poj 2229 Sumsets

Sumsets

Time Limit: 2000MS		Memory Limit: 200000K
Total Submissions: 18373		Accepted: 7190

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

USACO 2005 January Silver

 

#include <iostream>
#include <cstdio>
#include <cmath>

using namespace std;

const int maxn = 1000010;
const int M = 1000000000;

int dp[maxn];

void solve(){
    dp[0] = 1;
    for(int i = 1;i<maxn;++i){
        if(i%2){
            dp[i] = dp[i-1];
        }else{
            dp[i] = (dp[i/2]+dp[i-2])%M;
        }
    }
}

int main(){
    int n;
    solve();
    while(cin>>n){
        cout<<dp[n]<<endl;
    }
    return 0;
}