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;}