bzoj 1677 求和

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).

给出一个N(1≤N≤10^6)，使用一些2的若干次幂的数相加来求之．问有多少种方法

Input

   一个整数N.

Output

方法数．这个数可能很大，请输出其在十进制下的最后9位．

Sample Input

7

Sample Output

6

 

思路： 本题可以递推

#include<bits/stdc++.h>
using namespace std; 
#define R register int 
#define rep(i,a,b) for(R i=a;i<=b;i++) 
#define ms(i,a)  memset(a,i,sizeof(a)) 
int const N=1e6+1;  
int const mod=1e9;  
int f[N],n; 
int main(){
    scanf("%d",&n); 
    f[0]=1;  
    rep(i,1,n) if(i&1) f[i]=f[i-1]; else  f[i]=(f[i-1]+f[i/2])% mod ;  
    cout<<f[n]<<endl; 
    return 0; 
}