// G. Hagopian -- PPP4 exercise 8
/*
8. There is an old story that the emperor wanted to thank the
inventor of the game of chess and asked the inventor to name
his reward. The inventor asked for one grain of rice for the
first square, 2 for the second, 4 for the third, and so on,
doubling for each of the 64 squares. That may sound modest,
but there wasn’t that much rice in the empire! Write a program
to calculate how many squares are required to give the
inventor at least 1000 grains of rice, at least 1,000,000
grains, and at least 1,000,000,000 grains. You’ll need a loop,
of course, and probably an int to keep track of which square
you are at, an int to keep the number of grains on the current
square, and an int to keep track of the grains on all previous
squares. We suggest that you write out the value of all your
variables for each iteration of the loop so that you can
see what’s going on.
*/
#include
#include
#include
using namespace std;
// input: number of squares
// output: total number of grains of rice
int grains(int n) {
int pow2 = 1;
int output{};
for (int i = 0; i < n; ++i) {
output += pow2;
pow2 *= 2;
}
return output;
}
int main() {
int totalGrains{};
int squares{};
cout << "How many grains of rice do you want? ";
while (cin >> totalGrains) {
while (grains(squares) < totalGrains) ++squares;
cout << "To get " << totalGrains << " grains of rice, you'll need at least "
<< squares << " squares.";
cout << "\nNote this is the same as (int)log2(" << totalGrains << ")+1 = "
<< (int)log2(totalGrains) + 1 << endl;
cout << "\nHow many grains of rice do you want? ";
squares = 0;
}
}