Problem Description
Farmer John commanded his cows to search for different sets of numbers that sum to a given number. The cows use only numbers that are an integer power of 2. Here are the possible sets of numbers that sum to 7:
1) 1+1+1+1+1+1+1
2) 1+1+1+1+1+2
3) 1+1+1+2+2
4) 1+1+1+4
5) 1+2+2+2
6) 1+2+4
Help FJ count all possible representations for a given integer N (1 <= N <= 1,000,000).
1) 1+1+1+1+1+1+1
2) 1+1+1+1+1+2
3) 1+1+1+2+2
4) 1+1+1+4
5) 1+2+2+2
6) 1+2+4
Help FJ count all possible representations for a given integer N (1 <= N <= 1,000,000).
Input
A single line with a single integer, N.
Output
The number of ways to represent N as the indicated sum. Due to the potential huge size of this number, print only last 9 digits (in base 10 representation).
Sample Input
7
Sample Output
6
#include <iostream>
using namespace std;
__int64 a[1000001];
int main()
{
//freopen("C:\\in.txt","r",stdin);
__int64 n;
int i;
a[1]=1;a[2]=2;
for(i=3;i<1000001;i++)
{
if(i%2==0)
a[i]=a[i-2]+a[i/2];
else
a[i]=a[i-1];
a[i]%=1000000000;
}
while(scanf("%I64d",&n)!=EOF)
printf("%I64d\n",a[n]);
return 0;
}