From 59948dfca04dc55b3feb257965a8f9aadd9c00b4 Mon Sep 17 00:00:00 2001
From: Jorge <uo288800@uniovi.es>
Date: Fri, 13 Dec 2024 18:23:01 +0100
Subject: [PATCH] I changed the prime_factorial.m file into a function with a
 more advanced algorithm in order to calculate the factorization of prime
 numbers. The script is easy to read and to understand for the user

---
 algorithms/maths/prime_factorial.m | 103 +++++++++++++++--------------
 1 file changed, 55 insertions(+), 48 deletions(-)

diff --git a/algorithms/maths/prime_factorial.m b/algorithms/maths/prime_factorial.m
index 94510ee..991baad 100644
--- a/algorithms/maths/prime_factorial.m
+++ b/algorithms/maths/prime_factorial.m
@@ -1,51 +1,58 @@
-clear all
-clc
-
-%% Prime Factors
-% This code gets user input number, calculates and displays its prime factors.
-% For this, first it determines prime numbers which are less than or equal to
-% user input number. Then if the input is dividable by that prime number,
-% it becomes one of input's prime factors.
-
-%% Request user input
-prompt = 'Input your number: ';
-n = input(prompt);
-
-%%
-counter = 0; % initialize number of prime factors
-
-if n <= 1
-    disp('input must be positive integer greater than 1')
-else if floor(n)~= n 
-       disp('input must be positive integer') 
-    else
-        for i = 2:1:n
-            if i == 2
-               isprime = 1;
-            else 
-            half_i = floor(i/2)+1;
-            j = 2;
-            while j <= half_i         %lines 16 to 30 check if i is prime or not.
-                  residual = mod(i,j); 
-                 if residual == 0
-                    isprime = 0;
-                    break
-                 else if j == half_i
-                         isprime = 1;
-                         break
-                     else
-                         j=j+1;
-                     end
-                 end
-            end
-            end
-            if isprime == 1 && mod(n,i) == 0
-                   counter=counter+1;
-                   f(counter) = i;         % prime factors of n will be storing 
-            end
-        end
+%% Prime Factorization
+
+function prime_factorization()
+
+% This function gets user input number, calculates and displays its prime factors.
+%
+% 1) Input: The code asks the user to enter a number to decompose into prime factors.
+%
+% 2) Input Validation: It checks if the number is a positive integer greater than 1. 
+% If not, it throws an error.
+%
+% 3) Prime Factorization: 
+% Firstly, it divides the number by 2 repeatedly (if it's divisible by 2).
+% Then, it checks for odd divisors (starting from 3) up to the square root 
+% of the remaining number, dividing when it finds a factor.
+%
+% 4) Output: The prime factors are stored in an array and displayed in the 
+% format n = p1 * p2 * ...
+
+% Ask the user to enter a number
+number = input('Enter a number to decompose into prime factors: ');
+
+% Check if the number is a positive integer greater than 1
+if mod(number, 1) ~= 0 || number <= 1
+    error('The number must be a positive integer greater than 1.');
+end
+
+% Initialize an empty array to store the prime factors
+primeFactors = [];
+    
+% Check for factor 2 (the smallest prime)
+while mod(number, 2) == 0
+    primeFactors = [primeFactors, 2];
+    number = number / 2;
+end
+
+% Check for odd factors starting from 3
+divisor = 3;
+while divisor * divisor <= number
+    while mod(number, divisor) == 0
+        primeFactors = [primeFactors, divisor];
+        number = number / divisor;
     end
+    divisor = divisor + 2; % Skip even numbers as they are not primes
+end
+
+% If the remaining number is greater than 2, it must be prime
+if number > 2
+    primeFactors = [primeFactors, number];
+end
+
+% Display the prime factorization
+disp('The prime factorization is:');
+fprintf('%d = ', prod(primeFactors)); % Print the original number
+disp(strjoin(arrayfun(@num2str, primeFactors, 'UniformOutput', false), ' * '));
+
 end
 
-disp('Prime factors of input number are: ')
-disp(f)