EASYPROB

Input

There's no input.

Output

Output some form of these numbers: 137, 1315, 73, 136, 255, 1384, 16385, one per line in the listed order.

Example

The first two lines of the CORRECT output file are:

137=2(2(2)+2+2(0))+2(2+2(0))+2(0)
1315=2(2(2+2(0))+2)+2(2(2+2(0)))+2(2(2)+2(0))+2+2(0)

The correct output file should contain 7 lines.

Code

#include <iostream>
#include <string>
#include <bitset>

using namespace std;

string expressInPowersOfTwo(unsigned long long n) {  
    string final = "";
    if(n == 2 || n == 0) {
        return final + char('0' + n);
    }
    bitset<64> bitRep(n);
    for (int i = 63; i >= 0; --i) {
        if (bitRep[i]) {
            string ans = (i == 1 ? "2" : 
                         "2(" + expressInPowersOfTwo(i) + ")");
            final += (final == "" ? ans : "+" + ans);
        }
    }
    return final;
}

int main() {  
    unsigned long long n;
    while((cin >> n) && n != -1) {
        cout << n << "=" << expressInPowersOfTwo(n) << "\n";
    }
    return 0;
}

Solution

137=2(2(2)+2+2(0))+2(2+2(0))+2(0)  
1315=2(2(2+2(0))+2)+2(2(2+2(0)))+2(2(2)+2(0))+2+2(0)  
73=2(2(2)+2)+2(2+2(0))+2(0)  
136=2(2(2)+2+2(0))+2(2+2(0))  
255=2(2(2)+2+2(0))+2(2(2)+2)+2(2(2)+2(0))+2(2(2))+2(2+2(0))+2(2)+2+2(0)  
1384=2(2(2+2(0))+2)+2(2(2+2(0)))+2(2(2)+2)+2(2(2)+2(0))+2(2+2(0))  
16385=2(2(2+2(0))+2(2)+2)+2(0)