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).
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
這題沒啥說的，找規律，遞推下去就行了，最後找出來的規律是
i爲奇數時，dp[i]=dp[i-1]
i爲偶數時，dp[i]=dp[i-1]+dp[i/2]
My Code：
#include<iostream>
#define ll long long
using namespace std;
ll a[1000005];
int main()
{
a[1]=1;
a[2]=2;
for(int i=3;i<=1000000;i++)
{
if(i%2==0) a[i]=a[i-2]+a[i/2];
else a[i]=a[i-1];
if(a[i]>1000000000)a[i]%=1000000000;
}
ll t;
cin>>t;
cout<<a[t]%1000000000<<endl;
}