Question

You have a block of platinum that can be exchanged in your bank either for cash
or for smaller blocks of platinum. If you exchange a block of m grams, you get
three blocks of weight m/2, m/3 and m/4 grams each. You don't get any fractional
part, as the division process rounds down the value. If you exchange the block of
platinum for cash, you get m units of currency. You can do any number of
exchanges for smaller blocks or currency.Given the value of a block in grams as input, write a program that would print the largest possible currency value that you can receive as the output. Assume that
the maximum value of a block that can be given as an input is 1,000,000,000
grams and the minimum value is 2 grams.

Answer 1

Program

#include <iostream>
#define MIN_SIZE 2

using namespace std;

//cost of pieces size m
//calc recursive
double cost(int m)
{
//bottom of recursion - minimal size less MIN_SIZE
//i.e. m~m/2+m/3+m/4; m/4<2 or m<8
if(m<8)
return m;
else
{
//check: is round of dividing less pieces?
if((m/2+m/3+m/4)<m)
return m;
else
return cost(m/2)+cost(m/3)+cost(m/4);
}
}
int main( )
{
int m;
cout<<"Input weight block ofplatinum (g): ";
cin>>m;
cout<<"\nYou can receive currencyvalue: "<<cost(m)<<endl;
return 0;
}

Example of execute program:
Input weight block of platinum (g): 24
You can receive currency value: 27

Input weight block of platinum (g): 10
You can receive currency value: 10