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Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\basic_orbital_capture.py
python
Python
""" These two functions will return the radii of impact for a target object of mass M and radius R as well as it's effective cross sectional area sigma. That is to say any projectile with velocity v passing within sigma, will impact the target object with mass M. The derivation of which is given at the bottom of this f...
5,702
178
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\casimir_effect.py
python
Python
""" Title : Finding the value of magnitude of either the Casimir force, the surface area of one of the plates or distance between the plates provided that the other two parameters are given. Description : In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined...
4,753
121
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\center_of_mass.py
python
Python
""" Calculating the center of mass for a discrete system of particles, given their positions and masses. Description: In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position ...
3,556
111
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\centripetal_force.py
python
Python
""" Description : Centripetal force is the force acting on an object in curvilinear motion directed towards the axis of rotation or centre of curvature. The unit of centripetal force is newton. The centripetal force is always directed perpendicular to the direction of the object's displacement. Using Newton's second ...
1,726
50
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\coulombs_law.py
python
Python
""" Coulomb's law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. F = k * q1 * q2 / r^2 k is Coulomb's constant and equa...
1,213
43
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\doppler_frequency.py
python
Python
""" Doppler's effect The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The Doppler effect is named after the physicist Christian Doppler. A common example of Doppler shift is the change of pitch heard when a v...
4,574
105
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\escape_velocity.py
python
Python
import math def escape_velocity(mass: float, radius: float) -> float: """ Calculates the escape velocity needed to break free from a celestial body's gravitational field. The formula used is: v = sqrt(2 * G * M / R) where: v = escape velocity (m/s) G = gravitational const...
2,129
68
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\grahams_law.py
python
Python
""" Title: Graham's Law of Effusion Description: Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of the molar mass of its particles: r1/r2 = sqrt(m2/m1) r1 = Rate of effusion for the first gas. r2 = Rate of effusion for the second gas. m1 = Molar mass o...
7,177
209
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\horizontal_projectile_motion.py
python
Python
""" Horizontal Projectile Motion problem in physics. This algorithm solves a specific problem in which the motion starts from the ground as can be seen below:: (v = 0) * * * * * * * * * ...
4,546
167
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\hubble_parameter.py
python
Python
""" Title : Calculating the Hubble Parameter Description : The Hubble parameter H is the Universe expansion rate in any time. In cosmology is customary to use the redshift redshift in place of time, becausethe redshift is directily mensure in the light of galaxies moving away from us. So, the general relation that we...
3,426
110
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\ideal_gas_law.py
python
Python
""" The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empir...
3,148
94
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\in_static_equilibrium.py
python
Python
""" Checks if a system of forces is in static equilibrium. """ from __future__ import annotations from numpy import array, cos, cross, float64, radians, sin from numpy.typing import NDArray def polar_force( magnitude: float, angle: float, radian_mode: bool = False ) -> list[float]: """ Resolves force al...
2,709
96
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\kinetic_energy.py
python
Python
""" Find the kinetic energy of an object, given its mass and velocity. Description : In physics, the kinetic energy of an object is the energy that it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.Having gained this energy during its ...
1,750
51
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\lens_formulae.py
python
Python
""" This module has functions which calculate focal length of lens, distance of image from the lens and distance of object from the lens. The above is calculated using the lens formula. In optics, the relationship between the distance of the image (v), the distance of the object (u), and the focal length (f) of the le...
4,755
132
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\lorentz_transformation_four_vector.py
python
Python
""" Lorentz transformations describe the transition between two inertial reference frames F and F', each of which is moving in some direction with respect to the other. This code only calculates Lorentz transformations for movement in the x direction with no spatial rotation (i.e., a Lorentz boost in the x direction). ...
6,608
190
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\malus_law.py
python
Python
import math """ Finding the intensity of light transmitted through a polariser using Malus Law and by taking initial intensity and angle between polariser and axis as input Description : Malus's law, which is named after Étienne-Louis Malus, says that when a perfect polarizer is placed in a polarized beam of light, t...
3,506
81
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\mass_energy_equivalence.py
python
Python
""" Title: Finding the energy equivalence of mass and mass equivalence of energy by Einstein's equation. Description: Einstein's mass-energy equivalence is a pivotal concept in theoretical physics. It asserts that energy (E) and mass (m) are directly related by the speed of light in vacuum (c) squared, as described in...
2,189
78
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\mirror_formulae.py
python
Python
""" This module contains the functions to calculate the focal length, object distance and image distance of a mirror. The mirror formula is an equation that relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror. It is commonly used in optics to determine the position and chara...
5,119
128
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\n_body_simulation.py
python
Python
""" In physics and astronomy, a gravitational N-body simulation is a simulation of a dynamical system of particles under the influence of gravity. The system consists of a number of bodies, each of which exerts a gravitational force on all other bodies. These forces are calculated using Newton's law of universal gravit...
11,787
348
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\newtons_law_of_gravitation.py
python
Python
""" Title : Finding the value of either Gravitational Force, one of the masses or distance provided that the other three parameters are given. Description : Newton's Law of Universal Gravitation explains the presence of force of attraction between bodies having a definite mass situated at a distance. It is usually sta...
3,632
100
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\newtons_second_law_of_motion.py
python
Python
r""" Description: Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The accelera...
2,916
93
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\orbital_transfer_work.py
python
Python
def orbital_transfer_work( mass_central: float, mass_object: float, r_initial: float, r_final: float ) -> str: """ Calculates the work required to move an object from one orbit to another in a gravitational field based on the change in total mechanical energy. The formula used is: W = (G * ...
2,680
74
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\period_of_pendulum.py
python
Python
""" Title : Computing the time period of a simple pendulum The simple pendulum is a mechanical system that sways or moves in an oscillatory motion. The simple pendulum comprises of a small bob of mass m suspended by a thin string of length L and secured to a platform at its upper end. Its motion occurs in a vertical p...
1,633
54
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\photoelectric_effect.py
python
Python
""" The photoelectric effect is the emission of electrons when electromagnetic radiation , such as light, hits a material. Electrons emitted in this manner are called photoelectrons. In 1905, Einstein proposed a theory of the photoelectric effect using a concept that light consists of tiny packets of energy known as p...
2,420
68
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\potential_energy.py
python
Python
from scipy.constants import g """ Finding the gravitational potential energy of an object with reference to the earth,by taking its mass and height above the ground as input Description : Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massiv...
2,096
62
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\rainfall_intensity.py
python
Python
""" Rainfall Intensity ================== This module contains functions to calculate the intensity of a rainfall event for a given duration and return period. This function uses the Sherman intensity-duration-frequency curve. References ---------- - Aparicio, F. (1997): Fundamentos de Hidrología de Superficie. B...
4,183
144
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\reynolds_number.py
python
Python
""" Title : computing the Reynolds number to find out the type of flow (laminar or turbulent) Reynolds number is a dimensionless quantity that is used to determine the type of flow pattern as laminar or turbulent while flowing through a pipe. Reynolds number is defined by the ratio of inertial forces to that o...
2,263
64
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\rms_speed_of_molecule.py
python
Python
""" The root-mean-square speed is essential in measuring the average speed of particles contained in a gas, defined as, ----------------- | Vrms = √3RT/M | ----------------- In Kinetic Molecular Theory, gasified particles are in a condition of constant random motion; each particle moves at a completely different pa...
1,990
52
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\shear_stress.py
python
Python
from __future__ import annotations """ Shear stress is a component of stress that is coplanar to the material cross-section. It arises due to a shear force, the component of the force vector parallel to the material cross-section. https://en.wikipedia.org/wiki/Shear_stress """ def shear_stress( stress: float, ...
1,689
60
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\speed_of_sound.py
python
Python
""" Title : Calculating the speed of sound Description : The speed of sound (c) is the speed that a sound wave travels per unit time (m/s). During propagation, the sound wave propagates through an elastic medium. Sound propagates as longitudinal waves in liquids and gases and as transverse waves in so...
1,487
49
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\speeds_of_gas_molecules.py
python
Python
""" The root-mean-square, average and most probable speeds of gas molecules are derived from the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a probability distribution that describes the distribution of speeds of particles in an ideal gas. The distribution is given by the following equation::...
4,219
114
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
physics\terminal_velocity.py
python
Python
""" Title : Computing the terminal velocity of an object falling through a fluid. Terminal velocity is defined as the highest velocity attained by an object falling through a fluid. It is observed when the sum of drag force and buoyancy is equal to the downward gravity force acting on the object. The accelerat...
2,095
61
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_001\sol1.py
python
Python
""" Project Euler Problem 1: https://projecteuler.net/problem=1 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ def solution(n: int = 1000) -> int: ...
692
34
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_001\sol2.py
python
Python
""" Project Euler Problem 1: https://projecteuler.net/problem=1 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ def solution(n: int = 1000) -> int: ...
889
39
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_001\sol3.py
python
Python
""" Project Euler Problem 1: https://projecteuler.net/problem=1 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ def solution(n: int = 1000) -> int: ...
1,343
65
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_001\sol4.py
python
Python
""" Project Euler Problem 1: https://projecteuler.net/problem=1 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ def solution(n: int = 1000) -> int: ...
1,080
53
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_001\sol5.py
python
Python
""" Project Euler Problem 1: https://projecteuler.net/problem=1 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ def solution(n: int = 1000) -> int: ...
727
33
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_001\sol6.py
python
Python
""" Project Euler Problem 1: https://projecteuler.net/problem=1 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ def solution(n: int = 1000) -> int: ...
790
40
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_001\sol7.py
python
Python
""" Project Euler Problem 1: https://projecteuler.net/problem=1 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ def solution(n: int = 1000) -> int: ...
717
36
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_002\sol1.py
python
Python
""" Project Euler Problem 2: https://projecteuler.net/problem=2 Even Fibonacci Numbers Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequenc...
1,008
49
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_002\sol2.py
python
Python
""" Project Euler Problem 2: https://projecteuler.net/problem=2 Even Fibonacci Numbers Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequenc...
1,024
47
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_002\sol3.py
python
Python
""" Project Euler Problem 2: https://projecteuler.net/problem=2 Even Fibonacci Numbers Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequenc...
1,028
49
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_002\sol4.py
python
Python
""" Project Euler Problem 2: https://projecteuler.net/problem=2 Even Fibonacci Numbers Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequenc...
2,007
74
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_002\sol5.py
python
Python
""" Project Euler Problem 2: https://projecteuler.net/problem=2 Even Fibonacci Numbers Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequenc...
1,144
53
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_003\sol1.py
python
Python
""" Project Euler Problem 3: https://projecteuler.net/problem=3 Largest prime factor The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143? References: - https://en.wikipedia.org/wiki/Prime_number#Unique_factorization """ import math def is_prime(number: ...
2,767
106
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_003\sol2.py
python
Python
""" Project Euler Problem 3: https://projecteuler.net/problem=3 Largest prime factor The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143? References: - https://en.wikipedia.org/wiki/Prime_number#Unique_factorization """ def solution(n: int = 600851475143...
1,593
65
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_003\sol3.py
python
Python
""" Project Euler Problem 3: https://projecteuler.net/problem=3 Largest prime factor The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143? References: - https://en.wikipedia.org/wiki/Prime_number#Unique_factorization """ def solution(n: int = 600851475143...
1,628
67
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_004\sol1.py
python
Python
""" Project Euler Problem 4: https://projecteuler.net/problem=4 Largest palindrome product A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99. Find the largest palindrome made from the product of two 3-digit numbers. References: -...
1,506
52
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_004\sol2.py
python
Python
""" Project Euler Problem 4: https://projecteuler.net/problem=4 Largest palindrome product A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99. Find the largest palindrome made from the product of two 3-digit numbers. References: -...
1,040
40
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_005\sol1.py
python
Python
""" Project Euler Problem 5: https://projecteuler.net/problem=5 Smallest multiple 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is _evenly divisible_ by all of the numbers from 1 to 20? References: - https://e...
1,852
71
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_005\sol2.py
python
Python
from maths.greatest_common_divisor import greatest_common_divisor """ Project Euler Problem 5: https://projecteuler.net/problem=5 Smallest multiple 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is _evenly divisibl...
1,340
61
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_006\sol1.py
python
Python
""" Project Euler Problem 6: https://projecteuler.net/problem=6 Sum square difference The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)^2 = 55^2 = 3025 Hence the difference between the sum of...
1,113
45
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_006\sol2.py
python
Python
""" Project Euler Problem 6: https://projecteuler.net/problem=6 Sum square difference The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)^2 = 55^2 = 3025 Hence the difference between the sum of...
1,062
42
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_006\sol3.py
python
Python
""" Project Euler Problem 6: https://projecteuler.net/problem=6 Sum square difference The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)^2 = 55^2 = 3025 Hence the difference between the sum of...
1,111
44
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_006\sol4.py
python
Python
""" Project Euler Problem 6: https://projecteuler.net/problem=6 Sum square difference The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)^2 = 55^2 = 3025 Hence the difference between the sum of...
1,079
42
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_007\sol1.py
python
Python
""" Project Euler Problem 7: https://projecteuler.net/problem=7 10001st prime By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10001st prime number? References: - https://en.wikipedia.org/wiki/Prime_number """ from math import sqrt def is_prime(...
1,883
85
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_007\sol2.py
python
Python
""" Project Euler Problem 7: https://projecteuler.net/problem=7 10001st prime By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10001st prime number? References: - https://en.wikipedia.org/wiki/Prime_number """ import math def is_prime(number: in...
2,685
107
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_007\sol3.py
python
Python
""" Project Euler Problem 7: https://projecteuler.net/problem=7 10001st prime By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10001st prime number? References: - https://en.wikipedia.org/wiki/Prime_number """ import itertools import math def is...
1,885
87
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_008\sol1.py
python
Python
""" Project Euler Problem 8: https://projecteuler.net/problem=8 Largest product in a series The four adjacent digits in the 1000-digit number that have the greatest product are 9 x 9 x 8 x 9 = 5832. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 8586...
3,331
84
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_008\sol2.py
python
Python
""" Project Euler Problem 8: https://projecteuler.net/problem=8 Largest product in a series The four adjacent digits in the 1000-digit number that have the greatest product are 9 x 9 x 8 x 9 = 5832. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 8586...
3,283
82
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_008\sol3.py
python
Python
""" Project Euler Problem 8: https://projecteuler.net/problem=8 Largest product in a series The four adjacent digits in the 1000-digit number that have the greatest product are 9 x 9 x 8 x 9 = 5832. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 8586...
3,602
98
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_009\sol1.py
python
Python
""" Project Euler Problem 9: https://projecteuler.net/problem=9 Special Pythagorean triplet A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find th...
1,822
80
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_009\sol2.py
python
Python
""" Project Euler Problem 9: https://projecteuler.net/problem=9 Special Pythagorean triplet A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find th...
1,151
48
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_009\sol3.py
python
Python
""" Project Euler Problem 9: https://projecteuler.net/problem=9 Special Pythagorean triplet A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find th...
988
45
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_009\sol4.py
python
Python
""" Project Euler Problem 9: https://projecteuler.net/problem=9 Special Pythagorean triplet A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2. For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find t...
1,353
61
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_010\sol1.py
python
Python
""" Project Euler Problem 10: https://projecteuler.net/problem=10 Summation of primes The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. References: - https://en.wikipedia.org/wiki/Prime_number """ import math def is_prime(number: int) -> bool: """Chec...
1,650
70
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_010\sol2.py
python
Python
""" Project Euler Problem 10: https://projecteuler.net/problem=10 Summation of primes The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. References: - https://en.wikipedia.org/wiki/Prime_number """ import math from collections.abc import Iterator from iterto...
1,910
84
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_010\sol3.py
python
Python
""" Project Euler Problem 10: https://projecteuler.net/problem=10 Summation of primes The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. References: - https://en.wikipedia.org/wiki/Prime_number - https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes """ d...
1,726
62
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_011\sol1.py
python
Python
""" What is the greatest product of four adjacent numbers (horizontally, vertically, or diagonally) in this 20x20 array? 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 52 70 95 23 04 60 ...
3,153
90
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_011\sol2.py
python
Python
""" What is the greatest product of four adjacent numbers (horizontally, vertically, or diagonally) in this 20x20 array? 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 52 70 95 23 04 60 ...
2,915
82
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_012\sol1.py
python
Python
""" Highly divisible triangular numbers Problem 12 The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... Let us list the factors of the first seven triangle...
1,287
63
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_012\sol2.py
python
Python
""" Highly divisible triangular numbers Problem 12 The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... Let us list the factors of the first seven triangle...
1,327
58
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_013\sol1.py
python
Python
""" Problem 13: https://projecteuler.net/problem=13 Problem Statement: Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. """ import os def solution(): """ Returns the first ten digits of the sum of the array elements from the file num.txt >>> solution() '55...
583
27
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_014\sol1.py
python
Python
""" Problem 14: https://projecteuler.net/problem=14 Problem Statement: The following iterative sequence is defined for the set of positive integers: n → n/2 (n is even) n → 3n + 1 (n is odd) Using the rule above and starting with 13, we generate the following sequence: 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4...
1,739
67
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_014\sol2.py
python
Python
""" Problem 14: https://projecteuler.net/problem=14 Collatz conjecture: start with any positive integer n. Next term obtained from the previous term as follows: If the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. Th...
1,894
63
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_015\sol1.py
python
Python
""" Problem 15: https://projecteuler.net/problem=15 Starting in the top left corner of a 2x2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner. How many such routes are there through a 20x20 grid? """ from math import factorial def solution(n: int = 20) -...
1,190
46
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_015\sol2.py
python
Python
""" Problem 15: https://projecteuler.net/problem=15 Starting in the top left corner of a 2x2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner. How many such routes are there through a 20x20 grid? """ def solution(n: int = 20) -> int: """ Solve by ...
765
33
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_016\sol1.py
python
Python
""" Problem 16: https://projecteuler.net/problem=16 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 2^1000? """ def solution(power: int = 1000) -> int: """Returns the sum of the digits of the number 2^power. >>> solution(1000) 1366 >>> so...
811
37
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_016\sol2.py
python
Python
""" Problem 16: https://projecteuler.net/problem=16 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 2^1000? """ def solution(power: int = 1000) -> int: """Returns the sum of the digits of the number 2^power. >>> solution(1000) 1366 >>> s...
597
31
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_017\sol1.py
python
Python
""" Number letter counts Problem 17: https://projecteuler.net/problem=17 If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total. If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters woul...
2,216
64
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_018\solution.py
python
Python
""" By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom of the triangle below: 75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 ...
1,406
60
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_019\sol1.py
python
Python
""" Counting Sundays Problem 19 You are given the following information, but you may prefer to do some research for yourself. 1 Jan 1900 was a Monday. Thirty days has September, April, June and November. All the rest have thirty-one, Saving February alone, Which has twenty-eight, rain or shine. And on leap years, twe...
1,605
64
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_020\sol1.py
python
Python
""" Problem 20: https://projecteuler.net/problem=20 n! means n x (n - 1) x ... x 3 x 2 x 1 For example, 10! = 10 x 9 x ... x 3 x 2 x 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27. Find the sum of the digits in the number 100! """ def factorial(num: int) -> int: """F...
1,265
55
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_020\sol2.py
python
Python
""" Problem 20: https://projecteuler.net/problem=20 n! means n x (n - 1) x ... x 3 x 2 x 1 For example, 10! = 10 x 9 x ... x 3 x 2 x 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27. Find the sum of the digits in the number 100! """ from math import factorial def solution...
784
37
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_020\sol3.py
python
Python
""" Problem 20: https://projecteuler.net/problem=20 n! means n x (n - 1) x ... x 3 x 2 x 1 For example, 10! = 10 x 9 x ... x 3 x 2 x 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27. Find the sum of the digits in the number 100! """ from math import factorial def solution...
874
43
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_020\sol4.py
python
Python
""" Problem 20: https://projecteuler.net/problem=20 n! means n x (n - 1) x ... x 3 x 2 x 1 For example, 10! = 10 x 9 x ... x 3 x 2 x 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27. Find the sum of the digits in the number 100! """ def solution(num: int = 100) -> int: ...
857
43
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_021\sol1.py
python
Python
""" Amicable Numbers Problem 21 Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers. For example, the proper divisors of 220 are 1, 2, 4, 5, 10,...
1,314
54
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_022\sol1.py
python
Python
""" Name scores Problem 22 Using names.txt (right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a ...
1,234
47
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_022\sol2.py
python
Python
""" Name scores Problem 22 Using names.txt (right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a ...
1,207
44
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_023\sol1.py
python
Python
""" A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number. A number n is called deficient if the sum of its proper divisors is less than n and it i...
1,694
53
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_024\sol1.py
python
Python
""" A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are: 012 021 102 120 201 210...
791
29
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_025\sol1.py
python
Python
""" The Fibonacci sequence is defined by the recurrence relation: Fn = Fn-1 + Fn-2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be: F1 = 1 F2 = 1 F3 = 2 F4 = 3 F5 = 5 F6 = 8 F7 = 13 F8 = 21 F9 = 34 F10 = 55 F11 = 89 F12 = 144 The 12th term, F12, is the ...
2,122
102
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_025\sol2.py
python
Python
""" The Fibonacci sequence is defined by the recurrence relation: Fn = Fn-1 + Fn-2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be: F1 = 1 F2 = 1 F3 = 2 F4 = 3 F5 = 5 F6 = 8 F7 = 13 F8 = 21 F9 = 34 F10 = 55 F11 = 89 F12 = 144 The 12th term, F12, is the ...
1,410
74
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_025\sol3.py
python
Python
""" The Fibonacci sequence is defined by the recurrence relation: Fn = Fn-1 + Fn-2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be: F1 = 1 F2 = 1 F3 = 2 F4 = 3 F5 = 5 F6 = 8 F7 = 13 F8 = 21 F9 = 34 F10 = 55 F11 = 89 F12 = 144 The 12th term, F12, is the ...
1,060
57
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_026\sol1.py
python
Python
""" Euler Problem 26 https://projecteuler.net/problem=26 Problem Statement: A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given: 1/2 = 0.5 1/3 = 0.(3) 1/4 = 0.25 1/5 = 0.2 1/6 = 0.1(6) 1/7 = 0.(142857) 1/8 = 0.125 1/9 = 0.(1) 1/10 ...
1,565
61
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_027\sol1.py
python
Python
""" Project Euler Problem 27 https://projecteuler.net/problem=27 Problem Statement: Euler discovered the remarkable quadratic formula: n2 + n + 41 It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and ...
2,740
92
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_028\sol1.py
python
Python
""" Problem 28 Url: https://projecteuler.net/problem=28 Statement: Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: 21 22 23 24 25 20 7 8 9 10 19 6 1 2 11 18 5 4 3 12 17 16 15 14 13 It can be verified that the sum of the num...
1,280
59
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_029\sol1.py
python
Python
""" Consider all integer combinations of ab for 2 <= a <= 5 and 2 <= b <= 5: 2^2=4, 2^3=8, 2^4=16, 2^5=32 3^2=9, 3^3=27, 3^4=81, 3^5=243 4^2=16, 4^3=64, 4^4=256, 4^5=1024 5^2=25, 5^3=125, 5^4=625, 5^5=3125 If they are then placed in numerical order, with any repeats removed, we get the following sequence of 1...
1,289
51
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_030\sol1.py
python
Python
"""Problem Statement (Digit Fifth Powers): https://projecteuler.net/problem=30 Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: 1634 = 1^4 + 6^4 + 3^4 + 4^4 8208 = 8^4 + 2^4 + 0^4 + 8^4 9474 = 9^4 + 4^4 + 7^4 + 4^4 As 1 = 1^4 is not a sum it is not included. ...
1,229
45
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_031\sol1.py
python
Python
""" Coin sums Problem 31: https://projecteuler.net/problem=31 In England the currency is made up of pound, f, and pence, p, and there are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p, 50p, f1 (100p) and f2 (200p). It is possible to make f2 in the following way: 1xf1 + 1x50p + 2x20p + 1x5p + 1x2p + 3x1p H...
1,513
66