Sumsets

Time Limit: 2000MS		Memory Limit: 200000K
Total Submissions: 15052		Accepted: 6001

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). 

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

Source

 

题目很有意思， 没想到是个递推， 脑子不够用。

#include 
      
       #include 
       
         const int  MOD = 1e9;const int N = 1000001;int num[N];void Sieve(){    num[1] = 1;    num[2] = 2;    num[3] = 2;    for(int i = 4; i <= N; i++){        if(i & 1)            num[i] = num[i-1];        else            num[i] = (num[i-2]%MOD + num[i/2]%MOD)%MOD;    }}int main(){    Sieve();    int n;    while(scanf("%d", &n) != EOF)        printf("%d\n", num[n]);    return 0;}