-
-
Notifications
You must be signed in to change notification settings - Fork 7.1k
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
1 changed file
with
121 additions
and
0 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,121 @@ | ||
/** | ||
* @file | ||
* @brief Iterative implementation of | ||
* [Factorial](https://en.wikipedia.org/wiki/Factorial) | ||
* | ||
* @author [Renjian-buchai](https://github.com/Renjian-buchai) | ||
* | ||
* @details Calculates factorial iteratively. | ||
* \f[n! = n\times(n-1)\times(n-2)\times(n-3)\times\ldots\times3\times2\times1 | ||
* = n\times(n-1)!\f] | ||
* for example: | ||
* \f$4! = 4\times3! = 4\times3\times2\times1 = 24\f$ | ||
* | ||
* @example | ||
* | ||
* 5! = 5 * 4 * 3 * 2 * 1 | ||
* | ||
* Recursive implementation of factorial pseudocode: | ||
* | ||
* function factorial(n): | ||
* if n == 1: | ||
* return 1 | ||
* else: | ||
* return factorial(n-1) | ||
* | ||
*/ | ||
|
||
#include <cassert> /// for assert | ||
#include <cstdint> /// for integral types | ||
#include <exception> /// for std::invalid_argument | ||
#include <iostream> /// for std::cout | ||
|
||
/** | ||
* @namespace | ||
* @brief Mathematical algorithms | ||
*/ | ||
namespace math { | ||
|
||
/** | ||
* @brief Calculates the factorial iteratively. | ||
* @param n Nth factorial. | ||
* @return Factorial. | ||
* @note 0! = 1. | ||
* @warning Maximum=20 because there are no 128-bit integers in C++. 21! | ||
* returns 1.419e+19, which is not 21! but (21! % UINT64_MAX). | ||
*/ | ||
uint64_t iterativeFactorial(uint8_t n) { | ||
if (n > 20) { | ||
throw new std::invalid_argument("Maximum n value is 20"); | ||
} | ||
|
||
// 1 because it is the identity number of multiplication. | ||
uint64_t accumulator = 1; | ||
|
||
while (n > 1) { | ||
accumulator *= n; | ||
--n; | ||
} | ||
|
||
return accumulator; | ||
} | ||
|
||
} // namespace math | ||
|
||
/** | ||
* @brief Self-test implementations to test iterativeFactorial function. | ||
* @note There is 1 special case: 0! = 1. | ||
*/ | ||
static void test() { | ||
// Special case test | ||
std::cout << "Exception case test \n" | ||
"Input: 0 \n" | ||
"Expected output: 1 \n\n"; | ||
assert(math::iterativeFactorial(0) == 1); | ||
|
||
// Base case | ||
std::cout << "Base case test \n" | ||
"Input: 1 \n" | ||
"Expected output: 1 \n\n"; | ||
assert(math::iterativeFactorial(1) == 1); | ||
|
||
// Small case | ||
std::cout << "Small number case test \n" | ||
"Input: 5 \n" | ||
"Expected output: 120 \n\n"; | ||
assert(math::iterativeFactorial(5) == 120); | ||
|
||
// Medium case | ||
std::cout << "Medium number case test \n" | ||
"Input: 10 \n" | ||
"Expected output: 3628800 \n\n"; | ||
assert(math::iterativeFactorial(10) == 3628800); | ||
|
||
// Maximum case | ||
std::cout << "Maximum case test \n" | ||
"Input: 20 \n" | ||
"Expected output: 2432902008176640000\n\n"; | ||
assert(math::iterativeFactorial(20) == 2432902008176640000); | ||
|
||
// Exception test | ||
std::cout << "Exception test \n" | ||
"Input: 21 \n" | ||
"Expected output: Exception thrown \n"; | ||
try { | ||
math::iterativeFactorial(21); | ||
} catch (std::invalid_argument* e) { | ||
std::cout << "Exception thrown successfully \nContent: " << e->what() | ||
<< "\n"; | ||
} | ||
|
||
std::cout << "All tests have passed successfully.\n"; | ||
} | ||
|
||
/** | ||
* @brief Main function | ||
* @returns 0 on exit | ||
*/ | ||
int main() { | ||
test(); // Run self-test implementation | ||
return 0; | ||
} |