[BZOJ] 1677: [Usaco2005 Jan]Sumsets 求和

1677: [Usaco2005 Jan]Sumsets 求和

Time Limit: 5 Sec  Memory Limit: 64 MB
Submit: 1028  Solved: 601
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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

有以下六种方式
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

HINT

 

Source

Silver

Analysis

DP,,,

Code

#include<cstdio>
#include<iostream>
#define maxn 10000000
using namespace std;

int n,DP[maxn];

int main(){
    scanf("%d",&n);
    DP[1] = 1;
    for(int i = 2;i <= n;i++){
        if(i%2) DP[i] = DP[i-1];
        else DP[i] = (DP[i-1]+DP[i/2])%1000000000;
    }
    
    printf("%d",DP[n]);
    
    return 0;
}