POJ2229--Sumsets(动态规划)

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

#include<iostream>
#include<algorithm>
using namespace std;
int dp[1000005];
int mod=1e9;
int main(){
    int n;
    cin>>n;
    dp[0]=1;
    for(int i=1;i<=n;i++){
        if(i%2==1){
            dp[i]=dp[i-1];
        }
        else{
            dp[i]=(dp[i-1]+dp[i>>1])%mod;
        }
    }
    cout<<dp[n]<<endl;
    return 0;
}