traceback (most recent call last): ... IndexError: dequeue from

Inserts a node into the Priority Queue. Examples: >>> priority_queue_test = PriorityQueue() >>> priority_queue_test.

Insert a new node at the end of a linked list and return the new head. Parameters: head (Node | None): The head of the linked list.

Insert data to the end of linked list. >>> linked_list = LinkedList() >>> linked_list.insert_tail("tail") >>> linked_

Returns the left child index for a given index in a binary tree. >>> s = SegmentTree([1, 2, 3]) >>> s.left(1) 2

Query the maximum value in the range [a,b]. >>> s = SegmentTree([1, 2, 3, 4, 5]) >>> s.query(1, 3) 3 >>> s.q

query(1, 1, size, a, b) for query max of [a,b] >>> A = [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8] >>> segment_tree

Returns the right child index for a given index in a binary tree. >>> s = SegmentTree([1, 2, 3]) >>> s.right(1) 3

Searches a node in the tree >>> t = BinarySearchTree() >>> t.put(8) >>> t.put(10) >>> node = t.search(8)

Add two numbers as 32-bit ints. Arguments: a {[int]} -- [first given int] b {[int]} -- [second given int] Returns:

Set the value of index in O(lg N) Parameters: index (int): index to set value to value (int): value to set i

Input Parameters: ----------------- effusion_rate_1: Effustion rate of first gas (m^2/s, mm^2/s, etc.) effusion_rate_2: Effustion rat

r""" | Calculate the Volume of a Sphere. | Wikipedia reference: https://en.wikipedia.org/wiki/Sphere :return: :math:`\frac{4}{3} \cdot \p

Two cases: 1: Sample[index] is non-bound, fetch error from list: _error 2: sample[index] is bound, use predicted valu

Download the data from source url, unless it's already here. Args: filename: string, name of the file in the directory. work_dire

Private helper function to implement the summation functionality. @param digit_pos_to_extract: digit position to extract @param denom

>>> _validate_point(None) Traceback (most recent call last): ... ValueError: Missing an input >>> _validate_point([1,"one"])

Adds a new node to the end of the linked list. Args: data (Any): The data to be stored in the new node. Example

Given the numerators and denominators of three fractions, return the numerator and denominator of their sum in lowest form. >>> add_three

Adds val to the beginning of the deque. Time complexity: O(1) >>> our_deque_1 = Deque([2, 3]) >>> our_deque_1.appendl

Eliminate all the other values (except d) from values[s] and propagate. Return values, except return False if a contradiction is detected.

Assign values to literals of the clause as given by model.

Builds a KD-Tree from a list of points. Args: points: The list of points to build the KD-Tree from. depth: The current depth

Clear the heap. >>> sh = SkewHeap([3, 1, 3, 7]) >>> sh.clear() >>> sh.pop() Traceback (most recent call last

Convert time from one unit to another using the time_chart above. >>> convert_time(3600, "seconds", "hours") 1.0 >>> convert_time(35

Deletes a word in a Trie :param word: word to delete :return: None

Delete the first node and return the node's data. >>> linked_list = LinkedList() >>> linked_list.insert_tail("first")

Delete node at given index and return the node's data. >>> linked_list = LinkedList() >>> linked_list.insert_tail("fi