TheAlgorithms-C-Plus-Plus/math
Benjamin Walton a41b707919
feat: added integral approximation algorithm (#1485)
* Setup general integral aprroximation algorithm template

* feat: added integral approximation algorithm

* updating DIRECTORY.md

* feat: added integral approximation algorithm

* test: added tests for integral approximation algorithm

* docs: added comments and explanation for integral approximation algorithm

* fix: updated for loop within algorithm

* fix: data type conversions

* Modified dividing by 2

Maintains functionality but dividing by 2 is easier to read/understand

* Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* fix: Apply suggestions from code review

* feat: added Wikipedia link and detailed description

* fix: Apply suggestions from code review

* Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* style: updated what the library/header is for

* docs: Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* fix: changed int to uint64_t

* Update math/integral_approximation.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Shiqi Sheng <shiqisheng00@gmail.com>
Co-authored-by: David Leal <halfpacho@gmail.com>
2021-04-22 22:11:44 +05:30
..
armstrong_number.cpp formatting source-code for ca70c3097e 2020-06-25 09:51:24 +00:00
binary_exponent.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
binomial_calculate.cpp feat: add program to calculate binomial coefficients (#1448) 2021-02-23 00:51:58 +05:30
check_amicable_pair.cpp formatting source-code for 1d7a73ea58 2020-06-23 19:34:19 +00:00
check_factorial.cpp feat: added check_factorial (#1155) 2020-10-05 08:52:27 -04:00
check_prime.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
CMakeLists.txt Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
complex_numbers.cpp formatting source-code for 247301c5b5 2020-07-02 12:48:35 +00:00
double_factorial.cpp formatting source-code for e1b1c71e7c 2020-06-25 18:41:27 +00:00
eulers_totient_function.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
extended_euclid_algorithm.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
factorial.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
fast_power.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
fibonacci_fast.cpp formatting source-code for c7ff9d66f1 2020-06-24 17:14:57 +00:00
fibonacci_large.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
fibonacci_matrix_exponentiation.cpp Nth fibonacci number using matrix exponentiation (#1215) 2021-02-05 15:12:13 +05:30
fibonacci_sum.cpp feat: Add ncr mod p code (#1325) 2020-11-22 23:05:01 +05:30
fibonacci.cpp fix: math/fibonacci linter warnings. (#1047) 2020-08-25 18:56:49 -05:00
gcd_iterative_euclidean.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
gcd_of_n_numbers.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
gcd_recursive_euclidean.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
integral_approximation.cpp feat: added integral approximation algorithm (#1485) 2021-04-22 22:11:44 +05:30
large_factorial.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
large_number.h make multiplication 64-bit 2020-06-22 16:21:57 -04:00
largest_power.cpp feat: largest_power (#1406) 2020-11-25 04:18:50 -05:00
lcm_sum.cpp feat: Add ncr mod p code (#1325) 2020-11-22 23:05:01 +05:30
least_common_multiple.cpp fix: Integer overflow of least_common_multiple. (#970) 2020-07-22 08:01:06 -04:00
linear_recurrence_matrix.cpp feat: Solving linear recurrence using Matrix Exponentiation (with examples). (#1463) 2021-03-17 23:57:51 +05:30
magic_number.cpp Update math/magic_number.cpp 2020-10-27 06:33:29 +05:30
miller_rabin.cpp formatting source-code for a48d05fb62 2020-06-21 17:42:09 +00:00
modular_division.cpp clang-format and clang-tidy fixes for 7293e15a 2021-01-18 10:45:57 +00:00
modular_exponentiation.cpp feat: Add modular_exponentiation.cpp (#1276) 2020-10-30 01:52:32 +05:30
modular_inverse_fermat_little_theorem.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
n_choose_r.cpp feat: Add ncr mod p code (#1325) 2020-11-22 23:05:01 +05:30
ncr_modulo_p.cpp feat: Add ncr mod p code (#1325) 2020-11-22 23:05:01 +05:30
number_of_positive_divisors.cpp fix, test: simplification and tests for number_of_positive_divisors (#975) 2020-07-24 22:59:49 -04:00
power_for_huge_numbers.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
power_of_two.cpp Create power_of_two.cpp (#1315) 2021-02-12 10:14:01 +05:30
prime_factorization.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
prime_numbers.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
primes_up_to_billion.cpp fix: integer overflow due to multiplication fixed (#886) 2020-06-23 23:50:45 +05:30
README.md Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
realtime_stats.cpp fix: Various LGTM fixes 2020-06-23 15:13:28 -05:00
sieve_of_eratosthenes.cpp fix, test: Refactor of sieve_of_eratosthenes (#969) 2020-07-23 07:50:38 -04:00
sqrt_double.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
string_fibonacci.cpp Major rework to improve code quality and add automation checks (#805) 2020-06-19 21:34:56 +05:30
sum_of_binomial_coefficient.cpp feat: Add ncr mod p code (#1325) 2020-11-22 23:05:01 +05:30
sum_of_digits.cpp formatting source-code for 9bc80876e8 2020-06-22 12:05:13 +00:00
vector_cross_product.cpp cross product of two vectors (#1292) 2021-02-05 15:13:45 +05:30

Prime factorization

Prime Factorization is a very important and useful technique to factorize any number into its prime factors. It has various applications in the field of number theory.

The method of prime factorization involves two function calls. First: Calculating all the prime number up till a certain range using the standard Sieve of Eratosthenes.

Second: Using the prime numbers to reduce the the given number and thus find all its prime factors.

The complexity of the solution involves approx. O(n logn) in calculating sieve of eratosthenes O(log n) in calculating the prime factors of the number. So in total approx. O(n logn).

Requirements: For compile you need the compiler flag for C++ 11