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Write documentation strings for class attributes
from __future__ import annotations def is_sorted(head: object | None) -> bool: if not head: return True current = head while current.next: if current.val > current.next.val: return False current = current.next return True
--- +++ @@ -1,8 +1,32 @@+""" +Is Sorted Linked List + +Given a linked list, determine whether the list is sorted in non-decreasing +order. An empty list is considered sorted. + +Reference: https://en.wikipedia.org/wiki/Linked_list + +Complexity: + Time: O(n) + Space: O(1) +""" from __future__ import annotatio...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/linked_list/is_sorted.py
Help me document legacy Python code
from __future__ import annotations class Dijkstra: def __init__(self, vertex_count: int) -> None: self.vertex_count = vertex_count self.graph: list[list[int]] = [ [0 for _ in range(vertex_count)] for _ in range(vertex_count) ] def min_distance(self, dist: list[float], mi...
--- +++ @@ -1,16 +1,43 @@+""" +Dijkstra's Single-Source Shortest-Path Algorithm + +Finds shortest distances from a source vertex to every other vertex in a +graph with non-negative edge weights. + +Reference: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm + +Complexity: + Time: O(V^2) (adjacency-matrix repre...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/dijkstra.py
Provide clean and structured docstrings
from __future__ import annotations import random from collections.abc import Iterator from typing import Any def _choose_state(state_map: dict[Any, float]) -> Any | None: choice = random.random() probability_reached = 0.0 for state, probability in state_map.items(): probability_reached += probab...
--- +++ @@ -1,3 +1,15 @@+""" +Markov Chain + +Provides utilities for stepping through and iterating a discrete Markov chain +described as a dictionary of transition probabilities. + +Reference: https://en.wikipedia.org/wiki/Markov_chain + +Complexity: + Time: O(S) per step, where S is the number of states + Spac...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/markov_chain.py
Document this script properly
from __future__ import annotations import heapq def dijkstra( graph: dict[str, dict[str, int | float]], source: str, target: str = "", ) -> tuple[int | float, list[str]]: dist: dict[str, int | float] = {v: float("inf") for v in graph} dist[source] = 0 prev: dict[str, str | None] = {v: None f...
--- +++ @@ -1,3 +1,18 @@+""" +Dijkstra's Shortest-Path Algorithm (Heap-Optimised) + +Computes single-source shortest paths in a graph with non-negative edge +weights using a min-heap (priority queue) for efficient vertex selection. + +This adjacency-list implementation is faster than the O(V²) matrix version +for spars...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/dijkstra_heapq.py
Add inline docstrings for readability
from __future__ import annotations def rotate_right(head: object | None, k: int) -> object | None: if not head or not head.next: return head current = head length = 1 while current.next: current = current.next length += 1 current.next = head k = k % length for _ in...
--- +++ @@ -1,8 +1,33 @@+""" +Rotate List + +Given a linked list, rotate the list to the right by k places, where k is +non-negative. + +Reference: https://leetcode.com/problems/rotate-list/ + +Complexity: + Time: O(n) + Space: O(1) +""" from __future__ import annotations def rotate_right(head: object | ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/linked_list/rotate_list.py
Write documentation strings for class attributes
from __future__ import annotations _INF = float("inf") def min_cost(cost: list[list[int]]) -> int: length = len(cost) dist = [_INF] * length dist[0] = 0 for i in range(length): for j in range(i + 1, length): dist[j] = min(dist[j], dist[i] + cost[i][j]) return dist[length -...
--- +++ @@ -1,3 +1,16 @@+""" +Minimum Cost Path + +Find the minimum cost to travel from station 0 to station N-1 given +a cost matrix where cost[i][j] is the price of going from station i +to station j (for i < j). + +Reference: https://en.wikipedia.org/wiki/Shortest_path_problem + +Complexity: + Time: O(n^2) + ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/dynamic_programming/min_cost_path.py
Include argument descriptions in docstrings
from __future__ import annotations def is_anagram(s: str, t: str) -> bool: freq_s: dict[str, int] = {} freq_t: dict[str, int] = {} for char in s: freq_s[char] = freq_s.get(char, 0) + 1 for char in t: freq_t[char] = freq_t.get(char, 0) + 1 return freq_s == freq_t
--- +++ @@ -1,12 +1,39 @@+""" +Is Anagram + +Determine whether two strings are anagrams of each other by comparing +character frequency maps. + +Reference: https://leetcode.com/problems/valid-anagram/description/ + +Complexity: + Time: O(n) + Space: O(n) +""" from __future__ import annotations def is_ana...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/map/is_anagram.py
Generate missing documentation strings
from __future__ import annotations def is_isomorphic(s: str, t: str) -> bool: if len(s) != len(t): return False mapping: dict[str, str] = {} mapped_values: set[str] = set() for i in range(len(s)): if s[i] not in mapping: if t[i] in mapped_values: return Fal...
--- +++ @@ -1,8 +1,36 @@+""" +Isomorphic Strings + +Determine if two strings are isomorphic. Two strings are isomorphic if +characters in s can be mapped to characters in t while preserving order, +with a one-to-one mapping. + +Reference: https://leetcode.com/problems/isomorphic-strings/description/ + +Complexity: + ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/map/is_isomorphic.py
Write docstrings for data processing functions
from __future__ import annotations class Node: def __init__(self, val: object = None) -> None: self.val = val self.next: Node | None = None def remove_dups(head: Node | None) -> None: seen: set[object] = set() prev = Node() while head: if head.val in seen: prev.n...
--- +++ @@ -1,3 +1,16 @@+""" +Remove Duplicates from Linked List + +Remove duplicate values from an unsorted linked list. Two approaches are +provided: hash-set-based (O(n) time, O(n) space) and runner technique +(O(n^2) time, O(1) space). + +Reference: https://en.wikipedia.org/wiki/Linked_list + +Complexity (hash set)...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/linked_list/remove_duplicates.py
Add docstrings explaining edge cases
from __future__ import annotations def is_palindrome(head: object | None) -> bool: if not head: return True fast, slow = head.next, head while fast and fast.next: fast = fast.next.next slow = slow.next second = slow.next slow.next = None node = None while second: ...
--- +++ @@ -1,8 +1,32 @@+""" +Palindrome Linked List + +Determine whether a singly linked list is a palindrome. Three approaches are +provided: reverse-half, stack-based, and dictionary-based. + +Reference: https://leetcode.com/problems/palindrome-linked-list/ + +Complexity (reverse-half): + Time: O(n) + Space: ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/linked_list/is_palindrome.py
Create Google-style docstrings for my code
from __future__ import annotations def max_common_sub_string(s1: str, s2: str) -> str: char_index = {s2[i]: i for i in range(len(s2))} max_length = 0 best_substring = "" i = 0 while i < len(s1): if s1[i] in char_index: j = char_index[s1[i]] k = i while ...
--- +++ @@ -1,8 +1,36 @@+""" +Longest Common Substring + +Given two strings where the second contains all distinct characters, +find the longest common substring using index mapping. + +Reference: https://en.wikipedia.org/wiki/Longest_common_substring_problem + +Complexity: + Time: O(n log n) expected, O(n * m) wor...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/map/longest_common_subsequence.py
Document all endpoints with docstrings
from __future__ import annotations import random class RandomizedSet: def __init__(self) -> None: self.nums: list[int] = [] self.idxs: dict[int, int] = {} def insert(self, val: int) -> bool: if val not in self.idxs: self.nums.append(val) self.idxs[val] = len...
--- +++ @@ -1,3 +1,16 @@+""" +Randomized Set + +Design a data structure that supports insert, remove, and getRandom +in average O(1) time. Uses a list for random access and a dictionary +for O(1) lookup/removal. + +Reference: https://leetcode.com/problems/insert-delete-getrandom-o1/ + +Complexity: + Time: O(1) aver...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/map/randomized_set.py
Document functions with clear intent
from __future__ import annotations def longest_palindromic_subsequence(s: str) -> int: length = len(s) previous_row = [0] * length current_row = [0] * length longest_length = 0 for end in range(length): for start in range(end + 1): if end - start <= 1: if s[st...
--- +++ @@ -1,8 +1,34 @@+""" +Longest Palindromic Substring + +Find the length of the longest palindromic substring using dynamic +programming with two rolling arrays. + +Reference: https://en.wikipedia.org/wiki/Longest_palindromic_substring + +Complexity: + Time: O(n^2) + Space: O(n) +""" from __future__ imp...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/map/longest_palindromic_subsequence.py
Can you add docstrings to this Python file?
from __future__ import annotations def combination(n: int, r: int) -> int: if n == r or r == 0: return 1 return combination(n - 1, r - 1) + combination(n - 1, r) def combination_memo(n: int, r: int) -> int: memo: dict[tuple[int, int], int] = {} def _recur(n: int, r: int) -> int: if...
--- +++ @@ -1,14 +1,54 @@+""" +Combinations (nCr) + +Calculate the number of ways to choose r items from n items (binomial +coefficient) using recursive and memoized approaches. + +Reference: https://en.wikipedia.org/wiki/Combination + +Complexity: + Time: O(2^n) naive recursive, O(n*r) memoized + Space: O(n) re...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/combination.py
Add verbose docstrings with examples
from __future__ import annotations def max_subarray(array: list[int]) -> int: max_so_far = max_now = array[0] for i in range(1, len(array)): max_now = max(array[i], max_now + array[i]) max_so_far = max(max_so_far, max_now) return max_so_far
--- +++ @@ -1,10 +1,33 @@+""" +Maximum Subarray (Kadane's Algorithm) + +Find the contiguous subarray with the largest sum. + +Reference: https://en.wikipedia.org/wiki/Maximum_subarray_problem + +Complexity: + Time: O(n) + Space: O(1) +""" from __future__ import annotations def max_subarray(array: list[in...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/dynamic_programming/max_subarray.py
Generate helpful docstrings for debugging
from __future__ import annotations def word_pattern(pattern: str, string: str) -> bool: mapping: dict[str, str] = {} mapped_values: set[str] = set() words = string.split() if len(words) != len(pattern): return False for i in range(len(pattern)): if pattern[i] not in mapping: ...
--- +++ @@ -1,8 +1,35 @@+""" +Word Pattern + +Given a pattern and a string, determine if the string follows the same +pattern via a bijection between pattern letters and words. + +Reference: https://leetcode.com/problems/word-pattern/description/ + +Complexity: + Time: O(n) + Space: O(n) +""" from __future__ ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/map/word_pattern.py
Create Google-style docstrings for my code
from __future__ import annotations import copy import math import queue def maximum_flow_bfs(adjacency_matrix: list[list[int]]) -> int: new_array = copy.deepcopy(adjacency_matrix) total = 0 while True: min_flow = math.inf visited = [0] * len(new_array) path = [0] * len(new_array...
--- +++ @@ -1,3 +1,15 @@+""" +Maximum Flow via BFS + +Computes maximum flow in a network represented as an adjacency matrix, +using BFS to find augmenting paths. + +Reference: https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm + +Complexity: + Time: O(V * E^2) + Space: O(V^2) +""" from __future__ ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/maximum_flow_bfs.py
Write reusable docstrings
from __future__ import annotations import string def int_to_base(num: int, base: int) -> str: is_negative = False if num == 0: return "0" if num < 0: is_negative = True num *= -1 digit = string.digits + string.ascii_uppercase res = "" while num > 0: res += dig...
--- +++ @@ -1,3 +1,15 @@+""" +Integer Base Conversion + +Convert integers between arbitrary bases (2-36). Supports conversion from +integer to string representation in a given base, and vice versa. + +Reference: https://en.wikipedia.org/wiki/Positional_notation + +Complexity: + Time: O(log_base(num)) for both direc...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/base_conversion.py
Write reusable docstrings
from __future__ import annotations def extended_gcd(num1: int, num2: int) -> tuple[int, int, int]: old_s, s = 1, 0 old_t, t = 0, 1 old_r, r = num1, num2 while r != 0: quotient = old_r / r old_r, r = r, old_r - quotient * r old_s, s = s, old_s - quotient * s old_t, t ...
--- +++ @@ -1,8 +1,35 @@+""" +Extended Euclidean Algorithm + +Find coefficients s and t (Bezout's identity) such that: +num1 * s + num2 * t = gcd(num1, num2). + +Reference: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm + +Complexity: + Time: O(log(min(num1, num2))) + Space: O(1) +""" from __futur...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/extended_gcd.py
Document all endpoints with docstrings
from __future__ import annotations import math def _l2_distance(vec: list[float]) -> float: norm = 0.0 for element in vec: norm += element * element norm = math.sqrt(norm) return norm def cosine_similarity(vec1: list[float], vec2: list[float]) -> float: if len(vec1) != len(vec2): ...
--- +++ @@ -1,3 +1,16 @@+""" +Cosine Similarity + +Calculate the cosine similarity between two vectors, which measures the +cosine of the angle between them. Values range from -1 (opposite) to 1 +(identical direction). + +Reference: https://en.wikipedia.org/wiki/Cosine_similarity + +Complexity: + Time: O(n) + Sp...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/cosine_similarity.py
Generate consistent docstrings
from __future__ import annotations def decimal_to_binary_util(val: str) -> str: bits = [128, 64, 32, 16, 8, 4, 2, 1] val_int = int(val) binary_rep = "" for bit in bits: if val_int >= bit: binary_rep += str(1) val_int -= bit else: binary_rep += str(0...
--- +++ @@ -1,8 +1,32 @@+""" +Decimal to Binary IP Conversion + +Convert an IP address from dotted-decimal notation to its binary +representation. + +Reference: https://en.wikipedia.org/wiki/IP_address + +Complexity: + Time: O(1) (fixed 4 octets, 8 bits each) + Space: O(1) +""" from __future__ import annotati...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/decimal_to_binary_ip.py
Write docstrings for utility functions
from __future__ import annotations from cmath import exp, pi def fft(x: list[complex]) -> list[complex]: n = len(x) if n == 1: return x even = fft(x[0::2]) odd = fft(x[1::2]) y = [0 for _ in range(n)] for k in range(n // 2): q = exp(-2j * pi * k / n) * odd[k] y[k] =...
--- +++ @@ -1,3 +1,15 @@+""" +Fast Fourier Transform (Cooley-Tukey) + +Compute the Discrete Fourier Transform of a sequence using the Cooley-Tukey +radix-2 decimation-in-time algorithm. Input length must be a power of 2. + +Reference: https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm + +Complexity: + ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/fft.py
Add documentation for all methods
from __future__ import annotations def factorial(n: int, mod: int | None = None) -> int: if not (isinstance(n, int) and n >= 0): raise ValueError("'n' must be a non-negative integer.") if mod is not None and not (isinstance(mod, int) and mod > 0): raise ValueError("'mod' must be a positive in...
--- +++ @@ -1,8 +1,38 @@+""" +Factorial + +Compute the factorial of a non-negative integer, with optional modular +arithmetic support. + +Reference: https://en.wikipedia.org/wiki/Factorial + +Complexity: + Time: O(n) + Space: O(1) iterative, O(n) recursive +""" from __future__ import annotations def fact...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/factorial.py
Generate docstrings for this script
from __future__ import annotations from math import sqrt def distance_between_two_points(x1: float, y1: float, x2: float, y2: float) -> float: return sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)
--- +++ @@ -1,3 +1,15 @@+""" +Distance Between Two Points in 2D Space + +Calculate the Euclidean distance between two points using the distance +formula derived from the Pythagorean theorem. + +Reference: https://en.wikipedia.org/wiki/Euclidean_distance + +Complexity: + Time: O(1) + Space: O(1) +""" from __fu...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/distance_between_two_points.py
Write docstrings that follow conventions
from __future__ import annotations import math import secrets def _prime_check(num: int) -> bool: if num <= 1: return False if num == 2 or num == 3: return True if num % 2 == 0 or num % 3 == 0: return False j = 5 while j * j <= num: if num % j == 0 or num % (j + 2...
--- +++ @@ -1,3 +1,16 @@+""" +Diffie-Hellman Key Exchange + +Implements the Diffie-Hellman key exchange protocol, which enables two parties +to establish a shared secret over an insecure channel using discrete +logarithm properties. + +Reference: https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange + +Comp...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/diffie_hellman_key_exchange.py
Add docstrings that explain inputs and outputs
from __future__ import annotations import math def _find_order(a: int, n: int) -> int: if (a == 1) & (n == 1): return 1 if math.gcd(a, n) != 1: return -1 for i in range(1, n): if pow(a, i) % n == 1: return i return -1 def _euler_totient(n: int) -> int: resul...
--- +++ @@ -1,3 +1,16 @@+""" +Primitive Root Finder + +Find all primitive roots of a positive integer n. A primitive root modulo n +is an integer whose multiplicative order modulo n equals Euler's totient +of n. + +Reference: https://en.wikipedia.org/wiki/Primitive_root_modulo_n + +Complexity: + Time: O(n^2 log n) ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/find_primitive_root_simple.py
Generate consistent docstrings
from __future__ import annotations import math def find_order(a: int, n: int) -> int: if (a == 1) & (n == 1): return 1 if math.gcd(a, n) != 1: return -1 for i in range(1, n): if pow(a, i) % n == 1: return i return -1
--- +++ @@ -1,3 +1,15 @@+""" +Multiplicative Order + +Find the multiplicative order of a modulo n, which is the smallest positive +integer k such that a^k = 1 (mod n). Requires gcd(a, n) = 1. + +Reference: https://en.wikipedia.org/wiki/Multiplicative_order + +Complexity: + Time: O(n log n) + Space: O(1) +""" ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/find_order_simple.py
Write docstrings describing functionality
from __future__ import annotations def _is_prime(n: int) -> bool: if n < 2: return False if n < 4: return True if n % 2 == 0 or n % 3 == 0: return False i = 5 while i * i <= n: if n % i == 0 or n % (i + 2) == 0: return False i += 6 return Tr...
--- +++ @@ -1,8 +1,29 @@+""" +Goldbach's Conjecture + +Every even integer greater than 2 can be expressed as the sum of two primes. +This module provides a function to find such a pair of primes and a helper +to verify the conjecture over a range. + +Reference: https://en.wikipedia.org/wiki/Goldbach%27s_conjecture + +C...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/goldbach.py
Create structured documentation for my script
from __future__ import annotations def _find_factorial(n: int) -> int: fact = 1 while n != 0: fact *= n n -= 1 return fact def krishnamurthy_number(n: int) -> bool: if n == 0: return False sum_of_digits = 0 temp = n while temp != 0: sum_of_digits += _fin...
--- +++ @@ -1,8 +1,28 @@+""" +Krishnamurthy Number + +A Krishnamurthy number is a number whose sum of the factorials of its digits +equals the number itself (e.g., 145 = 1! + 4! + 5!). + +Reference: https://en.wikipedia.org/wiki/Factorion + +Complexity: + Time: O(d * m) where d is number of digits and m is max digi...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/krishnamurthy_number.py
Add docstrings to incomplete code
from __future__ import annotations def is_strobogrammatic(num: str) -> bool: comb = "00 11 88 69 96" i = 0 j = len(num) - 1 while i <= j: if comb.find(num[i] + num[j]) == -1: return False i += 1 j -= 1 return True def is_strobogrammatic2(num: str) -> bool: ...
--- +++ @@ -1,8 +1,34 @@+""" +Strobogrammatic Number Check + +Determine whether a number (as a string) is strobogrammatic, meaning it +looks the same when rotated 180 degrees. + +Reference: https://en.wikipedia.org/wiki/Strobogrammatic_number + +Complexity: + Time: O(n) where n is the length of the number string + ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/is_strobogrammatic.py
Add standardized docstrings across the file
from __future__ import annotations def euler_totient(n: int) -> int: result = n for i in range(2, int(n**0.5) + 1): if n % i == 0: while n % i == 0: n //= i result -= result // i if n > 1: result -= result // n return result
--- +++ @@ -1,8 +1,34 @@+""" +Euler's Totient Function + +Compute Euler's totient function phi(n), which counts the number of integers +from 1 to n inclusive that are coprime to n. + +Reference: https://en.wikipedia.org/wiki/Euler%27s_totient_function + +Complexity: + Time: O(sqrt(n)) + Space: O(1) +""" from ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/euler_totient.py
Insert docstrings into my code
from __future__ import annotations def next_bigger(num: int) -> int: digits = [int(i) for i in str(num)] idx = len(digits) - 1 while idx >= 1 and digits[idx - 1] >= digits[idx]: idx -= 1 if idx == 0: return -1 pivot = digits[idx - 1] swap_idx = len(digits) - 1 while pi...
--- +++ @@ -1,8 +1,35 @@+""" +Next Bigger Number with Same Digits + +Given a number, find the next higher number that uses the exact same set of +digits. This is equivalent to finding the next permutation. + +Reference: https://en.wikipedia.org/wiki/Permutation#Generation_in_lexicographic_order + +Complexity: + Time...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/next_bigger.py
Generate docstrings with examples
from __future__ import annotations from collections.abc import Iterable from fractions import Fraction from functools import reduce from numbers import Rational class Monomial: def __init__( self, variables: dict[int, int], coeff: int | float | Fraction | None = None ) -> None: self.variabl...
--- +++ @@ -1,3 +1,16 @@+""" +Polynomial and Monomial Arithmetic + +A symbolic algebra system for polynomials and monomials supporting addition, +subtraction, multiplication, division, substitution, and polynomial long +division with Fraction-based exact arithmetic. + +Reference: https://en.wikipedia.org/wiki/Polynomia...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/polynomial.py
Write docstrings including parameters and return values
from __future__ import annotations def gcd(a: int, b: int) -> int: a_int = isinstance(a, int) b_int = isinstance(b, int) a = abs(a) b = abs(b) if not (a_int or b_int): raise ValueError("Input arguments are not integers") if (a == 0) or (b == 0): raise ValueError("One or more ...
--- +++ @@ -1,8 +1,38 @@+""" +Greatest Common Divisor and Least Common Multiple + +Compute the GCD and LCM of two integers using Euclid's algorithm and +a bitwise variant. + +Reference: https://en.wikipedia.org/wiki/Euclidean_algorithm + +Complexity: + Time: O(log(min(a, b))) for gcd, O(log(min(a, b))) for lcm + ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/gcd.py
Help me write clear docstrings
from __future__ import annotations def hailstone(n: int) -> list[int]: sequence = [n] while n > 1: n = 3 * n + 1 if n % 2 != 0 else int(n / 2) sequence.append(n) return sequence
--- +++ @@ -1,10 +1,36 @@+""" +Hailstone Sequence (Collatz Conjecture) + +Generate the hailstone sequence starting from n: if n is even, next is n/2; +if n is odd, next is 3n + 1. The sequence ends when it reaches 1. + +Reference: https://en.wikipedia.org/wiki/Collatz_conjecture + +Complexity: + Time: O(unknown) - ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/hailstone.py
Include argument descriptions in docstrings
from __future__ import annotations def find_next_square(sq: float) -> float: root = sq**0.5 if root.is_integer(): return (root + 1) ** 2 return -1 def find_next_square2(sq: float) -> float: root = sq**0.5 return -1 if root % 1 else (root + 1) ** 2
--- +++ @@ -1,8 +1,34 @@+""" +Next Perfect Square + +Given a number, find the next perfect square if the input is itself a perfect +square. Otherwise, return -1. + +Reference: https://en.wikipedia.org/wiki/Square_number + +Complexity: + Time: O(1) + Space: O(1) +""" from __future__ import annotations def...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/next_perfect_square.py
Generate docstrings for exported functions
from __future__ import annotations def gen_strobogrammatic(n: int) -> list[str]: return _helper(n, n) def _helper(n: int, length: int) -> list[str]: if n == 0: return [""] if n == 1: return ["1", "0", "8"] middles = _helper(n - 2, length) result = [] for middle in middles: ...
--- +++ @@ -1,12 +1,45 @@+""" +Generate Strobogrammatic Numbers + +A strobogrammatic number looks the same when rotated 180 degrees. Generate +all strobogrammatic numbers of a given length or count them within a range. + +Reference: https://en.wikipedia.org/wiki/Strobogrammatic_number + +Complexity: + Time: O(5^(n/...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/generate_strobogrammtic.py
Write docstrings describing each step
from __future__ import annotations def magic_number(n: int) -> bool: total_sum = 0 while n > 0 or total_sum > 9: if n == 0: n = total_sum total_sum = 0 total_sum += n % 10 n //= 10 return total_sum == 1
--- +++ @@ -1,8 +1,34 @@+""" +Magic Number + +A magic number is a number where recursively summing its digits eventually +yields 1. For example, 199 -> 1+9+9=19 -> 1+9=10 -> 1+0=1. + +Reference: https://en.wikipedia.org/wiki/Digital_root + +Complexity: + Time: O(log n) amortized + Space: O(1) +""" from __futu...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/magic_number.py
Replace inline comments with docstrings
from __future__ import annotations import math def linear_regression(x: list[float], y: list[float]) -> tuple[float, float]: n = len(x) if n != len(y) or n < 2: msg = "x and y must have at least 2 equal-length elements" raise ValueError(msg) sum_x = sum(x) sum_y = sum(y) sum_xy =...
--- +++ @@ -1,3 +1,10 @@+"""Simple linear regression — fit a line to (x, y) data. + +Computes the ordinary least-squares regression line y = mx + b +without external libraries. + +Inspired by PR #871 (MakanFar). +""" from __future__ import annotations @@ -5,6 +12,14 @@ def linear_regression(x: list[float], y: ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/linear_regression.py
Create Google-style docstrings for my code
from __future__ import annotations import math def num_digits(n: int) -> int: n = abs(n) if n == 0: return 1 return int(math.log10(n)) + 1
--- +++ @@ -1,3 +1,15 @@+""" +Number of Digits + +Count the number of digits in an integer using logarithmic computation +for O(1) time complexity. + +Reference: https://en.wikipedia.org/wiki/Logarithm + +Complexity: + Time: O(1) + Space: O(1) +""" from __future__ import annotations @@ -5,7 +17,23 @@ de...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/num_digits.py
Add documentation for all methods
from __future__ import annotations def modular_exponential(base: int, exponent: int, mod: int) -> int: if exponent < 0: raise ValueError("Exponent must be positive.") base %= mod result = 1 while exponent > 0: if exponent & 1: result = (result * base) % mod expone...
--- +++ @@ -1,8 +1,37 @@+""" +Modular Exponentiation + +Compute (base ^ exponent) % mod efficiently using binary exponentiation +(repeated squaring). + +Reference: https://en.wikipedia.org/wiki/Modular_exponentiation + +Complexity: + Time: O(log exponent) + Space: O(1) +""" from __future__ import annotations ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/modular_exponential.py
Generate consistent documentation across files
from __future__ import annotations def manhattan_distance(a: tuple[float, ...], b: tuple[float, ...]) -> float: return sum(abs(x - y) for x, y in zip(a, b, strict=False))
--- +++ @@ -1,6 +1,22 @@+"""Manhattan distance — L1 distance between two points. + +Also known as taxicab distance or city-block distance, it is the sum +of absolute differences of coordinates. + +Inspired by PR #877 (ChinZhengSheng). +""" from __future__ import annotations def manhattan_distance(a: tuple[float...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/manhattan_distance.py
Add docstrings for production code
from __future__ import annotations import math def num_perfect_squares(number: int) -> int: if int(math.sqrt(number)) ** 2 == number: return 1 while number > 0 and number % 4 == 0: number /= 4 if number % 8 == 7: return 4 for i in range(1, int(math.sqrt(number)) + 1): ...
--- +++ @@ -1,3 +1,15 @@+""" +Minimum Perfect Squares Sum + +Determine the minimum number of perfect squares that sum to a given integer. +By Lagrange's four-square theorem, the answer is always between 1 and 4. + +Reference: https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem + +Complexity: + Time: O(sq...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/num_perfect_squares.py
Document functions with detailed explanations
from __future__ import annotations def prime_check(n: int) -> bool: if n <= 1: return False if n == 2 or n == 3: return True if n % 2 == 0 or n % 3 == 0: return False j = 5 while j * j <= n: if n % j == 0 or n % (j + 2) == 0: return False j += 6...
--- +++ @@ -1,8 +1,34 @@+""" +Primality Test + +Check whether a given integer is prime using trial division with 6k +/- 1 +optimization. + +Reference: https://en.wikipedia.org/wiki/Primality_test + +Complexity: + Time: O(sqrt(n)) + Space: O(1) +""" from __future__ import annotations def prime_check(n: in...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/prime_check.py
Document helper functions with docstrings
from __future__ import annotations from collections import deque def maze_search(maze: list[list[int]]) -> int: blocked, allowed = 0, 1 unvisited, visited = 0, 1 initial_x, initial_y = 0, 0 if maze[initial_x][initial_y] == blocked: return -1 directions = [(0, -1), (0, 1), (-1, 0), (1,...
--- +++ @@ -1,3 +1,14 @@+""" +Maze Search (BFS) + +Find the minimum number of steps from the top-left corner to the +bottom-right corner of a grid. Only cells with value 1 may be traversed. +Returns -1 if no path exists. + +Complexity: + Time: O(M * N) + Space: O(M * N) +""" from __future__ import annotation...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/maze_search_bfs.py
Generate docstrings with examples
from __future__ import annotations def get_primes(n: int) -> list[int]: if n <= 0: raise ValueError("'n' must be a positive integer.") sieve_size = (n // 2 - 1) if n % 2 == 0 else (n // 2) sieve = [True for _ in range(sieve_size)] primes: list[int] = [] if n >= 2: primes.append(2)...
--- +++ @@ -1,8 +1,35 @@+""" +Sieve of Eratosthenes + +Generate all prime numbers less than n using an optimized sieve that skips +even numbers. + +Reference: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes + +Complexity: + Time: O(n log log n) + Space: O(n) +""" from __future__ import annotations de...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/primes_sieve_of_eratosthenes.py
Generate docstrings with parameter types
from __future__ import annotations def find_nth_digit(n: int) -> int: length = 1 count = 9 start = 1 while n > length * count: n -= length * count length += 1 count *= 10 start *= 10 start += (n - 1) / length s = str(start) return int(s[(n - 1) % length])
--- +++ @@ -1,8 +1,32 @@+""" +Find the Nth Digit + +Find the nth digit in the infinite sequence 1, 2, 3, ..., 9, 10, 11, 12, ... +by determining which number contains it and extracting the specific digit. + +Reference: https://en.wikipedia.org/wiki/Positional_notation + +Complexity: + Time: O(log n) + Space: O(l...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/nth_digit.py
Create Google-style docstrings for my code
from __future__ import annotations def _extended_gcd(a: int, b: int) -> tuple[int, int, int]: old_s, s = 1, 0 old_t, t = 0, 1 old_r, r = a, b while r != 0: quotient = old_r // r old_r, r = r, old_r - quotient * r old_s, s = s, old_s - quotient * s old_t, t = t, old_t...
--- +++ @@ -1,8 +1,29 @@+""" +Modular Multiplicative Inverse + +Find x such that a * x = 1 (mod m) using the Extended Euclidean Algorithm. +Requires a and m to be coprime. + +Reference: https://en.wikipedia.org/wiki/Modular_multiplicative_inverse + +Complexity: + Time: O(log(min(a, m))) + Space: O(1) +""" fro...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/modular_inverse.py
Add standardized docstrings across the file
from __future__ import annotations def power(a: int, n: int, mod: int | None = None) -> int: ans = 1 while n: if n & 1: ans = ans * a a = a * a if mod: ans %= mod a %= mod n >>= 1 return ans def power_recur(a: int, n: int, mod: int | N...
--- +++ @@ -1,8 +1,36 @@+""" +Binary Exponentiation + +Compute a^n efficiently using binary exponentiation (exponentiation by +squaring), with optional modular arithmetic. + +Reference: https://en.wikipedia.org/wiki/Exponentiation_by_squaring + +Complexity: + Time: O(log n) + Space: O(1) iterative, O(log n) recu...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/power.py
Generate descriptive docstrings automatically
from __future__ import annotations import math def cholesky_decomposition(matrix: list[list[float]]) -> list[list[float]] | None: size = len(matrix) for row in matrix: if len(row) != size: return None result = [[0.0] * size for _ in range(size)] for j in range(size): diag...
--- +++ @@ -1,3 +1,16 @@+""" +Cholesky Matrix Decomposition + +Decompose a Hermitian positive-definite matrix A into a lower-triangular +matrix V such that V * V^T = A. Mainly used for numerical solution of +linear equations Ax = b. + +Reference: https://en.wikipedia.org/wiki/Cholesky_decomposition + +Complexity: + ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/cholesky_matrix_decomposition.py
Add missing documentation to my Python functions
from __future__ import annotations def recursive_binomial_coefficient(n: int, k: int) -> int: if k > n: raise ValueError("Invalid Inputs, ensure that n >= k") if k == 0 or n == k: return 1 if k > n / 2: return recursive_binomial_coefficient(n, n - k) return int((n / k) * recur...
--- +++ @@ -1,12 +1,42 @@+""" +Recursive Binomial Coefficient + +Calculate the binomial coefficient C(n, k) using a recursive formula with +the identity C(n, k) = (n/k) * C(n-1, k-1). + +Reference: https://en.wikipedia.org/wiki/Binomial_coefficient + +Complexity: + Time: O(k) + Space: O(k) recursive stack +""" ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/recursive_binomial_coefficient.py
Provide docstrings following PEP 257
from __future__ import annotations def sum_dig_pow(low: int, high: int) -> list[int]: result = [] for number in range(low, high + 1): exponent = 1 summation = 0 number_as_string = str(number) tokens = list(map(int, number_as_string)) for k in tokens: sum...
--- +++ @@ -1,8 +1,35 @@+""" +Summing Digits Power + +Find all integers in a range where each digit raised to its positional power +(1-indexed) sums to the number itself (e.g., 89 = 8^1 + 9^2). + +Reference: https://en.wikipedia.org/wiki/Perfect_digit-to-digit_invariant + +Complexity: + Time: O((high - low) * d) wh...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/summing_digits.py
Improve documentation using docstrings
from __future__ import annotations import secrets def is_prime(n: int, k: int) -> bool: def _pow2_factor(num: int) -> tuple[int, int]: power = 0 while num % 2 == 0: num //= 2 power += 1 return power, num def _valid_witness(a: int) -> bool: x = pow(in...
--- +++ @@ -1,3 +1,16 @@+""" +Rabin-Miller Primality Test + +A probabilistic primality test where returning False guarantees the number +is composite, and returning True means the number is probably prime with +a 4^(-k) chance of error. + +Reference: https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test + +...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/rabin_miller.py
Add documentation for all methods
from __future__ import annotations def max_killed_enemies(grid: list[list[str]]) -> int: if not grid: return 0 rows, cols = len(grid), len(grid[0]) max_killed = 0 row_enemies, col_enemies = 0, [0] * cols for i in range(rows): for j in range(cols): if j == 0 or grid[i][...
--- +++ @@ -1,8 +1,35 @@+""" +Bomb Enemy + +Given a 2D grid, each cell is either a wall 'W', an enemy 'E' or empty '0' +(the number zero). Return the maximum enemies you can kill using one bomb. +The bomb kills all the enemies in the same row and column from the planted +point until it hits the wall since it is too str...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/bomb_enemy.py
Annotate my code with docstrings
from __future__ import annotations from math import pi def surface_area_of_torus(major_radius: float, minor_radius: float) -> float: if major_radius < 0 or minor_radius < 0: raise ValueError("Radii must be non-negative") return 4 * pi**2 * major_radius * minor_radius
--- +++ @@ -1,3 +1,15 @@+""" +Surface Area of a Torus + +Calculate the surface area of a torus given its major and minor radii +using the formula A = 4 * pi^2 * R * r. + +Reference: https://en.wikipedia.org/wiki/Torus + +Complexity: + Time: O(1) + Space: O(1) +""" from __future__ import annotations @@ -5,7 ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/surface_area_of_torus.py
Provide docstrings following PEP 257
from __future__ import annotations def square_root(n: float, epsilon: float = 0.001) -> float: guess = n / 2 while abs(guess * guess - n) > epsilon: guess = (guess + (n / guess)) / 2 return guess
--- +++ @@ -1,11 +1,36 @@+""" +Square Root by Newton's Method + +Compute the square root of a positive number using Newton's method +(Babylonian method) with a configurable precision factor. + +Reference: https://en.wikipedia.org/wiki/Newton%27s_method#Square_root + +Complexity: + Time: O(log(1/epsilon)) iterations...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/sqrt_precision_factor.py
Improve documentation using docstrings
from __future__ import annotations def vector_to_index_value_list( vector: list[float], ) -> list[tuple[int, float]]: return [(i, v) for i, v in enumerate(vector) if v != 0.0] def dot_product( iv_list1: list[tuple[int, float]], iv_list2: list[tuple[int, float]], ) -> float: product = 0 p1 =...
--- +++ @@ -1,3 +1,15 @@+""" +Sparse Dot Vector + +Compute the dot product of two large sparse vectors efficiently by +converting them to index-value pair representations and merging. + +Reference: https://leetcode.com/problems/dot-product-of-two-sparse-vectors/ + +Complexity: + Time: O(n) for conversion, O(k) for ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/sparse_dot_vector.py
Generate docstrings for this script
from __future__ import annotations from fractions import Fraction from algorithms.math.gcd import lcm from algorithms.math.polynomial import Monomial, Polynomial def cycle_product(m1: Monomial, m2: Monomial) -> Monomial: assert isinstance(m1, Monomial) and isinstance(m2, Monomial) a_vars = m1.variables ...
--- +++ @@ -1,3 +1,16 @@+""" +Symmetry Group Cycle Index + +Compute the cycle index polynomial of the symmetric group S_n and use it +to count distinct configurations of grids under row/column permutations +via Burnside's lemma. + +Reference: https://en.wikipedia.org/wiki/Cycle_index#Symmetric_group_Sn + +Complexity: +...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/symmetry_group_cycle_index.py
Generate descriptive docstrings automatically
from __future__ import annotations import secrets def _extended_gcd(a: int, b: int) -> tuple[int, int, int]: old_r, r = a, b old_s, s = 1, 0 old_t, t = 0, 1 while r != 0: q = old_r // r old_r, r = r, old_r - q * r old_s, s = s, old_s - q * s old_t, t = t, old_t - q * ...
--- +++ @@ -1,3 +1,15 @@+""" +RSA Encryption Algorithm + +Implements RSA key generation, encryption, and decryption. RSA uses separate +public and private keys where ((x^e)^d) % n == x % n. + +Reference: https://en.wikipedia.org/wiki/RSA_(cryptosystem) + +Complexity: + Time: O(k^3) for key generation (k = bit lengt...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/rsa.py
Write docstrings for algorithm functions
from __future__ import annotations def rotate(mat: list[list[int]]) -> list[list[int]]: if not mat: return mat mat.reverse() for i in range(len(mat)): for j in range(i): mat[i][j], mat[j][i] = mat[j][i], mat[i][j] return mat
--- +++ @@ -1,12 +1,36 @@+""" +Rotate Image + +Rotate an n x n 2D matrix representing an image by 90 degrees clockwise, +in-place. First reverse the rows top-to-bottom, then transpose. + +Reference: https://leetcode.com/problems/rotate-image/ + +Complexity: + Time: O(n^2) + Space: O(1) +""" from __future__ im...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/rotate_image.py
Create structured documentation for my script
from __future__ import annotations def rotate_clockwise(matrix: list[list[int]]) -> list[list[int]]: result: list[list[int]] = [] for row in reversed(matrix): for i, elem in enumerate(row): try: result[i].append(elem) except IndexError: result.i...
--- +++ @@ -1,8 +1,33 @@+""" +Copy Transform + +Rotate and invert a matrix by creating transformed copies. +Provides clockwise rotation, counterclockwise rotation, top-left +inversion (transpose), and bottom-left inversion (anti-transpose). + +Reference: https://en.wikipedia.org/wiki/Transpose + +Complexity: + Time:...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/copy_transform.py
Document all endpoints with docstrings
from __future__ import annotations def crout_matrix_decomposition( matrix: list[list[float]], ) -> tuple[list[list[float]], list[list[float]]]: size = len(matrix) lower = [[0.0] * size for _ in range(size)] upper = [[0.0] * size for _ in range(size)] for j in range(size): upper[j][j] = 1....
--- +++ @@ -1,3 +1,17 @@+""" +Crout Matrix Decomposition + +Decompose a matrix A into lower-triangular matrix L and upper-triangular +matrix U such that L * U = A. L has non-zero elements only on and below +the diagonal; U has non-zero elements only on and above the diagonal +with ones on the diagonal. + +Reference: ht...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/crout_matrix_decomposition.py
Document this script properly
from __future__ import annotations def reconstruct_queue(people: list[list[int]]) -> list[list[int]]: queue: list[list[int]] = [] people.sort(key=lambda x: (-x[0], x[1])) for height, count in people: queue.insert(count, [height, count]) return queue
--- +++ @@ -1,10 +1,35 @@+""" +Reconstruct Queue by Height + +Given a list of people described by (height, k) pairs where k is the +number of taller-or-equal people in front, reconstruct the queue by +sorting and inserting. + +Reference: https://leetcode.com/problems/queue-reconstruction-by-height/ + +Complexity: + ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/queue/reconstruct_queue.py
Improve my code by adding docstrings
from __future__ import annotations import fractions def invert_matrix( matrix: list[list[int | float]], ) -> list[list[int | float | fractions.Fraction]]: if not _array_is_matrix(matrix): return [[-1]] elif len(matrix) != len(matrix[0]): return [[-2]] elif len(matrix) < 2: re...
--- +++ @@ -1,3 +1,17 @@+""" +Matrix Inversion + +Compute the inverse of an invertible n x n matrix A, returning an n x n +matrix B such that A * B = B * A = I (the identity matrix). Uses cofactor +expansion: compute the matrix of minors with checkerboard signs, adjugate +(transpose), and multiply by 1/determinant. + +...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/matrix_inversion.py
Add docstrings including usage examples
from __future__ import annotations def sparse_multiply( mat_a: list[list[int]], mat_b: list[list[int]] ) -> list[list[int]] | None: if mat_a is None or mat_b is None: return None rows_a, cols_a = len(mat_a), len(mat_a[0]) cols_b = len(mat_b[0]) if len(mat_b) != cols_a: raise Excep...
--- +++ @@ -1,3 +1,16 @@+""" +Sparse Matrix Multiplication + +Given two sparse matrices A and B, return their product A * B. +Skips zero elements for efficiency. A's column count must equal +B's row count. + +Reference: https://leetcode.com/problems/sparse-matrix-multiplication/ + +Complexity: + Time: O(m * n * p) ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/sparse_mul.py
Include argument descriptions in docstrings
from __future__ import annotations from collections import defaultdict def valid_solution_hashtable(board: list[list[int]]) -> bool: for i in range(len(board)): row_seen = defaultdict(int) col_seen = defaultdict(int) for j in range(len(board[0])): value_row = board[i][j] ...
--- +++ @@ -1,3 +1,16 @@+""" +Sudoku Validator + +Validate whether a completed 9x9 Sudoku board is a valid solution. +Each row, column, and 3x3 sub-box must contain digits 1-9 without +repetition. Boards containing zeroes are considered invalid. + +Reference: https://en.wikipedia.org/wiki/Sudoku + +Complexity: + Tim...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/sudoku_validator.py
Create simple docstrings for beginners
from __future__ import annotations def multiply( multiplicand: list[list[int]], multiplier: list[list[int]] ) -> list[list[int]]: multiplicand_rows, multiplicand_cols = len(multiplicand), len(multiplicand[0]) multiplier_rows, multiplier_cols = len(multiplier), len(multiplier[0]) if multiplicand_cols ...
--- +++ @@ -1,3 +1,15 @@+""" +Matrix Multiplication + +Multiply two compatible matrices and return their product. The number of +columns in the multiplicand must equal the number of rows in the multiplier. + +Reference: https://en.wikipedia.org/wiki/Matrix_multiplication + +Complexity: + Time: O(m * n * p) for (m ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/multiply.py
Improve documentation using docstrings
from __future__ import annotations def search_in_a_sorted_matrix( mat: list[list[int]], rows: int, cols: int, key: int ) -> bool: i, j = rows - 1, 0 while i >= 0 and j < cols: if key == mat[i][j]: return True if key < mat[i][j]: i -= 1 else: j +...
--- +++ @@ -1,3 +1,16 @@+""" +Search in Sorted Matrix + +Search for a key in a matrix that is sorted row-wise and column-wise +in non-decreasing order. Start from the bottom-left corner and move +up or right depending on the comparison. + +Reference: https://leetcode.com/problems/search-a-2d-matrix-ii/ + +Complexity: +...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/search_in_sorted_matrix.py
Add detailed documentation for each class
from __future__ import annotations from collections import deque class MovingAverage: def __init__(self, size: int) -> None: self.queue: deque[int] = deque(maxlen=size) def next(self, val: int) -> float: self.queue.append(val) return sum(self.queue) / len(self.queue)
--- +++ @@ -1,3 +1,15 @@+""" +Moving Average from Data Stream + +Calculate the moving average of integers in a sliding window of fixed +size using a bounded deque. + +Reference: https://leetcode.com/problems/moving-average-from-data-stream/ + +Complexity: + Time: O(1) per call to next + Space: O(size) +""" fr...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/queue/moving_average.py
Add return value explanations in docstrings
from __future__ import annotations from heapq import heappop, heappush def sort_diagonally(mat: list[list[int]]) -> list[list[int]]: if len(mat) == 1 or len(mat[0]) == 1: return mat num_rows = len(mat) num_cols = len(mat[0]) for i in range(num_rows + num_cols - 1): if i + 1 < num_r...
--- +++ @@ -1,3 +1,16 @@+""" +Sort Matrix Diagonally + +Given an m x n matrix of integers, sort each diagonal from top-left to +bottom-right in ascending order and return the sorted matrix. Uses a +min-heap for each diagonal. + +Reference: https://leetcode.com/problems/sort-the-matrix-diagonally/ + +Complexity: + Ti...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/sort_matrix_diagonally.py
Write docstrings including parameters and return values
from __future__ import annotations import collections def max_sliding_window(arr: list[int], k: int) -> list[int]: index_deque: collections.deque[int] = collections.deque() result: list[int] = [] for i, value in enumerate(arr): while index_deque and arr[index_deque[-1]] < value: inde...
--- +++ @@ -1,3 +1,16 @@+""" +Max Sliding Window (Deque-based) + +Given an array and a window size k, find the maximum element in each +sliding window using a monotonic deque that stores indices of elements +in decreasing order of their values. + +Reference: https://leetcode.com/problems/sliding-window-maximum/ + +Comp...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/queue/max_sliding_window.py
Add docstrings to my Python code
from __future__ import annotations def pythagoras( opposite: float | str, adjacent: float | str, hypotenuse: float | str ) -> str: try: if opposite == "?": return "Opposite = " + str(((hypotenuse**2) - (adjacent**2)) ** 0.5) if adjacent == "?": return "Adjacent = " + s...
--- +++ @@ -1,3 +1,15 @@+""" +Pythagorean Theorem + +Given the lengths of two sides of a right-angled triangle, compute the +length of the third side using the Pythagorean theorem. + +Reference: https://en.wikipedia.org/wiki/Pythagorean_theorem + +Complexity: + Time: O(1) + Space: O(1) +""" from __future__ im...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/math/pythagoras.py
Create documentation strings for testing functions
from __future__ import annotations import copy import math def maximum_flow_dfs(adjacency_matrix: list[list[int]]) -> int: new_array = copy.deepcopy(adjacency_matrix) total = 0 while True: min_flow = math.inf visited = [0] * len(new_array) path = [0] * len(new_array) st...
--- +++ @@ -1,3 +1,15 @@+""" +Maximum Flow via DFS + +Computes maximum flow in a network represented as an adjacency matrix, +using DFS to find augmenting paths. + +Reference: https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm + +Complexity: + Time: O(E * f) where f is the max flow value + Space: O(...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/maximum_flow_dfs.py
Add well-formatted docstrings
from __future__ import annotations def sum_sub_squares(matrix: list[list[int]], k: int) -> list[list[int]] | None: size = len(matrix) if k > size: return None result_size = size - k + 1 result = [[0] * result_size for _ in range(result_size)] for i in range(result_size): for j in ...
--- +++ @@ -1,8 +1,33 @@+""" +Sum of Sub-Squares + +Given a square matrix of size n x n and an integer k, compute the sum +of all k x k sub-squares and return the results as a matrix. + +Reference: https://www.geeksforgeeks.org/given-n-x-n-square-matrix-find-sum-sub-squares-size-k-x-k/ + +Complexity: + Time: O(n^2 ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/sum_sub_squares.py
Add docstrings for utility scripts
from __future__ import annotations class Edge: def __init__(self, source: int, target: int, weight: int) -> None: self.source = source self.target = target self.weight = weight class DisjointSet: def __init__(self, size: int) -> None: self.parent = list(range(size)) ...
--- +++ @@ -1,8 +1,21 @@+""" +Minimum Spanning Tree (Kruskal's Algorithm) + +Finds the MST of an undirected graph using Kruskal's algorithm with a +disjoint-set (union-find) data structure. + +Reference: https://en.wikipedia.org/wiki/Kruskal%27s_algorithm + +Complexity: + Time: O(E log E) + Space: O(V) +""" f...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/minimum_spanning_tree.py
Document my Python code with docstrings
from __future__ import annotations def spiral_traversal(matrix: list[list[int]]) -> list[int]: result: list[int] = [] if len(matrix) == 0: return result row_begin = 0 row_end = len(matrix) - 1 col_begin = 0 col_end = len(matrix[0]) - 1 while row_begin <= row_end and col_begin <= ...
--- +++ @@ -1,8 +1,32 @@+""" +Spiral Traversal + +Return all elements of an m x n matrix in spiral order, traversing +right, down, left, and up repeatedly while shrinking the boundaries. + +Reference: https://leetcode.com/problems/spiral-matrix/ + +Complexity: + Time: O(m * n) + Space: O(m * n) +""" from __fu...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/spiral_traversal.py
Add well-formatted docstrings
from __future__ import annotations def count_paths(rows: int, cols: int) -> int: if rows < 1 or cols < 1: return -1 count = [[None for _ in range(cols)] for _ in range(rows)] for i in range(cols): count[0][i] = 1 for j in range(rows): count[j][0] = 1 for i in range(1, ro...
--- +++ @@ -1,8 +1,34 @@+""" +Count Paths + +Count the number of unique paths from the top-left corner to the +bottom-right corner of an m x n grid. Movement is restricted to +right or down only. Uses dynamic programming. + +Reference: https://leetcode.com/problems/unique-paths/ + +Complexity: + Time: O(m * n) + ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/matrix/count_paths.py
Create docstrings for each class method
from __future__ import annotations class Graph: def __init__(self, vertices: int) -> None: self.vertex_count = vertices self.graph: dict[int, list[int]] = {} self.closure = [[0 for _ in range(vertices)] for _ in range(vertices)] def add_edge(self, source: int, target: int) -> None: ...
--- +++ @@ -1,21 +1,51 @@+""" +Transitive Closure via DFS + +Computes the transitive closure of a directed graph using depth-first +search. + +Reference: https://en.wikipedia.org/wiki/Transitive_closure#In_graph_theory + +Complexity: + Time: O(V * (V + E)) + Space: O(V^2) +""" from __future__ import annotatio...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/transitive_closure_dfs.py
Create docstrings for all classes and functions
from __future__ import annotations def binary_search(array: list[int], query: int) -> int: low, high = 0, len(array) - 1 while low <= high: mid = low + (high - low) // 2 val = array[mid] if val == query: return mid if val < query: low = mid + 1 ...
--- +++ @@ -1,8 +1,35 @@+""" +Binary Search + +Search for an element in a sorted array by repeatedly dividing the search +interval in half. + +Reference: https://en.wikipedia.org/wiki/Binary_search_algorithm + +Complexity: + Time: O(1) best / O(log n) average / O(log n) worst + Space: O(1) iterative, O(log n) re...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/binary_search.py
Write docstrings for data processing functions
from __future__ import annotations def bead_sort(array: list[int]) -> list[int]: if any(num < 0 for num in array): raise ValueError("Bead sort only works with non-negative integers.") max_value = max(array) if array else 0 grid = [[0] * len(array) for _ in range(max_value)] # Drop beads (pl...
--- +++ @@ -1,8 +1,35 @@+""" +Bead Sort + +Bead sort (also known as gravity sort) simulates how beads settle under +gravity on an abacus. It only works with non-negative integers. + +Reference: https://en.wikipedia.org/wiki/Bead_sort + +Complexity: + Time: O(n) best / O(n * max_value) average / O(n * max_value) wo...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/sorting/bead_sort.py
Improve documentation using docstrings
from __future__ import annotations _GRAY, _BLACK = 0, 1 def top_sort_recursive(graph: dict[str, list[str]]) -> list[str]: order: list[str] = [] enter = set(graph) state: dict[str, int] = {} def _dfs(node: str) -> None: state[node] = _GRAY for neighbour in graph.get(node, ()): ...
--- +++ @@ -1,3 +1,17 @@+""" +Topological Sort + +Topological sort produces a linear ordering of vertices in a directed +acyclic graph (DAG) such that for every directed edge (u, v), vertex u +comes before v. Two implementations are provided: one recursive +(DFS-based) and one iterative. + +Reference: https://en.wikip...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/topological_sort_dfs.py
Write docstrings that follow conventions
from __future__ import annotations def find_min_rotate(array: list[int]) -> int: low = 0 high = len(array) - 1 while low < high: mid = (low + high) // 2 if array[mid] > array[high]: low = mid + 1 else: high = mid return array[low] def find_min_rotate_...
--- +++ @@ -1,8 +1,34 @@+""" +Find Minimum in Rotated Sorted Array + +Find the minimum element in a sorted array that has been rotated at some +unknown pivot. Assumes no duplicates exist in the array. + +Reference: https://en.wikipedia.org/wiki/Binary_search_algorithm + +Complexity: + Time: O(1) best / O(log n) ave...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/find_min_rotate.py
Create docstrings for API functions
from __future__ import annotations def linear_search(array: list[int], query: int) -> int: for i, value in enumerate(array): if value == query: return i return -1
--- +++ @@ -1,9 +1,36 @@+""" +Linear Search + +Search for a target value in an array by checking every element sequentially. +The array does not need to be sorted. + +Reference: https://en.wikipedia.org/wiki/Linear_search + +Complexity: + Time: O(1) best / O(n) average / O(n) worst + Space: O(1) +""" from __f...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/linear_search.py
Document this script properly
from __future__ import annotations def search_insert(array: list[int], val: int) -> int: low = 0 high = len(array) - 1 while low <= high: mid = low + (high - low) // 2 if val > array[mid]: low = mid + 1 else: high = mid - 1 return low
--- +++ @@ -1,8 +1,41 @@+""" +Search Insert Position + +Given a sorted array and a target value, return the index if the target is +found. If not, return the index where it would be if it were inserted in +order. + +Reference: https://en.wikipedia.org/wiki/Binary_search_algorithm + +Complexity: + Time: O(1) best /...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/search_insert.py
Improve my code by adding docstrings
from __future__ import annotations def find_path(maze: list[list[int]]) -> int: cnt = _dfs(maze, 0, 0, 0, -1) return cnt def _dfs( maze: list[list[int]], i: int, j: int, depth: int, cnt: int, ) -> int: directions = [(0, -1), (0, 1), (-1, 0), (1, 0)] row = len(maze) col = le...
--- +++ @@ -1,8 +1,31 @@+""" +Maze Search (DFS) + +Find the shortest path from the top-left corner to the bottom-right corner +of a grid using depth-first search with backtracking. Only cells with +value 1 may be traversed. Returns -1 if no path exists. + +Complexity: + Time: O(4^(M*N)) worst case (backtracking) ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/maze_search_dfs.py
Document classes and their methods
from __future__ import annotations def first_occurrence(array: list[int], query: int) -> int: low, high = 0, len(array) - 1 while low <= high: mid = low + (high - low) // 2 if low == high: break if array[mid] < query: low = mid + 1 else: hig...
--- +++ @@ -1,8 +1,35 @@+""" +First Occurrence + +Find the index of the first occurrence of a target value in a sorted array +using binary search. + +Reference: https://en.wikipedia.org/wiki/Binary_search_algorithm + +Complexity: + Time: O(1) best / O(log n) average / O(log n) worst + Space: O(1) +""" from __...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/first_occurrence.py
Add docstrings to make code maintainable
from __future__ import annotations _KEYBOARD_ROWS: list[set[str]] = [ set("qwertyuiop"), set("asdfghjkl"), set("zxcvbnm"), ] def find_keyboard_row(words: list[str]) -> list[str]: result: list[str] = [] for word in words: for row in _KEYBOARD_ROWS: if set(word.lower()).issubse...
--- +++ @@ -1,3 +1,15 @@+""" +Keyboard Row Filter + +Given a list of words, return the words that can be typed using letters from +only one row of an American QWERTY keyboard. + +Reference: https://leetcode.com/problems/keyboard-row/description/ + +Complexity: + Time: O(n * m) where n is the number of words and m i...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/set/find_keyboard_row.py
Help me comply with documentation standards
from __future__ import annotations from itertools import chain, combinations def _powerset(iterable: list[str]) -> chain[tuple[str, ...]]: items = list(iterable) return chain.from_iterable(combinations(items, r) for r in range(len(items) + 1)) def optimal_set_cover( universe: set[int], subsets: di...
--- +++ @@ -1,3 +1,19 @@+""" +Set Cover Problem + +Given a universe U of n elements, a collection S of subsets of U, and a cost +for each subset, find the minimum-cost sub-collection that covers all of U. + +Reference: https://en.wikipedia.org/wiki/Set_cover_problem + +Complexity: + optimal_set_cover: + Time:...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/set/set_covering.py
Write documentation strings for class attributes
from __future__ import annotations import random class RandomizedSet: def __init__(self) -> None: self.elements: list[int] = [] self.index_map: dict[int, int] = {} def insert(self, new_one: int) -> None: if new_one in self.index_map: return self.index_map[new_on...
--- +++ @@ -1,3 +1,15 @@+""" +Randomized Set + +A data structure that supports insert, remove, and get-random-element +operations, all in average O(1) time. + +Reference: https://leetcode.com/problems/insert-delete-getrandom-o1/ + +Complexity: + Time: O(1) average for insert, remove, and random_element + Space: ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/set/randomized_set.py
Add verbose docstrings with examples
from __future__ import annotations def last_occurrence(array: list[int], query: int) -> int: low, high = 0, len(array) - 1 while low <= high: mid = (high + low) // 2 if (array[mid] == query and mid == len(array) - 1) or ( array[mid] == query and array[mid + 1] > query ): ...
--- +++ @@ -1,8 +1,35 @@+""" +Last Occurrence + +Find the index of the last occurrence of a target value in a sorted array +using binary search. + +Reference: https://en.wikipedia.org/wiki/Binary_search_algorithm + +Complexity: + Time: O(1) best / O(log n) average / O(log n) worst + Space: O(1) +""" from __fu...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/last_occurrence.py
Add docstrings that explain purpose and usage
from __future__ import annotations def ternary_search(left: int, right: int, key: int, array: list[int]) -> int: while right >= left: mid1 = left + (right - left) // 3 mid2 = right - (right - left) // 3 if key == array[mid1]: return mid1 if key == array[mid2]: ...
--- +++ @@ -1,8 +1,38 @@+""" +Ternary Search + +Search for a target value in a sorted array by dividing the search range into +three equal parts instead of two. At each step two midpoints are computed and +the search range is narrowed to one third. + +Reference: https://en.wikipedia.org/wiki/Ternary_search + +Complexi...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/ternary_search.py
Add docstrings for internal functions
from __future__ import annotations def search_rotate(array: list[int], val: int) -> int: low, high = 0, len(array) - 1 while low <= high: mid = (low + high) // 2 if val == array[mid]: return mid if array[low] <= array[mid]: if array[low] <= val <= array[mid]: ...
--- +++ @@ -1,8 +1,37 @@+""" +Search in Rotated Sorted Array + +Search for a target value in an array that was sorted in ascending order and +then rotated at some unknown pivot. One half of the array is always in sorted +order; we identify that half and decide which side to search. + +Reference: https://en.wikipedia.o...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/search_rotate.py
Add docstrings for better understanding
from __future__ import annotations from collections.abc import Callable def binary_search_first_true( low: int, high: int, predicate: Callable[[int], bool], ) -> int: result = -1 while low <= high: mid = low + (high - low) // 2 if predicate(mid): result = mid ...
--- +++ @@ -1,3 +1,17 @@+""" +Generalized Binary Search + +Find the smallest value in a numeric range for which a monotonic boolean +predicate evaluates to True. Instead of searching for a specific value in +an array, this version accepts an arbitrary predicate, allowing the same +binary search logic to be reused acro...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/generalized_binary_search.py
Write docstrings for algorithm functions
from __future__ import annotations from collections import deque class ZigZagIterator: def __init__(self, v1: list[int], v2: list[int]) -> None: self.queue: deque[list[int]] = deque(lst for lst in (v1, v2) if lst) def next(self) -> int: current_list = self.queue.popleft() ret = cur...
--- +++ @@ -1,3 +1,15 @@+""" +Zigzag Iterator + +Interleave elements from two lists in a zigzag fashion. Elements are +yielded alternately from each list until both are exhausted. + +Reference: https://leetcode.com/problems/zigzag-iterator/ + +Complexity: + Time: O(n) total across all next() calls + Space: O(n) ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/queue/zigzagiterator.py
Add docstrings to improve collaboration
from __future__ import annotations def bitonic_sort(array: list[int], reverse: bool = False) -> list[int]: n = len(array) if n <= 1: return array if not (n and not (n & (n - 1))): raise ValueError("the size of input should be power of two") left = bitonic_sort(array[: n // 2], True) ...
--- +++ @@ -1,8 +1,37 @@+""" +Bitonic Sort + +Bitonic sort is a comparison-based sorting algorithm designed for parallel +execution. This implementation is sequential. The input size must be a +power of two. + +Reference: https://en.wikipedia.org/wiki/Bitonic_sorter + +Complexity: + Time: O(n log^2 n) best / O(n ...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/sorting/bitonic_sort.py
Write docstrings for utility functions
from __future__ import annotations from collections import defaultdict, deque def topological_sort(vertices: int, edges: list[tuple[int, int]]) -> list[int]: graph: dict[int, list[int]] = defaultdict(list) in_degree = [0] * vertices for u, v in edges: graph[u].append(v) in_degree[v] +=...
--- +++ @@ -1,37 +1,65 @@- -from __future__ import annotations - -from collections import defaultdict, deque - - -def topological_sort(vertices: int, edges: list[tuple[int, int]]) -> list[int]: - graph: dict[int, list[int]] = defaultdict(list) - - in_degree = [0] * vertices - - for u, v in edges: - grap...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/graph/topological_sort_bfs.py
Document classes and their methods
from __future__ import annotations def sentinel_search(arr: list[int], target: int) -> int: n = len(arr) if n == 0: return -1 last = arr[-1] arr[-1] = target i = 0 while arr[i] != target: i += 1 arr[-1] = last if i < n - 1 or arr[-1] == target: return i ret...
--- +++ @@ -1,8 +1,21 @@+"""Sentinel linear search — a small optimisation over naive linear search. + +By placing the target at the end of the array (as a sentinel), we can +remove the bounds check from the inner loop, roughly halving comparisons. + +Time: O(n) — same asymptotic complexity but fewer comparisons in prac...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/searching/sentinel_search.py
Add clean documentation to messy code
from __future__ import annotations def bubble_sort(array: list[int]) -> list[int]: n = len(array) swapped = True passes = 0 while swapped: swapped = False for i in range(1, n - passes): if array[i - 1] > array[i]: array[i - 1], array[i] = array[i], array[i ...
--- +++ @@ -1,8 +1,32 @@+""" +Bubble Sort + +Bubble sort repeatedly steps through the list, compares adjacent elements +and swaps them if they are in the wrong order. + +Reference: https://en.wikipedia.org/wiki/Bubble_sort + +Complexity: + Time: O(n) best / O(n^2) average / O(n^2) worst + Space: O(1) +""" fro...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/sorting/bubble_sort.py
Help me add docstrings to my project
from __future__ import annotations import random def bogo_sort(array: list[int]) -> list[int]: while not _is_sorted(array): random.shuffle(array) return array def _is_sorted(array: list[int]) -> bool: return all( array[i] <= array[i + 1] for i in range(len(array) - 1) )
--- +++ @@ -1,3 +1,15 @@+""" +Bogo Sort + +Bogo sort repeatedly shuffles the array at random until it happens to be +sorted. It is extremely inefficient and used only for educational purposes. + +Reference: https://en.wikipedia.org/wiki/Bogosort + +Complexity: + Time: O(n) best / O(n * n!) average / O(infinity) wo...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/sorting/bogo_sort.py
Write docstrings describing each step
from __future__ import annotations def cocktail_shaker_sort(array: list[int]) -> list[int]: n = len(array) swapped = True while swapped: swapped = False for i in range(1, n): if array[i - 1] > array[i]: array[i - 1], array[i] = array[i], array[i - 1] ...
--- +++ @@ -1,8 +1,32 @@+""" +Cocktail Shaker Sort + +Cocktail shaker sort is a variation of bubble sort that traverses the +list alternately from left-to-right and right-to-left. + +Reference: https://en.wikipedia.org/wiki/Cocktail_shaker_sort + +Complexity: + Time: O(n) best / O(n^2) average / O(n^2) worst + S...
https://raw.githubusercontent.com/keon/algorithms/HEAD/algorithms/sorting/cocktail_shaker_sort.py