poj 2229 Sumsets （DP）

http://poj.org/problem?id=2229

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

思路很简单直接看代码：分奇数偶数

#include<iostream>
#include<cstring>
#include<cstdlib>
using namespace std;
const int MAXN=1000001;
const int M=1000000000;
int dp[MAXN];
int main()
{
	int N;
	while(cin>>N){
		dp[0]=dp[1]=1;
		for(int i=2;i<=N;i++){
			if( i&1 ) dp[i]=dp[i-1];
			else dp[i]=(dp[i-2]+dp[i>>1])%M;
		}
		cout<<dp[N]<<endl;
	}
	return 0;
}