Create mentoring.md for grains exercice in cpp

tracks/cpp/exercises/grains/mentoring.md

@@ -0,0 +1,79 @@
+# Mentoring
+
+## Reasonable solutions
+
+### First function
+
+The first way to implement this function is to use a for loop:
+```cpp
+unsigned long long square(int index) {
+    unsigned long long result = 1;
+    for (int i = 0; i < index; i++) result *= 2;
+    return result;
+}
+```
+Another good way to do this is to use a recursive function:
+```cpp
+unsigned long long square(int index) {
+    if (index == 1) return 1;
+    else return square(index - 1) * 2;
+}
+```
+This way, the code is shorter and in my mind, easier to read.
+
+The last option and the more direct one is:
+```cpp
+unsigned long long square(int index)
+{
+    return 1ULL << (index - 1);
+}
+```
+This code use left bitshifting. Left bitshifting consists in adding 0 at the end of the binary writing of the number.
+
+If you do `5 << 2`, you are taking 5, which is 101 in binary, and you shift the bits by 2, so you end up with 10100 and that equal to 20.
+
+### Second function
+At first sight, we want to use the first function to do it easily:
+```cpp
+unsigned long long total() {
+    unsigned long long sum = 0;
+    for (int i = 1; i <= 64; i++) sum += square(i);
+    return sum;
+}
+```
+However with this solution only works with a direct implementation of the first function, else each time you call the function square with the index i, you do i products.
+In the following solution, you only do 64 products and by adding to the sum each time you multiply by 2:
+```cpp
+unsigned long long total() {
+    unsigned long long total = 0;
+    unsigned long long square = 1;
+
+    for (int k = 0; k < 64; k++) {
+        total += square;
+        square *= 2;
+    }
+
+    return total;
+}
+```
+Moreover, this is also possible to use a direct implementation for this function:
+```cpp
+unsigned long long total() {
+    return ~0ULL;
+}
+```
+With this way we use the fact that a ULL is 64 bits long and we use the ~ to do the complement.
+
+## Common issues
+
+- Not using unsigned long long types
+- Using ULLONG_MAX, for the second function, which works, however this is like returning directly the good number
+- Using std::pow that implies conversion from float to int and could lead to errors mainly in the total function
+- Hard coding the solution for the total
+
+## Common suggestions
+
+- Use the square function in total only if square use a direct implementation
+- The optimal way is to use bitwise operations
+
+