repo stringlengths 7 90 | file_url stringlengths 81 315 | file_path stringlengths 4 228 | content stringlengths 0 32.8k | language stringclasses 1
value | license stringclasses 7
values | commit_sha stringlengths 40 40 | retrieved_at stringdate 2026-01-04 14:38:15 2026-01-05 02:33:18 | truncated bool 2
classes |
|---|---|---|---|---|---|---|---|---|
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/perfect_square.py | maths/perfect_square.py | import math
def perfect_square(num: int) -> bool:
"""
Check if a number is perfect square number or not
:param num: the number to be checked
:return: True if number is square number, otherwise False
>>> perfect_square(9)
True
>>> perfect_square(16)
True
>>> perfect_square(1)
T... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/floor.py | maths/floor.py | """
https://en.wikipedia.org/wiki/Floor_and_ceiling_functions
"""
def floor(x: float) -> int:
"""
Return the floor of x as an Integral.
:param x: the number
:return: the largest integer <= x.
>>> import math
>>> all(floor(n) == math.floor(n) for n
... in (1, -1, 0, -0, 1.1, -1.1, 1.0, ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/pi_monte_carlo_estimation.py | maths/pi_monte_carlo_estimation.py | import random
class Point:
def __init__(self, x: float, y: float) -> None:
self.x = x
self.y = y
def is_in_unit_circle(self) -> bool:
"""
True, if the point lies in the unit circle
False, otherwise
"""
return (self.x**2 + self.y**2) <= 1
@classmeth... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/gamma.py | maths/gamma.py | """
Gamma function is a very useful tool in math and physics.
It helps calculating complex integral in a convenient way.
for more info: https://en.wikipedia.org/wiki/Gamma_function
In mathematics, the gamma function is one commonly
used extension of the factorial function to complex numbers.
The gamma function is defin... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/factors.py | maths/factors.py | from doctest import testmod
from math import sqrt
def factors_of_a_number(num: int) -> list:
"""
>>> factors_of_a_number(1)
[1]
>>> factors_of_a_number(5)
[1, 5]
>>> factors_of_a_number(24)
[1, 2, 3, 4, 6, 8, 12, 24]
>>> factors_of_a_number(-24)
[]
"""
facs: list[int] = []
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/check_polygon.py | maths/check_polygon.py | from __future__ import annotations
def check_polygon(nums: list[float]) -> bool:
"""
Takes list of possible side lengths and determines whether a
two-dimensional polygon with such side lengths can exist.
Returns a boolean value for the < comparison
of the largest side length with sum of the rest.... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/volume.py | maths/volume.py | """
Find the volume of various shapes.
* https://en.wikipedia.org/wiki/Volume
* https://en.wikipedia.org/wiki/Spherical_cap
"""
from __future__ import annotations
from math import pi, pow # noqa: A004
def vol_cube(side_length: float) -> float:
"""
Calculate the Volume of a Cube.
>>> vol_cube(1)
1... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/triplet_sum.py | maths/triplet_sum.py | """
Given an array of integers and another integer target,
we are required to find a triplet from the array such that it's sum is equal to
the target.
"""
from __future__ import annotations
from itertools import permutations
from random import randint
from timeit import repeat
def make_dataset() -> tuple[list[int],... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/euler_modified.py | maths/euler_modified.py | from collections.abc import Callable
import numpy as np
def euler_modified(
ode_func: Callable, y0: float, x0: float, step_size: float, x_end: float
) -> np.ndarray:
"""
Calculate solution at each step to an ODE using Euler's Modified Method
The Euler Method is straightforward to implement, but can't... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/perfect_cube.py | maths/perfect_cube.py | def perfect_cube(n: int) -> bool:
"""
Check if a number is a perfect cube or not.
>>> perfect_cube(27)
True
>>> perfect_cube(4)
False
"""
val = n ** (1 / 3)
return (val * val * val) == n
def perfect_cube_binary_search(n: int) -> bool:
"""
Check if a number is a perfect cub... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/trapezoidal_rule.py | maths/trapezoidal_rule.py | """
Numerical integration or quadrature for a smooth function f with known values at x_i
"""
def trapezoidal_rule(boundary, steps):
"""
Implements the extended trapezoidal rule for numerical integration.
The function f(x) is provided below.
:param boundary: List containing the lower and upper bounds ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/geometric_mean.py | maths/geometric_mean.py | """
The Geometric Mean of n numbers is defined as the n-th root of the product
of those numbers. It is used to measure the central tendency of the numbers.
https://en.wikipedia.org/wiki/Geometric_mean
"""
def compute_geometric_mean(*args: int) -> float:
"""
Return the geometric mean of the argument numbers.
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/prime_check.py | maths/prime_check.py | """Prime Check."""
import math
import unittest
import pytest
def is_prime(number: int) -> bool:
"""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)
False
>>> is_prime(1)
False
>>> is_prime(2)
True
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/matrix_exponentiation.py | maths/matrix_exponentiation.py | """Matrix Exponentiation"""
import timeit
"""
Matrix Exponentiation is a technique to solve linear recurrences in logarithmic time.
You read more about it here:
https://zobayer.blogspot.com/2010/11/matrix-exponentiation.html
https://www.hackerearth.com/practice/notes/matrix-exponentiation-1/
"""
class Matrix:
d... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/entropy.py | maths/entropy.py | #!/usr/bin/env python3
"""
Implementation of entropy of information
https://en.wikipedia.org/wiki/Entropy_(information_theory)
"""
from __future__ import annotations
import math
from collections import Counter
from string import ascii_lowercase
def calculate_prob(text: str) -> None:
"""
This method takes p... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/hardy_ramanujanalgo.py | maths/hardy_ramanujanalgo.py | # This theorem states that the number of prime factors of n
# will be approximately log(log(n)) for most natural numbers n
import math
def exact_prime_factor_count(n: int) -> int:
"""
>>> exact_prime_factor_count(51242183)
3
"""
count = 0
if n % 2 == 0:
count += 1
while n % 2 ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/euler_method.py | maths/euler_method.py | from collections.abc import Callable
import numpy as np
def explicit_euler(
ode_func: Callable, y0: float, x0: float, step_size: float, x_end: float
) -> np.ndarray:
"""Calculate numeric solution at each step to an ODE using Euler's Method
For reference to Euler's method refer to https://en.wikipedia.or... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/prime_sieve_eratosthenes.py | maths/prime_sieve_eratosthenes.py | """
Sieve of Eratosthenes
Input: n = 10
Output: 2 3 5 7
Input: n = 20
Output: 2 3 5 7 11 13 17 19
you can read in detail about this at
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""
def prime_sieve_eratosthenes(num: int) -> list[int]:
"""
Print the prime numbers up to n
>>> prime_sieve_eratos... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/solovay_strassen_primality_test.py | maths/solovay_strassen_primality_test.py | """
This script implements the Solovay-Strassen Primality test.
This probabilistic primality test is based on Euler's criterion. It is similar
to the Fermat test but uses quadratic residues. It can quickly identify
composite numbers but may occasionally classify composite numbers as prime.
More details and concepts a... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/perfect_number.py | maths/perfect_number.py | """
== Perfect Number ==
In number theory, a perfect number is a positive integer that is equal to the sum of
its positive divisors, excluding the number itself.
For example: 6 ==> divisors[1, 2, 3, 6]
Excluding 6, the sum(divisors) is 1 + 2 + 3 = 6
So, 6 is a Perfect Number
Other examples of Perfect Numbers: ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/binary_multiplication.py | maths/binary_multiplication.py | """
Binary Multiplication
This is a method to find a*b in a time complexity of O(log b)
This is one of the most commonly used methods of finding result of multiplication.
Also useful in cases where solution to (a*b)%c is required,
where a,b,c can be numbers over the computers calculation limits.
Done using iteration, c... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/sum_of_harmonic_series.py | maths/sum_of_harmonic_series.py | def sum_of_harmonic_progression(
first_term: float, common_difference: float, number_of_terms: int
) -> float:
"""
https://en.wikipedia.org/wiki/Harmonic_progression_(mathematics)
Find the sum of n terms in an harmonic progression. The calculation starts with the
first_term and loops adding the co... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/jaccard_similarity.py | maths/jaccard_similarity.py | """
The Jaccard similarity coefficient is a commonly used indicator of the
similarity between two sets. Let U be a set and A and B be subsets of U,
then the Jaccard index/similarity is defined to be the ratio of the number
of elements of their intersection and the number of elements of their union.
Inspired from Wikip... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/dual_number_automatic_differentiation.py | maths/dual_number_automatic_differentiation.py | from math import factorial
"""
https://en.wikipedia.org/wiki/Automatic_differentiation#Automatic_differentiation_using_dual_numbers
https://blog.jliszka.org/2013/10/24/exact-numeric-nth-derivatives.html
Note this only works for basic functions, f(x) where the power of x is positive.
"""
class Dual:
def __init__... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/power_using_recursion.py | maths/power_using_recursion.py | """
== Raise base to the power of exponent using recursion ==
Input -->
Enter the base: 3
Enter the exponent: 4
Output -->
3 to the power of 4 is 81
Input -->
Enter the base: 2
Enter the exponent: 0
Output -->
2 to the power of 0 is 1
"""
def power(base... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/interquartile_range.py | maths/interquartile_range.py | """
An implementation of interquartile range (IQR) which is a measure of statistical
dispersion, which is the spread of the data.
The function takes the list of numeric values as input and returns the IQR.
Script inspired by this Wikipedia article:
https://en.wikipedia.org/wiki/Interquartile_range
"""
from __future_... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/number_of_digits.py | maths/number_of_digits.py | import math
from timeit import timeit
def num_digits(n: int) -> int:
"""
Find the number of digits in a number.
>>> num_digits(12345)
5
>>> num_digits(123)
3
>>> num_digits(0)
1
>>> num_digits(-1)
1
>>> num_digits(-123456)
6
>>> num_digits('123') # Raises a TypeEr... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/test_factorial.py | maths/test_factorial.py | # /// script
# requires-python = ">=3.13"
# dependencies = [
# "pytest",
# ]
# ///
import pytest
from maths.factorial import factorial, factorial_recursive
@pytest.mark.parametrize("function", [factorial, factorial_recursive])
def test_zero(function):
assert function(0) == 1
@pytest.mark.parametrize("func... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/sigmoid.py | maths/sigmoid.py | """
This script demonstrates the implementation of the Sigmoid function.
The function takes a vector of K real numbers as input and then 1 / (1 + exp(-x)).
After through Sigmoid, the element of the vector mostly 0 between 1. or 1 between -1.
Script inspired from its corresponding Wikipedia article
https://en.wikipedi... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/binary_exponentiation.py | maths/binary_exponentiation.py | """
Binary Exponentiation
This is a method to find a^b in O(log b) time complexity and is one of the most commonly
used methods of exponentiation. The method is also useful for modular exponentiation,
when the solution to (a^b) % c is required.
To calculate a^b:
- If b is even, then a^b = (a * a)^(b / 2)
- If b is od... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/polynomial_evaluation.py | maths/polynomial_evaluation.py | from collections.abc import Sequence
def evaluate_poly(poly: Sequence[float], x: float) -> float:
"""Evaluate a polynomial f(x) at specified point x and return the value.
Arguments:
poly -- the coefficients of a polynomial as an iterable in order of
ascending degree
x -- the point at whic... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/pythagoras.py | maths/pythagoras.py | """Uses Pythagoras theorem to calculate the distance between two points in space."""
import math
class Point:
def __init__(self, x, y, z):
self.x = x
self.y = y
self.z = z
def __repr__(self) -> str:
return f"Point({self.x}, {self.y}, {self.z})"
def distance(a: Point, b: Poi... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/fibonacci.py | maths/fibonacci.py | """
Calculates the Fibonacci sequence using iteration, recursion, memoization,
and a simplified form of Binet's formula
NOTE 1: the iterative, recursive, memoization functions are more accurate than
the Binet's formula function because the Binet formula function uses floats
NOTE 2: the Binet's formula function is mu... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/euclidean_distance.py | maths/euclidean_distance.py | from __future__ import annotations
import typing
from collections.abc import Iterable
import numpy as np
Vector = typing.Union[Iterable[float], Iterable[int], np.ndarray] # noqa: UP007
VectorOut = typing.Union[np.float64, int, float] # noqa: UP007
def euclidean_distance(vector_1: Vector, vector_2: Vector) -> Vec... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/points_are_collinear_3d.py | maths/points_are_collinear_3d.py | """
Check if three points are collinear in 3D.
In short, the idea is that we are able to create a triangle using three points,
and the area of that triangle can determine if the three points are collinear or not.
First, we create two vectors with the same initial point from the three points,
then we will calculate t... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/continued_fraction.py | maths/continued_fraction.py | """
Finding the continuous fraction for a rational number using python
https://en.wikipedia.org/wiki/Continued_fraction
"""
from fractions import Fraction
from math import floor
def continued_fraction(num: Fraction) -> list[int]:
"""
:param num:
Fraction of the number whose continued fractions to be fou... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/line_length.py | maths/line_length.py | from __future__ import annotations
import math
from collections.abc import Callable
def line_length(
fnc: Callable[[float], float],
x_start: float,
x_end: float,
steps: int = 100,
) -> float:
"""
Approximates the arc length of a line segment by treating the curve as a
sequence of linear l... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/softmax.py | maths/softmax.py | """
This script demonstrates the implementation of the Softmax function.
Its a function that takes as input a vector of K real numbers, and normalizes
it into a probability distribution consisting of K probabilities proportional
to the exponentials of the input numbers. After softmax, the elements of the
vector always... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/germain_primes.py | maths/germain_primes.py | """
A Sophie Germain prime is any prime p, where 2p + 1 is also prime.
The second number, 2p + 1 is called a safe prime.
Examples of Germain primes include: 2, 3, 5, 11, 23
Their corresponding safe primes: 5, 7, 11, 23, 47
https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes
"""
from maths.prime_check import... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/minkowski_distance.py | maths/minkowski_distance.py | def minkowski_distance(
point_a: list[float],
point_b: list[float],
order: int,
) -> float:
"""
This function calculates the Minkowski distance for a given order between
two n-dimensional points represented as lists. For the case of order = 1,
the Minkowski distance degenerates to the Manhat... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/basic_maths.py | maths/basic_maths.py | """Implementation of Basic Math in Python."""
import math
def prime_factors(n: int) -> list:
"""Find Prime Factors.
>>> prime_factors(100)
[2, 2, 5, 5]
>>> prime_factors(0)
Traceback (most recent call last):
...
ValueError: Only positive integers have prime factors
>>> prime_facto... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/sum_of_geometric_progression.py | maths/sum_of_geometric_progression.py | def sum_of_geometric_progression(
first_term: int, common_ratio: int, num_of_terms: int
) -> float:
""" "
Return the sum of n terms in a geometric progression.
>>> sum_of_geometric_progression(1, 2, 10)
1023.0
>>> sum_of_geometric_progression(1, 10, 5)
11111.0
>>> sum_of_geometric_progre... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/prime_numbers.py | maths/prime_numbers.py | import math
from collections.abc import Generator
def slow_primes(max_n: int) -> Generator[int]:
"""
Return a list of all primes numbers up to max.
>>> list(slow_primes(0))
[]
>>> list(slow_primes(-1))
[]
>>> list(slow_primes(-10))
[]
>>> list(slow_primes(25))
[2, 3, 5, 7, 11, ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/segmented_sieve.py | maths/segmented_sieve.py | """Segmented Sieve."""
import math
def sieve(n: int) -> list[int]:
"""
Segmented Sieve.
Examples:
>>> sieve(8)
[2, 3, 5, 7]
>>> sieve(27)
[2, 3, 5, 7, 11, 13, 17, 19, 23]
>>> sieve(0)
Traceback (most recent call last):
...
ValueError: Number 0 must instead be a posi... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/print_multiplication_table.py | maths/print_multiplication_table.py | def multiplication_table(number: int, number_of_terms: int) -> str:
"""
Prints the multiplication table of a given number till the given number of terms
>>> print(multiplication_table(3, 5))
3 * 1 = 3
3 * 2 = 6
3 * 3 = 9
3 * 4 = 12
3 * 5 = 15
>>> print(multiplication_table(-4, 6))
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/fermat_little_theorem.py | maths/fermat_little_theorem.py | # Python program to show the usage of Fermat's little theorem in a division
# According to Fermat's little theorem, (a / b) mod p always equals
# a * (b ^ (p - 2)) mod p
# Here we assume that p is a prime number, b divides a, and p doesn't divide b
# Wikipedia reference: https://en.wikipedia.org/wiki/Fermat%27s_little_... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/area.py | maths/area.py | """
Find the area of various geometric shapes
Wikipedia reference: https://en.wikipedia.org/wiki/Area
"""
from math import pi, sqrt, tan
def surface_area_cube(side_length: float) -> float:
"""
Calculate the Surface Area of a Cube.
>>> surface_area_cube(1)
6
>>> surface_area_cube(1.6)
15.3600... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/extended_euclidean_algorithm.py | maths/extended_euclidean_algorithm.py | """
Extended Euclidean Algorithm.
Finds 2 numbers a and b such that it satisfies
the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)
https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
"""
# @Author: S. Sharma <silentcat>
# @Date: 2019-02-25T12:08:53-06:00
# @Email: silentcat@protonmail.com
# @Last ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/dodecahedron.py | maths/dodecahedron.py | # dodecahedron.py
"""
A regular dodecahedron is a three-dimensional figure made up of
12 pentagon faces having the same equal size.
"""
def dodecahedron_surface_area(edge: float) -> float:
"""
Calculates the surface area of a regular dodecahedron
a = 3 * ((25 + 10 * (5** (1 / 2))) ** (1 / 2 )) * (e**2)
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/tanh.py | maths/tanh.py | """
This script demonstrates the implementation of the tangent hyperbolic
or tanh function.
The function takes a vector of K real numbers as input and
then (e^x - e^(-x))/(e^x + e^(-x)). After through tanh, the
element of the vector mostly -1 between 1.
Script inspired from its corresponding Wikipedia article
https:/... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/three_sum.py | maths/three_sum.py | """
https://en.wikipedia.org/wiki/3SUM
"""
def three_sum(nums: list[int]) -> list[list[int]]:
"""
Find all unique triplets in a sorted array of integers that sum up to zero.
Args:
nums: A sorted list of integers.
Returns:
A list of lists containing unique triplets that sum up to zero... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/simultaneous_linear_equation_solver.py | maths/simultaneous_linear_equation_solver.py | """
https://en.wikipedia.org/wiki/Augmented_matrix
This algorithm solves simultaneous linear equations of the form
λa + λb + λc + λd + ... = y as [λ, λ, λ, λ, ..., y]
Where λ & y are individual coefficients, the no. of equations = no. of coefficients - 1
Note in order to work there must exist 1 equation where all ins... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/monte_carlo.py | maths/monte_carlo.py | """
@author: MatteoRaso
"""
from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean
def pi_estimator(iterations: int) -> None:
"""
An implementation of the Monte Carlo method used to find pi.
1. Draw a 2x2 square centred at (0,0).
2. Inscr... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/qr_decomposition.py | maths/qr_decomposition.py | import numpy as np
def qr_householder(a: np.ndarray):
"""Return a QR-decomposition of the matrix A using Householder reflection.
The QR-decomposition decomposes the matrix A of shape (m, n) into an
orthogonal matrix Q of shape (m, m) and an upper triangular matrix R of
shape (m, n). Note that the ma... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/joint_probability_distribution.py | maths/joint_probability_distribution.py | """
Calculate joint probability distribution
https://en.wikipedia.org/wiki/Joint_probability_distribution
"""
def joint_probability_distribution(
x_values: list[int],
y_values: list[int],
x_probabilities: list[float],
y_probabilities: list[float],
) -> dict:
"""
>>> joint_distribution = joint... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/is_square_free.py | maths/is_square_free.py | """
References: wikipedia:square free number
psf/black : True
ruff : True
"""
from __future__ import annotations
def is_square_free(factors: list[int]) -> bool:
"""
# doctest: +NORMALIZE_WHITESPACE
This functions takes a list of prime factors as input.
returns True if the factors are square free.
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/monte_carlo_dice.py | maths/monte_carlo_dice.py | from __future__ import annotations
import random
class Dice:
NUM_SIDES = 6
def __init__(self):
"""Initialize a six sided dice"""
self.sides = list(range(1, Dice.NUM_SIDES + 1))
def roll(self):
return random.choice(self.sides)
def throw_dice(num_throws: int, num_dice: int = 2) ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/sum_of_digits.py | maths/sum_of_digits.py | def sum_of_digits(n: int) -> int:
"""
Find the sum of digits of a number.
>>> sum_of_digits(12345)
15
>>> sum_of_digits(123)
6
>>> sum_of_digits(-123)
6
>>> sum_of_digits(0)
0
"""
n = abs(n)
res = 0
while n > 0:
res += n % 10
n //= 10
return re... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/twin_prime.py | maths/twin_prime.py | """
== Twin Prime ==
A number n+2 is said to be a Twin prime of number n if
both n and n+2 are prime.
Examples of Twin pairs: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), ...
https://en.wikipedia.org/wiki/Twin_prime
"""
# Author : Akshay Dubey (https://github.com/itsAkshayDubey)
from maths.prime_check impo... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/integer_square_root.py | maths/integer_square_root.py | """
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
approach to find the integer square root without using any built-in exponent functions
or operators.
* https://en.wikipedia.org/wiki/Integer_... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/liouville_lambda.py | maths/liouville_lambda.py | """
== Liouville Lambda Function ==
The Liouville Lambda function, denoted by λ(n)
and λ(n) is 1 if n is the product of an even number of prime numbers,
and -1 if it is the product of an odd number of primes.
https://en.wikipedia.org/wiki/Liouville_function
"""
# Author : Akshay Dubey (https://github.com/itsAkshayDub... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/josephus_problem.py | maths/josephus_problem.py | """
The Josephus problem is a famous theoretical problem related to a certain
counting-out game. This module provides functions to solve the Josephus problem
for num_people and a step_size.
The Josephus problem is defined as follows:
- num_people are standing in a circle.
- Starting with a specified person, you count ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/two_sum.py | maths/two_sum.py | """
Given an array of integers, return indices of the two numbers such that they add up to
a specific target.
You may assume that each input would have exactly one solution, and you may not use the
same element twice.
Example:
Given nums = [2, 7, 11, 15], target = 9,
Because nums[0] + nums[1] = 2 + 7 = 9,
return [0,... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/eulers_totient.py | maths/eulers_totient.py | # Eulers Totient function finds the number of relative primes of a number n from 1 to n
def totient(n: int) -> list:
"""
>>> n = 10
>>> totient_calculation = totient(n)
>>> for i in range(1, n):
... print(f"{i} has {totient_calculation[i]} relative primes.")
1 has 0 relative primes.
2 ha... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/odd_sieve.py | maths/odd_sieve.py | from itertools import compress, repeat
from math import ceil, sqrt
def odd_sieve(num: int) -> list[int]:
"""
Returns the prime numbers < `num`. The prime numbers are calculated using an
odd sieve implementation of the Sieve of Eratosthenes algorithm
(see for reference https://en.wikipedia.org/wiki/Sie... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/bailey_borwein_plouffe.py | maths/bailey_borwein_plouffe.py | def bailey_borwein_plouffe(digit_position: int, precision: int = 1000) -> str:
"""
Implement a popular pi-digit-extraction algorithm known as the
Bailey-Borwein-Plouffe (BBP) formula to calculate the nth hex digit of pi.
Wikipedia page:
https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Pl... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/least_common_multiple.py | maths/least_common_multiple.py | import unittest
from timeit import timeit
from maths.greatest_common_divisor import greatest_common_divisor
def least_common_multiple_slow(first_num: int, second_num: int) -> int:
"""
Find the least common multiple of two numbers.
Learn more: https://en.wikipedia.org/wiki/Least_common_multiple
>>> ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/mobius_function.py | maths/mobius_function.py | """
References: https://en.wikipedia.org/wiki/M%C3%B6bius_function
References: wikipedia:square free number
psf/black : True
ruff : True
"""
from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors
def mobius(n: int) -> int:
"""
Mobius function
>>> mobius(24)
0
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/ceil.py | maths/ceil.py | """
https://en.wikipedia.org/wiki/Floor_and_ceiling_functions
"""
def ceil(x: float) -> int:
"""
Return the ceiling of x as an Integral.
:param x: the number
:return: the smallest integer >= x.
>>> import math
>>> all(ceil(n) == math.ceil(n) for n
... in (1, -1, 0, -0, 1.1, -1.1, 1.0... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/base_neg2_conversion.py | maths/base_neg2_conversion.py | def decimal_to_negative_base_2(num: int) -> int:
"""
This function returns the number negative base 2
of the decimal number of the input data.
Args:
int: The decimal number to convert.
Returns:
int: The negative base 2 number.
Examples:
>>> decimal_to_negative_base... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/gcd_of_n_numbers.py | maths/gcd_of_n_numbers.py | """
Gcd of N Numbers
Reference: https://en.wikipedia.org/wiki/Greatest_common_divisor
"""
from collections import Counter
def get_factors(
number: int, factors: Counter | None = None, factor: int = 2
) -> Counter:
"""
this is a recursive function for get all factors of number
>>> get_factors(45)
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/factorial.py | maths/factorial.py | """
Factorial of a positive integer -- https://en.wikipedia.org/wiki/Factorial
"""
def factorial(number: int) -> int:
"""
Calculate the factorial of specified number (n!).
>>> import math
>>> all(factorial(i) == math.factorial(i) for i in range(20))
True
>>> factorial(0.1)
Traceback (most... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/find_max.py | maths/find_max.py | from __future__ import annotations
def find_max_iterative(nums: list[int | float]) -> int | float:
"""
>>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
... find_max_iterative(nums) == max(nums)
True
True
True
True
>>> find_max_iterative([2, 4, 9, 7, 19, 94, 5... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/area_under_curve.py | maths/area_under_curve.py | """
Approximates the area under the curve using the trapezoidal rule
"""
from __future__ import annotations
from collections.abc import Callable
def trapezoidal_area(
fnc: Callable[[float], float],
x_start: float,
x_end: float,
steps: int = 100,
) -> float:
"""
Treats curve as a collection o... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/spearman_rank_correlation_coefficient.py | maths/spearman_rank_correlation_coefficient.py | from collections.abc import Sequence
def assign_ranks(data: Sequence[float]) -> list[int]:
"""
Assigns ranks to elements in the array.
:param data: List of floats.
:return: List of ints representing the ranks.
Example:
>>> assign_ranks([3.2, 1.5, 4.0, 2.7, 5.1])
[3, 1, 4, 2, 5]
>>> ... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/manhattan_distance.py | maths/manhattan_distance.py | def manhattan_distance(point_a: list, point_b: list) -> float:
"""
Expectts two list of numbers representing two points in the same
n-dimensional space
https://en.wikipedia.org/wiki/Taxicab_geometry
>>> manhattan_distance([1,1], [2,2])
2.0
>>> manhattan_distance([1.5,1.5], [2,2])
1.0
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/remove_digit.py | maths/remove_digit.py | def remove_digit(num: int) -> int:
"""
returns the biggest possible result
that can be achieved by removing
one digit from the given number
>>> remove_digit(152)
52
>>> remove_digit(6385)
685
>>> remove_digit(-11)
1
>>> remove_digit(2222222)
222222
>>> remove_digit(... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/sumset.py | maths/sumset.py | """
Calculates the SumSet of two sets of numbers (A and B)
Source:
https://en.wikipedia.org/wiki/Sumset
"""
def sumset(set_a: set, set_b: set) -> set:
"""
:param first set: a set of numbers
:param second set: a set of numbers
:return: the nth number in Sylvester's sequence
>>> sumset({1, 2... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/sieve_of_eratosthenes.py | maths/sieve_of_eratosthenes.py | """
Sieve of Eratosthones
The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or
equal to a given value.
Illustration:
https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif
Reference: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
doctest provider: Br... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/binomial_distribution.py | maths/binomial_distribution.py | """For more information about the Binomial Distribution -
https://en.wikipedia.org/wiki/Binomial_distribution"""
from math import factorial
def binomial_distribution(successes: int, trials: int, prob: float) -> float:
"""
Return probability of k successes out of n tries, with p probability for one
succes... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/average_median.py | maths/average_median.py | from __future__ import annotations
def median(nums: list) -> int | float:
"""
Find median of a list of numbers.
Wiki: https://en.wikipedia.org/wiki/Median
>>> median([0])
0
>>> median([4, 1, 3, 2])
2.5
>>> median([2, 70, 6, 50, 20, 8, 4])
8
Args:
nums: List of nums
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/find_min.py | maths/find_min.py | from __future__ import annotations
def find_min_iterative(nums: list[int | float]) -> int | float:
"""
Find Minimum Number in a List
:param nums: contains elements
:return: min number in list
>>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
... find_min_iterative(nu... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/gaussian.py | maths/gaussian.py | """
Reference: https://en.wikipedia.org/wiki/Gaussian_function
"""
from numpy import exp, pi, sqrt
def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> float:
"""
>>> float(gaussian(1))
0.24197072451914337
>>> float(gaussian(24))
3.342714441794458e-126
>>> float(gaussian(1, 4, 2))
0.... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/kth_lexicographic_permutation.py | maths/kth_lexicographic_permutation.py | def kth_permutation(k, n):
"""
Finds k'th lexicographic permutation (in increasing order) of
0,1,2,...n-1 in O(n^2) time.
Examples:
First permutation is always 0,1,2,...n
>>> kth_permutation(0,5)
[0, 1, 2, 3, 4]
The order of permutation of 0,1,2,3 is [0,1,2,3], [0,1,3,2], [0,2,1,3],
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/primelib.py | maths/primelib.py | """
Created on Thu Oct 5 16:44:23 2017
@author: Christian Bender
This Python library contains some useful functions to deal with
prime numbers and whole numbers.
Overview:
is_prime(number)
sieve_er(N)
get_prime_numbers(N)
prime_factorization(number)
greatest_prime_factor(number)
smallest_prime_factor(number)
get_p... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/persistence.py | maths/persistence.py | def multiplicative_persistence(num: int) -> int:
"""
Return the persistence of a given number.
https://en.wikipedia.org/wiki/Persistence_of_a_number
>>> multiplicative_persistence(217)
2
>>> multiplicative_persistence(-1)
Traceback (most recent call last):
...
ValueError: multi... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/average_mode.py | maths/average_mode.py | from typing import Any
def mode(input_list: list) -> list[Any]:
"""This function returns the mode(Mode as in the measures of
central tendency) of the input data.
The input list may contain any Datastructure or any Datatype.
>>> mode([2, 3, 4, 5, 3, 4, 2, 5, 2, 2, 4, 2, 2, 2])
[2]
>>> mode([3... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/collatz_sequence.py | maths/collatz_sequence.py | """
The Collatz conjecture is a famous unsolved problem in mathematics. Given a starting
positive integer, define the following sequence:
- If the current term n is even, then the next term is n/2.
- If the current term n is odd, then the next term is 3n + 1.
The conjecture claims that this sequence will always reach 1... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/average_absolute_deviation.py | maths/average_absolute_deviation.py | def average_absolute_deviation(nums: list[int]) -> float:
"""
Return the average absolute deviation of a list of numbers.
Wiki: https://en.wikipedia.org/wiki/Average_absolute_deviation
>>> average_absolute_deviation([0])
0.0
>>> average_absolute_deviation([4, 1, 3, 2])
1.0
>>> average_a... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/is_int_palindrome.py | maths/is_int_palindrome.py | def is_int_palindrome(num: int) -> bool:
"""
Returns whether `num` is a palindrome or not
(see for reference https://en.wikipedia.org/wiki/Palindromic_number).
>>> is_int_palindrome(-121)
False
>>> is_int_palindrome(0)
True
>>> is_int_palindrome(10)
False
>>> is_int_palindrome(1... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/zellers_congruence.py | maths/zellers_congruence.py | import argparse
import datetime
def zeller(date_input: str) -> str:
"""
| Zellers Congruence Algorithm
| Find the day of the week for nearly any Gregorian or Julian calendar date
>>> zeller('01-31-2010')
'Your date 01-31-2010, is a Sunday!'
Validate out of range month:
>>> zeller('13-31... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/prime_factors.py | maths/prime_factors.py | """
python/black : True
"""
from __future__ import annotations
def prime_factors(n: int) -> list[int]:
"""
Returns prime factors of n as a list.
>>> prime_factors(0)
[]
>>> prime_factors(100)
[2, 2, 5, 5]
>>> prime_factors(2560)
[2, 2, 2, 2, 2, 2, 2, 2, 2, 5]
>>> prime_factors(10... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/signum.py | maths/signum.py | """
Signum function -- https://en.wikipedia.org/wiki/Sign_function
"""
def signum(num: float) -> int:
"""
Applies signum function on the number
Custom test cases:
>>> signum(-10)
-1
>>> signum(10)
1
>>> signum(0)
0
>>> signum(-20.5)
-1
>>> signum(20.5)
1
>>> si... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/average_mean.py | maths/average_mean.py | from __future__ import annotations
def mean(nums: list) -> float:
"""
Find mean of a list of numbers.
Wiki: https://en.wikipedia.org/wiki/Mean
>>> mean([3, 6, 9, 12, 15, 18, 21])
12.0
>>> mean([5, 10, 15, 20, 25, 30, 35])
20.0
>>> mean([1, 2, 3, 4, 5, 6, 7, 8])
4.5
>>> mean([]... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/modular_division.py | maths/modular_division.py | from __future__ import annotations
def modular_division(a: int, b: int, n: int) -> int:
"""
Modular Division :
An efficient algorithm for dividing b by a modulo n.
GCD ( Greatest Common Divisor ) or HCF ( Highest Common Factor )
Given three integers a, b, and n, such that gcd(a,n)=1 and n>1, the... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/sylvester_sequence.py | maths/sylvester_sequence.py | """
Calculates the nth number in Sylvester's sequence
Source:
https://en.wikipedia.org/wiki/Sylvester%27s_sequence
"""
def sylvester(number: int) -> int:
"""
:param number: nth number to calculate in the sequence
:return: the nth number in Sylvester's sequence
>>> sylvester(8)
113423713055... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/modular_exponential.py | maths/modular_exponential.py | """
Modular Exponential.
Modular exponentiation is a type of exponentiation performed over a modulus.
For more explanation, please check
https://en.wikipedia.org/wiki/Modular_exponentiation
"""
"""Calculate Modular Exponential."""
def modular_exponential(base: int, power: int, mod: int):
"""
>>> modular_expo... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/lucas_lehmer_primality_test.py | maths/lucas_lehmer_primality_test.py | """
In mathematics, the Lucas-Lehmer test (LLT) is a primality test for Mersenne
numbers. https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test
A Mersenne number is a number that is one less than a power of two.
That is M_p = 2^p - 1
https://en.wikipedia.org/wiki/Mersenne_prime
The Lucas-Lehmer test is t... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/largest_of_very_large_numbers.py | maths/largest_of_very_large_numbers.py | # Author: Abhijeeth S
import math
def res(x, y):
"""
Reduces large number to a more manageable number
>>> res(5, 7)
4.892790030352132
>>> res(0, 5)
0
>>> res(3, 0)
1
>>> res(-1, 5)
Traceback (most recent call last):
...
ValueError: expected a positive input
"""
... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/maths/chudnovsky_algorithm.py | maths/chudnovsky_algorithm.py | from decimal import Decimal, getcontext
from math import ceil, factorial
def pi(precision: int) -> str:
"""
The Chudnovsky algorithm is a fast method for calculating the digits of PI,
based on Ramanujan's PI formulae.
https://en.wikipedia.org/wiki/Chudnovsky_algorithm
PI = constant_term / ((mult... | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
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