Add root simplification

Author: xathrya

Codes/Algorithm/mathematic/c++/cases/numbers/root-simplification.cpp

@@ -0,0 +1,97 @@
+/*
+    Root Simplification
+    Archive of Reversing.ID
+    Algorithm (Mathematics/Numbers)
+    
+Compile:
+    [clang]
+    $ clang++ root-simplification.cpp -o root-simplification
+
+    [gcc]
+    $ g++ root-simplification.cpp -o root-simplification
+
+    [msvc]
+    $ cl root-simplification.cpp
+
+Run:
+    $ root-simplification
+*/
+#include <tuple>
+#include <cmath>
+
+/*
+    Menyederhanakan bilangan akar √X Menjadi bentuk perfect dan radicand C√D
+    
+    √A = B√C
+        A = num
+        B = perfect number
+        C = radicand
+
+Contoh:
+    √20 = 2√5
+    √56 = 3√7
+
+    berlaku juga untuk akar lain (akar pangkat 3, akar pangkat 4, dsb).
+*/
+
+// ======================================================================================
+
+/* 
+    Iterative Solution
+    Melakukan faktorisasi, mencari faktor-faktor prima dari bilangan dan membangun
+    perfect number dan radicand di setiap iterasi.
+*/
+
+auto algorithm(size_t num, size_t degree)
+{
+    size_t power  = 0;
+    size_t number = 2;
+
+    size_t perfect = 1, radicand = 1;
+
+    // proses faktor 2 sebagai satu-satunya faktor prima genap.
+    power  = 0;
+    while (num % 2 == 0)
+    {
+        num = num / 2;
+
+        power ++;
+        if (power == degree)
+        {
+            power = 0;
+            perfect *= 2;
+        }
+    }
+
+    for (size_t j = 0; j < power; j++)
+            radicand *= 2;
+
+    // proses faktor prima dimulai dari 3
+    for (size_t i = 3, batas = sqrt(num); i <= batas; i += 2)
+    {
+        power = 0;
+
+        // mendapatkan bernilai sama
+        while (num % i == 0)
+        {
+            num = num / i;
+
+            power++;
+            if (power == degree)
+            {
+                power = 0;
+                perfect *= i;
+            }
+        }
+
+        for (size_t j = 0; j < power; j++)
+            radicand *= i;
+    }
+
+    // jika ada faktor yang lebih besar daripada sqrt(num)
+    if (num > 2)
+        radicand *= num;
+    
+    // get<0> -> perfect, get<0> -> radicand
+    return std::make_tuple(perfect, radicand);
+}